psf for resistance of steel frames to ec3 ec4

C.E.C. Agreement 7210-SA/322

PARTIAL SAFETY FACTORSFOR RESISTANCE OF STEEL ELEMENTS

TO EC3 & EC4.CALIBRATION FOR VARIOUS STEELPRODUCTS AND FAILURE CRITERIA

Final Report

i

ECSC RTD Contract SA 322 & al.

PARTIAL SAFETY FACTORS FOR RESISTANCE OF STEEL

ELEMENTS TO EC3 & EC4.

CALIBRATION FOR VARIOUS STEEL PRODUCTS

AND FAILURE CRITERIA

Final report

June 2001

Author:

Bruno CHABROLIN, CTICM

Domaine de St Paul

B.P. 64

F - 78470 St-Rémy-lès-Chevreuse

iii

FOREWORD

This report describes the investigations and results of a research project with a funding from theECSC Steel RTD Program. The partners in charge of this project were:

CTICM (France) – Coordinator

Labein (Spain)

ProfilARBED (Luxembourg)

Structura Engineering and University of Pisa (Italy)

StudienGesselschaft and RWTH (Germany)

The SCI and British Steel (United Kingdom)

TNO Building and Construction Research (Netherlands)

This report has been prepared by CTICM, the coordinator; contributions from the project’spartners are gratefully acknowledged

iv

PROJECT SUMMARY

• Eurocode 3 and Eurocode 4 are at present ENVs. Those standards incorporate partial safetyfactors γM for the resistance. γM0 is related to member resistance without instability, while γM1

is related to any limit state where instability governs. In the ENVs, γM0 is taken equal to 1,1 , contrary to the general opinion within the steel construction experts who had proposed avalue of 1,0.. Hence the first aim of this project is to collect data by anlysing the products ofas many as possible steel producers.

• On a second hand, the safety factors are now different from one country to another; So thepresent research project reconsiders a large number of design limit states, in order thatfuture decisions for the value of γM1 may be based on clear evidence, tending to limit thenational deviations.

The first objective (γM0) is addressed by measurement campaigns in steel mills for hot rolledproducts characteristics (dimensions and yield strength)

Those measured values are used to compute resistances, which are compared with resistancesresulting from the nominal values. A statistical analysis of deviations results in safety factors.

The results are quite satisfactory, a value of 1,0 being justified.

Concerning the second objective (γM1) , some experimentation was performed for specific cases,but the main methodology was to gather existing test results and to proceed with extensivestatistical recalibration of the safety factors. Recalibrations were based on the same statisticalmethod described in chapter II.

The analysis does not lead to a simple generally applicable conclusion concerning the choiceof γM1, but the background information is summarised in chapter IV for consideration by expertgroups responsible for the conversion of EC3 and EC4.

v

ABSTRACTThis research project has been motivated by two main reasons:

• Eurocode 3 and Eurocode 4 have been issued by CEN as ENVs in 1992 and 1993. Thosestandards incorporate so-called partial safety factors γM in the resistance functions. Inparticular, γM0 is related to member cross section resistance where no instability is governing,while γM1 is related to any limit state where instability governs. in the ENVs, γM0 is taken equalto 1,1 , contrary to the general opinion within the steel construction experts who hadproposed a value of 1,0. However, it is true that this opinion was not backed by extensivedata. Hence the first reason for this project is to collect those data by analysing the productsof as many as possible steel producers.

• On a second hand, member states have been allowed to fix specific national values for thosesafety factors. It follows that the application of ENVs is now different from one country toanother, which is not a good thing. For this matter, the present research project will try toreconsider a large number of design limit states, with a unique statistical method, in orderthat future decisions for the value of γM1 may be based on clear evidence, tending to limit thenational deviations.

The project partnership thus includes logically both steel producers and steel or compositedesign experts.

The first objective (γM0) is addressed by performing measurement campaigns in steel mills forhot rolled products characteristics (dimensions and yield strength). A large variety of sectionsand of steel grades (from S235 to S460) has been considered.Those measured values are used to compute actual axial or bending resistances, which arecompared with the resistances resulting from the nominal values. A statistical analysis of thedeviations results in an evaluation of the safety factors. This method will give a safe-sided result,since no advantage is considered from strength hardening for example.A further activity was to discuss methods or requirements for the future production to achieveidentical performances through production control.This first part of the research produced very positive results, as a gM0 safety factor of 1,0 insteadof 1,1 presently was proved to be safe-sided.

Concerning the second objective (γM1) , some experimentation was performed for specific cases,but the main methodology was to gather existing test results and to proceed with extensivestatistical recalibration of the safety factors. Recalibrations were based on the same statisticalmethod described in chapter II.Specific proposals have been made for bolted connections. For other limit state, the analysisdoes not lead to a single generally applicable conclusion concerning the choice of γM1. As thesolutions depend on possible modifications of relevant formulae in the code rules, thebackground information is summarised in chapter IV for consideration by expert groupsresponsible for the conversion of EC3 and EC4. In a few cases, however, the poordocumentation of many existing test results and the lack of suitable test results for specificdesign situations such as loading interactions may present difficulties.Thus, it is intended that the results of this project may be used by the experts in charge of theconversion of ENVs into ENs, from 1999 to 2001.

vi

TABLE OF CONTENTS

CHAPTER I - INTRODUCTION 1

CHAPTER II STATISTICAL PROCEDURES 2II-1. General 2II-2. Step 1: Agreement on sampling and measurements 2II- 3. Step 2: Evaluation of the data prepared in step 1 2II-4 Summary of formulae 5II-5 Agreed Procedure for Measurements 6

II-5-1. Generalities : 7II-5-2. Characteristics to be measured: 8II.5.3 Procedure of measurements: 8II.5.4. Sampling and test units: 9II.5.6. Presentation of results : 12

CHAPTER III - CROSS SECTION RESISTANCE AT ULS (γM0 for Hot Rolled profiles) 47III-1. Introduction 47III-2. Statistical evaluation 47III-3. Conclusions for hot rolled I/H profiles 48

CHAPTER IV - OTHER LIMIT STATES OF RESISTANCE AT ULS (γM1 and/or γM1) 49IV-1. Introduction 49IV-2 Steel Elements 49

IV-2-1 Buckling strength for I and H profiles 49IV-2-2 Lateral Torsional buckling 50IV-2-3 Welded sections bending resistance 51IV-2-4 Buckling of Hollow Sections 52

IV-2-4-1 Previous studies 52IV-2-4-2 Results and conclusions 52

IV-2-5 Plate buckling 58IV-2-5-1 Previous studies 58IV-2-5-2 Results and conclusions 61

IV-3 Composite Elements 62IV-3-1 Composite members 62IV-3-2 Composite floor slabs 63

IV-4 Connections 63IV-4-1 Bolted connections 63IV-4-2 Steel-concrete shear connectors 67

CHAPTER V – FUTURE USE AND FUTURE VALIDITY OF RESULTS 68V-1. Introduction 68V-2. Use of the results 68

V-3. Future (long term) validity of conclusions for γM0 68

vii

CHAPTER VI – CONCLUSIONS 70

CHAPTER VII - LIST OF REFERENCE DOCUMENTS AND WORK REPORTS 71VII-1 Documents elaborated during the research works 71VII-2 General references 76VII-3 Background documents to eurocode 80VII-4 References for Chapter IV 81

ANNEX A 85

ANNEX B 101

ANNEX C 139

CHAPTER I - INTRODUCTION

This research project has been motivated by two main reasons:

Eurocode 3 and Eurocode 4 have been issued by CEN as ENVs in 1992 and 1993. Thosestandards incorporate so-called partial safety factors γM in the resistance functions. In particular,γM0 is related to member cross section resistance where no instability is governing, while γM1 isrelated to any limit state where instability governs. in the ENVs, γM0 is taken equal to 1,1 ,contrary to the general opinion within the steel construction experts who had proposed a valueof 1,0. However, it is true that this opinion was not backed by extensive data. Hence the firstreason for this project is to collect those data by anlysing the products of as many as possiblesteel producers.

• On a second hand, member states have been allowed to fix specific national values for thosesafety factors. It follows that the application of ENVs is now different from one country toanother, which is not a good thing. For this matter, the present research project will try toreconsider a large number of design limit states, with a unique statistical method, in orderthat future decisions for the value of γM1 may be based on clear evidence, tending to limit thenational deviations.

The project partnership thus includes logically both steel producers and steel or compositedesign experts.

The first objective (γM0) is addressed by performing measurement campaigns in steel mills forhot rolled products characteristics (dimensions and yield strength). A large variety of sectionsand of steel grades (from S235 to S460) has been considered.

Those measured values are used to compute actual axial or bending resistances, which arecompared with the resistances resulting from the nominal values. A statistical analysis of thedeviations results in an evaluation of the safety factors. This method will give a safe-sided result,since no advantage is considered from strength hardening for example.

This work is reported in chapters II and III. The permanent nature of the results is discussed inchapter V.

Concerning the second objective (γM1) , some experimentation was performed for specific cases,but the main methodology was to gather existing test results and to proceed with extensivestatistical recalibration of the safety factors. Recalibrations were based on the same statisticalmethod described in chapter II.

This work is reported in chapter IV.

It is intended that the results of this project may be used in due time by the experts in charge ofthe conversion of ENVs into Ens, in 1999 and 2000.

CHAPTER II STATISTICAL PROCEDURES

II-1. General

This chapter gives detailed rules for the evaluation of the results of geometrical and strengthmeasurements on a series of profiles to determine adequate partial γM0 safety factors forresistances.

The procedure given in this chapter is stepwise and comprises the following parts

1st step: Agreement on sampling and measurements of geometrical and strength data of

profiles to account for the negative correlation between plate thickness and

strength and to produce statistical data for plastic or elastic strength distributions.

2nd step: Evaluation of the data produced in step 1 to determine the lower tail distribution of

plastic or elastic strength and related γM values.

II-2. Step 1: Agreement on sampling and measurements

Measurements are made for the yield strength and for dimensions of cross-sections. They are

simultaneous, in order to retain the correlation between mechanical and geometric

characteristics.

The agreement concerns in particular the definition of the location where measurements andsamples for the determination of the yield strength are taken.

The agreement also includes the way in which the cross-section resistances Npl and Mpl are

calculated on the basis of those measurements for each profile i.

Details are given in the procedure presented in II-5.

As a basis, measurements are performed according to the product En steel products standard.

Hence, products that do not pass the requirements for the guaranteed yield strength or for the

required tolerances for dimensions are rejected, out of the production and out of the present

study.

II- 3. Step 2: Evaluation of the data prepared in step 1

The basis for the evaluation of the data prepared in the 1st step is Annex Z of Eurocode 3. Annex

Z has been used in the latest available version, given in Annex A to this report. Annex Z is to be

included in the forthcoming EN Eurocode 0 (Basis of Design).

It is important to recognise that the cross-section strength depends heavily on the yield strength,

which is not a (statistical) characteristic value because it is guaranteed by the product standard.

This is the main reason why use is made of the so-called tangent method, stated in Annex Z to

Eurocodes, allowing for a precise account of the lower tail distribution of the strength.

The evaluation is carried out in the following way:

(a)Definition of the experimental values rei, equal to cross-sectional resistances calculated

from measured geometrical data and strength data fy,i for each beam i as follows:

Npl,i = Ai ⋅ fy,i ; see II-4

Mpl,i = Wpl,i ⋅ fy,i ; see II-4

Mel,i = Wel,i ⋅ fy,i ; see II-4

(b)Definition of the theoretical values rti, equal to the nominal values of cross-sectional

resistances calculated from nominal values of geometrical data and strength data.

Npl,nom

Mpl,nom

Mel,nom

For nominal geometrical data of rolled sections EN 10034 is used; for the nominal yield

strength two options might be applied.

option 1: definition of the nominal yield strength according to EC 3 (ENV 1993-1-1:1992)

option 2: definition of the nominal yield strength according to the material standards EN

10025 and EN 10113.

(c)The sensitivity investigations should be carried out for each type of profile, the steel

grades, production methods etc, to identify the test population for which all influences,

neglected in the cross-sectional strength formulae are approximatively constant.

(d)The tangent method shall be used to obtain fictive mean values and error terms for the

lower tail of the distribution. The values rei/rti shall be ordered in descending order and

plotted on Gaussian-log-paper using the value 1+n

i as the i-th fractile.

Example: for 3 measured values x, the fractiles are

x1 → 1/4 = 25 %

x2 → 2/4 = 50 %

x3 → 3/4 = 75 %

The fictive mean values and error terms of the lower tail distributions are determined from either:

(1) Mean linear curve for measured data below the 50 % fractile (half the log-normal-

distributed population).

(2) Tangent approximation for the lower tail comprising not less than 20 tests. (This

procedure is recommended where a systematic tendency of the lower tail distribution

towards such a tangent is evident).

(e)As sufficient measured data are available a penalty for a limited number of measured data

should not be considered. The design values should be calculated as the 3.04 fractile

(see EC Annex Z included as Annex A).

(f) The γΜ* value should be calculated using

rr =

id,

inom,*Mγ where rnom,i = nominal resistance value for each member i

rd,i = design resistance value for each member i

(g)The detailed formula flow is given in II-5.

II-4 Summary of formulae

(1) The resistances are determined according to:

Mpl,mes = Wpl,mes · fy,mes

Npl,mes = Ames · fy.,mes

Mpl,nom = Wpl,nom · fy,nom

Npl,nom = Wpl,nom · fy,nom

All the nominal values are according to II-5

Note: The nominal values for fy may be taken either from EC 3 or from EN 10025 or EN 10113

(2) Example with Moments:

1) Calculate:

MM = b

nompl,

mespl,i

2) b n1 = b i∑

3)bb = i

iδ

4) δi’ = ln δi = ln

bbi = ln bi - ln b

5) =δ mean of i'δ

6)

)†bn n1 - nb(

1 - n1 =

)†bn + nb n1 - bn - nb(

1 - n1 =

)† - ( 1 - n

1 = S

iin

1

iin

1

in

1

ll

llll

∑

∑

δδ

′

′

′δ′

∑

∑

∑

7) Use tangent method as described in this report.

8) Smδ’ = mb - (b (15.87 %))

9) Q = Smδ’

10) Finally the γM*-factor is derived as follows:

)S 0,5 - S u(- exp b1 =

)S 0,5 - S uexp(- M bM =

MM = *

mmdm

mmdnompl,m

nom.pl

dpl,

nompl,M

δ′δ′

δ′δ′

••

•

γ

II-5 Agreed Procedure for Measurements

The following describes the adopted procedure for in mills measurements (yield strength andgeometric dimensions).

It is based on standard procedures for production evaluation according to the relevant productstandards (EN).

Procedure to evaluate partial safety factors γM for H / I hot-rolled sections

II-5-1. Generalities :

(1) This procedure defines the way to carry out measurements of hot-rolled steel profileson production sites, in order to evaluate the following resistance models ofcross-sections according to Eurocode 3:

- model for tension or compression plastic resistance of cross-sections:

Npl = A . fv

- model for bending moment plastic resistance of cross-sections about major axis yy:

Mpl.y = Wpl.y . fv

- model for bending moment elastic resistance of cross-sections about major axis yy:

Mel.y = Wel.y . fv

- model for bending moment plastic resistance of cross-sections about minor axis zz:

Mpl.z = Wpl.z . fv

- model for bending moment elastic resistance of cross-sections about minor axis zz:

Mel.z = Wel.z . fv

The strength models correspond to cross-sections without holes for fasteners.

(2) The measurements of hot-rolled sections are related to profiles which are shipped onthe market. Consequently no measured data shall be excluded if their validity havebeen controlled being within the limits imposed by standardised tolerances, accordingto common practice in rolling mills.

(3) The values of the models which are issued from measurements on mills of differentsteel producers, will be analysed by statistical evaluations according to Annex Z ofEurocode 3, in order to determine the relevant partial safety factor: γm0 , which affectseach resistance model given above in clause 1. (1).

(4) This campaign of measurements and of statistical evaluations is intended to berepresentative of the European market. Thus as many as possible steel producersfrom différent countries should be involved as for instance:

- Aristrain (with mills in Spain),

- Preussag (with mills in Germany),

- British steel (with mills in United Kingdom),

- ProfilARBED (with mills in Luxembourg, France and Germany),

II-5-2. Characteristics to be measured:

(1) Geometrical characteristics:

h = depth of section,

b = width of section,

tw = web thickness,

tf = flange thickness,

r = radius of root fillet (which will be taken as nominal value given in relevantEuronorms: Euronorm 19-57 for IPE sections,

Euronorm 53-62 for HEA, HEB and HEM sections,

BS 4 part 1 - 1993 for HP, UB and UC sections).

(2) Mechanical characteristics:

fy = yield strength, according to EN 10025 and to EN 10113, which are both Europeanstandards specifying the technical delivery conditions of hot-rolledproducts of structural steels.

Important point: both mechanical and geometrical characteristics shall be measuredeach time on the same specimen . Those characteristics shall be measuredaccording to Euronorms and according to daily practice of factories (measurementsfrom Quality Control Departments, usual testing machines, ... ).

II.5.3 Procedure of measurements:

Geometrical characteristics: the following measurements shall be carried out

according to EN 10034 (specifying the tolerances on shape and dimensions) (seeattached sketch in Annex 1 to this chapter) :

- h = the depth of cross-section measured in the web axis;

- b1 and b2 = the width of each flange of cross-section;

- tw = the web thickness measured at mid-depth (= h/2) ofcross-section;

- tf1, tf2, tf3 and tf4 = the flange thicknesses measured at each quarter of each flange(= b1/4 and b2/4) of a cross-section.

It is recommended to control the following measurements in order to validate the cross-section within EN10034 limits but it should not be necessary to mention them in the databankof results; if those criteria are not fulfilled, specimens should be excluded as done by mills inusual practice (see present chapter 1. Generalities: clause (2»:

- flange parallelism (" k+k'" values) (see Annex 2);

- web excentricity (' e " values) (see Annex 2);

tolerances on masses (± 4%).

(2) Mechanical characteristics: according to EN 10025 and EN 10113:

- the tensile test shall be carried out in accordance with EN 10002- 1;

in accordance with Euronorrn 18 the location of samples and test pieces shall be inthe flange of sections, at the sixth of width (= b/6) (see attached sketch in Annex 3);according to EN 10025 and EN 10113, the yield strength fy shall be determined as:

* the upper yield strength ReH,

* or, if yield phenomenon is not present, the 0,2% proof strength Rp0,2(see Annex 4)

in the scope of this campaign of measurements, it should be useful to measure thefollowing features, for 10% (or more if possible) of all measured specimens and, tokeep them in stock:

* both values of ReH and Rp0,2 ,

* tensile strengths, Rm (or fu ) and ultimate strains εu and A5d (see Annex 4),

* full stress-strain curves.

- Those measurements (ReH, Rp0,2, Rm, εu, A5d, full stress-strain curves) will not begiven in a first step. Their use will be discussed afterwards because they couldimprove other partial safety factors γm1 (resistance of steel members to local andglobal buckling) and γmb (resistance of bolted connections).

II.5.4. Sampling and test units:

(1) Steel grades, qualities :

- Selection of steel grades and qualities:

I. "basic" steel grades: S 235 JR or S 275 JR,

II. high strength steels: S 355 J0,

II. very high strength steels: S 460 NL or S 460 ML.

Number of specimens to be measured for all mills of each steel producer for allseries of profiles and for différent steel grades and qualities :

Steel grades and qualitiesI II IIISerie of Profiles

S 235 JR or S 275 JR S 355 JO S 460 NL or S 460 MLIPE

HE

UB

UC

Total Number =600

Total Number =200

Total Number =100

(2) Sampling: according to EN 10025 (see Annex 5) and to EN 10113 (see Annex 6).

(3) Tests units: according to EN 10025 (see Annex 5) and to EN 10113 (see Annex 6).

(4) Types of cross-sections :

- It is proposed to carry out measurements by random selection of profiles in the scopeof usual works done by Quality Control Department of différent mills.

- The différent types of H and I cross-sections which shall be measured in the scope of thiscampaign, are :

IPE European 1-bearm

IPE 80 - 600 in accordance with Euronorm 19-57

HE European wide flange bearns

HE A, HE B and HE M 100 - 1000 in accordance with Euronorm 53-62

HP Wide flange bearing piles

in accordance with BS 4 part 1-1993

UB British universal bearns


UC British universal columns


Nominal geometrical and statical characteristics of these cross-sections are given inAnnex 8.

The types of cross-sections to be measured should be specified. by europeanspecifications (Euronorm 19-57, Euronorm 53-62, BS 4 part 1-1993) (see Annex 8)and should be selected at random according to the current production, trying tocover all différent types of profiles.

(5) Number of measured profiles

From the.point of view of statistical evaluations better results will be obtained if we havemore measurements per profile for a lower number of profiles, instead of lessmeasurements per profile for a higher number of profiles.

Mills should try to, carry out 30 measurements per profile .

per steel grade ,

and per rolling .

(6) Tables of profiles :

- The tables of Annex 8 provide the nominal data of cross-sections :

* the geometrical characteristics,

* the statical characteristics and,

* the classification according to Eurocode 3 (see Annex 7 for the definition of

classification):

. for different loading cases :

. NSd , compressive axial load,

. My.Sd , uniaxial bending moment about major axis yy,

. Mz.Sd , uniaxial bending moment about minor axis zz.

. for différent steel grades : S 235, S 355, S 460 (with yield strength (fy)depending on material thickness (tf) according to Eurocode 3).

- According to Eurocode 3 a cross-section is normally classified by quoting the highest(least favourable) class of its compression elements (web or flange). The tables ofAnnex 8 mention the element which has the highest class, for example:

* 3w means class 3 web, class 1 or 2 flange and class 3 cross-section,

* 4f means class 4 flange, class 1, 2 or 3 web and class 4 cross-section,

* 3 means class 3 web, class 3 flange and class 3 cross-section,

- For the evaluation of partial safety factor γM0 , measured cross-section should be:

* class 1. 2 or 3 for evaluation of model for tension or compression plastic' resistanceof cross-section: Npl = A. fy

* class 1 or 2 for evaluation of model for bending moment plastic resistance ofcross-sections about major axis yy and minor axis zz: M pl.y = Wpl.y.fy and M pl.z = W pl.z.fy

* class 3 for evaluation of model for bending moment elastic resistance ofcrosssections about major axis yy and minor axis zz: M el.y = Wel.y.fy and M el.z = W el.z.fy

No class 4 cross-sections should be used for the evaluation of partial safety factor γM0

for loading cases of M y.Sd and M z.Sd in priority and also for loading case of NSd ifpossible (see Annex 8 for the selection of profiles).

II.5.5. Evaluation of statical characteristics A, Wpl and Wel:

(1) The following formulas should be used in all mills to evaluate the statical characteristicsof each measured cross-section:

- sectional area, A :

A = 2 . tf . b + (h – 2. tf) . tw + (4 - π) .r2

- plastic section modulus about major axis yy, Wpl,y:

( )( ) ( ) 3r.3

103t2h.r.2

4t.th.tb4h.tW f

2ffw

2w

y.pl−π

+−π−

+−−+=

elastic section modulus about major axis yy Wel.y :

hI.2

W yy.el =

where the moment of inertia about major axis yy, Ey is

( )( )[ ] ( )2f243

fw3

y r.4468,0t2h.r.2146,0r.03,0t2h.tbh.b.121I −−++−−−=

- plastic section modulus about minor axis zz, Wpl.z :

( ) 3r.3

103t.r.2

4t.4

th.2b.tW w

22w

f2

fz.pl

−π−

π−+

−+=

- elastic section modulus about minor axis zz, Wel.z:

bI.2W z

z.el =

where the moment of inertia about minor axis zz. Iz is:

( )[ ] ( )2w243

wf3

fz r.4468,0t.r.2146,0r.03,0t.t2hb.t.2.121I +++−+=

and where

b = (b1 + b2) / 2(= mean values).

tf = (tf1 + tf2 + tf3 + tf4) / 4(= mean values).

h, b1 , b2 , tw , tf1 , tf2 , tf3 and tf4 are measured as prescribed in present chapterII.5.3 (according to EN 10034) and,

r is the nominal value given in relevant Euronorms (see present chapter II.5.2).

II.5.6. Presentation of results :

(1) Generalities:

The databank of results (nominal, measured and calculated characteristics) is proposedto

be presented as shown in Annex 9 (6 parts) and is given on a floppy disk with Excel and

Lotus/Wysiwyg files.

For each measured cross-section, steel producers should fulfill 24 columns of thetable given in Annex 9 (pages 1/6 and 2/6) with :

*references data (columns 1 to 6),

* nominal characteristics (columns 7 to 12) and,

* measurements (columns 16 to 27).

Other characteristics will be automatically calculated by Excel or Lotus:

* nominal yield strength (fy) depending on the material thickness according toEurocode 3 (column 13) and to Euronorms EN 10025 and EN 10 113 (column 14),

* statical properties of cross-sections (columns 29 to 44):

. for nominal characteristics (columns 29 to 35) and,

. for measured characteristics (columns 36 to 44).

* resistance models of cross-sections (columns 54 to 69):

. for measured data (columns 54 to 58) and,

. for nominal data :

. with yield strength (fy) depending on the material. thickness according toEurocode 3 (columns 60 to 64) and,

. with yield strength (fy) depending on the material thickness according toEuronorms EN 1 002YUd EN 10 113 (columns 65 to 69).

* ratios between measured and nominal resistance models (columns 71 to 80):

. with nominal resistance models using yield strength (fy) depending onthe material thickness according to Eurocode 3 (columns 71 to, 75) and,

. with nominal resistance models using yield strength (fy) depending onthe material thickness according to Euronorms EN 1 0OY5' and EN 10113 (columns 76 to 80).

For the evaluation of partial safety factor γM0 each steel producer should send toProfessor Sedlacek (RWTH, Aachen University) the 3 last parts of the table given inAnnex 9 (from pages 4/6 to 6/6) (= all rows for columns 45 to 80) :

* with calculated values of resistance models issued from measurements,

* with calculated values of resistance models issued from nominal values and,

* with comparative ratios of measured to nominal resistance models.

In a first step details on measurements shall not be given (Annex 9 (pages 2/6 and3/6): columns 16 to 27 and columns 36 to 44)

Details : Example and formulas (Units : N and mm) :

* The following data shall be introduced in the table by steel -producers:

Data given as example :- col. 1: the measurement number Ex. 1 ,- col. 2 : the date of measurement 20/9/95,- col. 3 : the cast number : 2,- col. 4 : the rolling process (c = cast or i = ingot) c ,- col. 5 : the designation of the profile serie(IPE, HEA, HEB, HEM, HP, UB or UC): HEA,- col. 6 : the profile number : 400,- col. 7 : the nominal depth of profile, h 390 mm ,- col. 8 the nominal width of profile, b 300 mm,- col. 9 the nominal web thickness of profile, tw 11 mm,- col. 10: the nominal flange thickness of profile, tf 19 mm,- col. 11 the nominal radius fillet of profile, r : 27 mm,- col. 12 the steel grade (S235 or s235, S275 or s275)(S355 or s355, S460 or s460): s460,- col. 16: the measured upper yield strength, ReH (put 0 if R p0,2 ≠ 0) 0 N/mm2,- col. 17 the measured. 0,2 % proof strength, R p0,2 (put 0 if ReH ≠ 0) : 472 N/mm2,- col. 18 the tensile strength, Rm : 570 N/mm2,- col. 19 the ultimate strain, A5d : 19%- col. 20 the measured depth of profile, h : 391 mm ,- col. 21 the measured width of profile, b1 : 301 mm ,- col. 22 the measured width of profile, b2 : 302 mm ,- col. 23 the measured web thickness of profile, tw 11,1 mm ,- col. 24 the measured flange thickness of profile, tfl 19,1 mm ,- col. 25 the measured flange thickness of profile, tf2 19,2 mm ,- col. 26 the measured flange thickness of profile, tf3 19,3 mm ,- col. 27 the measured flange thickness of profile, tf4 19,4 mm ,

* The following characteristics are automatically calculated:- col. 13: the nominal yield strength, fy (depending on material thickness (≤100 mm)

according to Eurocode 3 (EC3): see Annex 10) 460 N/mm2

- col. 14: the nominal yield strength, fy depending on material thickness (≤100 mm) accordingto Euronorms (EN 10025 & EN 10 113): see Annex 10): 440 N/mm2,

- from columns 29 to 35 nominal statical characteristics, are calculated with nominalgeometrical data (issued from colurans 7 to 11) and with formulas defined in presentchapter.5 :. col.29 : the nominal sectional area , (A)n : 15 898 mm2,. col. 30 : the nominal moment of inertia about major axis y, (Iy)n : 450 693 526 mm4,. col. 31 : the nominal elastic section modulus about major axis y, (W el.y)n : 2 311 249 mm3,. col 32. : the nominal plastic section modulus about major axis y, (W pl.y)n : 25 61 798 mm3,. col. 33. : the nominal moment of inertia about minor axis z, (Iz)n : 85 638 203 mm4,. col. 34. : the nominal elastic section modulus about minor axis z, (W el.z)n : 570 921 mm3,. col. 35 : the nominal plastic section modulus about minor axis z, (W pl.z)n : 872 864 mm3,. col. 36 : the mean value of measured widths of profile bm = (b1 + b2) / 2 301,5 mm,. col. 37 : the mean value of measured flange thicknesses of profile

tf = (tf1 + tf2 + tf3 + tf4) / 4 19,3 mm,

- from columns 38 to 44 measured statical characteristics, are calculated with measuredgeometrical data (issued from columns 20, 23 and 11 for respectively h, tw and r andusing mean values for b (col. 36) and for tf (col. 37)) and with formulas defined in presentchapter 5 :. col.38 : the measured sectional area , (A)m 16 146 mm2,. col.39 : the measured moment of inertia about major axis y, (Iy)m.: 460 063 148 mm4,. col.40 : the measured elastic section modulus about major axis y, (W el.y)m : 2 353 264 mm3,

col.41 : the measured plastic section modulus about major axis y, (W pl.y)m : 2 608 920 mm3,

. col.42 : the measured moment of inertia about minor axis z, (Iz)m : 88 070 940 mm4,

. col.43 the measured elastic section modulus about minor axis z, (W el.z)m : 584 219 mm3,

. col.44 : the measured plastic section modulus about minor axis z, (W pl.z)m : 893 039 mm3,

- columns 45 to 53 are copied from related left-hand columns 1 to 6 and 12 to, 14.

- from columns 54 to 58 the resistance models are calculated from measured yieldstrength fy (= ReH or R p0,2 , taken from columns 16 orl7 respectively) and irom calculatedstatical characteristics (issued from columns 38 to 44) which are evaluated frommeasured geometric al data:. col. 54 : (Npl)m = (A)m . fy 7 621 041 N,. col 55 : (M el.y)m = (W el.y)m . fy 1 110 740 695 Nmm,. col 56 : (M pl.y)m = (W pl.y)m . fy 1 231 410 336 Nmm,. col 57 : (M el.z)m = (W el.z)m . fy 275 751 136 Nmm,. col 58 : (M pl.z)m = (W pl.z)m . fy 421 514 455 Nmm.

- from columns 60 to 64 the resistance models are calculated from nominal yield strength(fy)EC3 (depending on material thickness according to Eurocode 3 (see Annex 10) : columns13 & 52) and from calculated statical characteristics (issued from columns 29 to 35) whichare evaluated from nominal geometrical data:

. col 60 : (Npl)n = (A)n . (fy)EC3 7 312 976 N,

. col 61 : (M el.y)n = (W el.y)n . (fy)EC3 1 063 174 471 Nmm,

. col 62 : (M pl.y)n = (W pl.y)n . (fy)EC3 1 178 427 142 Nmm,

. col 63 : (M el.z)n = (W el.z)n . (fy)EC3 262 623 822 Nmm,

. col 64 : (M pl.z)n = (W pl.z)n . (fy)EC3 401 517 336 Nmm.

- from columns 65 to 69 the resistance models are calculated from nominal yield strength(fy)EN (depending on material thickness according to Euronorms (EN 10025 and EN16113)(see Annex 10) : columns 14 & 53) and from calculated statical characteristics(issued from columns 29 to 35) which are evaluated from nominal geometrical data :

. col. 65 : (Npl)n = (A)n . (fy)EN 6 995 020 N,

. col. 66 : (M el.y)n = (W el.y)n . (fy)EN 1 016 949 494 Nmm,

. col. 67 : (M pl.y)n = (W pl.y)n . (fy)EN 1 127 191 179 Nmm,

. col. 68 : (M el.z)n = (W el.z)n . (fy)EN 251 205 395 Nmm,

. col. 69 : (M pl.z)n = (W pl.z)n . (fy)EN 384 060 060 Nmm.

- from columns 71 to 75 ratios between measured (m) and nominal (n) resistance modelsare calculated from measured values (columns 54 to 58) and from nominal values usingyield strength (fy)EC3 depending on material thickness according to Eurocode 3 (columns60 to 64) :

. col. 71 : EC3 (N pl)m / (N pl)n 1,042,

. col. 72 : EC3 (M el.y)m / (M el.y)n 1,045,

. col. 73 : EC3 (M pl.y)m / (M pl.y)n Class 3 or 4 ,

. col. 74: EC3 (M el.z)m / (M el.z)n 1,050,

. col. 75: EC3 (M pl.z)m / (M pl.z)n Class 3 or 4.

- from colunns 76 to 80 ratios between measured (m) and nominal (n) resistance modelsare calculated from measured values (columns 54 to 58) and from nominal values usingyield strength (fy)EN depending on material thickness according to Euronorms (EN 10025and EN 101 13)(columns 65 to 69):

. col. 76: EN (N pl)m / (N pl)n 1,089,

. col. 77 : EN (M el.y)m / (M el.y)n Class 1 or 2,

. col. 78: EN (M pl.y)m / (M pl.y)n 1,092,

. col. 79: EN (M el.z)m / (M el.z)n Class 1 or 2,

col. 80: EN (M pl.z)m / (M pl.z)n 1,098.

- remarks about calculations of ratios between resistance models (columns 71 to 80) :

. for calculations of Npl ratios, the result may be "Class 4", if the given crosssectionis Class 4,

. for calculations of Mel ratios, the result may be "Class 1 or 2" or "Class 4", if thegiven cross-section is respectively Class 1 or 2 or Class 4,

. for calculations of Mpl ratios, the result may be "Class 3 or 4", if the given cross-section is respectively Class 3 or Class 4.

. the calculation of the cross-section Class considers nominal geometrical data(column 7 to 11) and nominal yield strength depending on the material thicknesseither according to Eurocode 3 (columns 13 & 52) or to Euronorms (EN 10025and EN 101 13)(columns 14 & 53); differences in classification may appear asshown in this example n° 1 (EX. 1) for ratios about My and Mz.

Annexes : 10 Annexes (1 to 10) are given in the next pages.

Needed documents :

Euronorm 19-57, Euronorm 53-62, Euronorrn 18, BS 4 - Part 1 -1993, EN 10034,EN 10025, EN 10113, EN 10002.

ANNEXES TO § II-5

Annex 1 (2 pages): Geometrical characteristics (EN 10034)

measurements and tolerances of h, b, t, and tf

Annex 2 (1 page): Geometrical characteristics (EN 10034) :

tolerances of flange parallelisrn and web excentricity

Annex 3 (1 page) Mechanical characteristics (EN 10025 & EN 10 113) :

location of samples

Annex 4 (2 pages): Mechanical characteristics (EN 10025 & EN 10 113) :

refèrence points of stress-strain diagramms

Annex 5 (l page): Mechanical characteristics (EN 10025)

sampling & tests units

Annex 6 (3 pages): Mechanical characteristics (EN 10 113)

sampling & tests units

Annex 7 (4 pages) Definition of the cross-section classification according to

Eurocode 3

Annex 8 (10 pages): Tables of european profiles

(IPE, HEA, HEB, HEM, HP, UB and UC)

Annex 9 (6 pages) Presentation of results (Excel or Lotus application)

Annex 10 (1 page): Minimum guaranteed yield strength ReH (or R p0,2) in

function of nominal thickness t of material according to

Eurocode 3 and Euronorms (EN 10025 & EN 10 113).

Annexes 1 to 10 are given in the next pages.

BENDING AXES : yy major axisZz minor axis

Measurements of H or I hot-rolled sections Annex 1 (2/2)

Tableau 1 – Tolérances dimensionnelles des poutrelles I et H en acier de construction

Annex 4 (1/2) Measurements of H or I hot-rolled sections

Page 19 of EN 10025 :1990+A1 :1993

8.6.3.4 Chemical analysis samples

The preparation of samples for product analysis shall be in accordance withEURONORM 18.

8.7 Test methods

8.7.1 Chemical analysis

For the determination of the chemical composition the corresponding EuropeanStandard or EURONORMS (see footnote 2 of clause 2) shall apply in cases ofdispute.

8.7.2 Mechanical tests

Mechanical tests shall be carried out in the temperature range 10°C – 35°C,except where a specific temperature is specified for impact tests.

8.7.2.1 Tensile tests

The tensile test shall be carried out in accordance with EN 10002-1.

For the specified yield strength in table 5 the upper yield strength (ReH)shall be determined.

If a yield phenomenon is not present, the 0,2 % proof strength (R p0,2) or theR t0,5 shall be determined ; in cases of dispute the 0,2 % proof strength (Rp0,2) shall be determined.

If a non-proportional test piece is used for products with a thickness ≥ 3 mmthe percentage elongation value obtained shall be converted to the value for

a gauge length Lo = 5,65 So using the conversion tables given in ISO 2566/l.

8.7.2.2 Impact tests

The impact test shall be carried out in accordance with EN 10045-1.

The average value of the three test results shall meet the specifiedrequirement. One individual value may be below the minimum average valuespecified, provided that it is not less than 70 % of that value.

Three additional test pieces shall be taken from the same sample inaccordance with 8.6.1 and tested in any one of the following cases :

-- if the average of three impact values is lower than the minimum averagevalue specified;

-- if the average value meets the specified requirement, but twoindividual values are lower than the minimum average value specified;

-- if any one value is lower than 70 % of the minimum average valuespecified.

The average value of the six tests shall be not less than the minimum averagevalue specified. Not more than two of the individual values may be lower thanthe minimum average value specified and not more than one may be lower than70 % of this value.


NOTE : A5d = Elongation at failure for a gauge length of L0 = 5.65 0S(see EN 10025 / 10113)

Annex 5 Measurements of H or I hot-rolled sections

FOR S 235, S 275, S 355 Page 17

EN 10025 :1990+A1 :1993

8.3 Sampling

8.3.1 The verification of the mechanical properties shall be carried out :

-- by lot or by cast as specified at the time of the enquiry and order forthe quality JR and the steel grades E295, E335 and E360;

option 14;

-- by cast for the qualities J0, J2G3, J2G4, K2G3 and K2G4.

8.3.2 If it is specified at the time of the enquiry and order thatsampling should be by lot, it is permissible for the manufacturer tosubstitute sampling by cast, if the products are delivered by cast.

8.4 Test units

8.4.1 The test unit shall contain products of the same form and grade andof the same thickness range as specified in table 5 for the yield strengthand shall be:

-- by lot : 20 tonnes or part thereof,

-- by cast: 40 tonnes or part thereof,60 tonnes or part thereof for heavy sections with a mass > 100 kg/m.

8.4.2 If specified at the time of the enquiry and order for flatproducts of quality J2G3, J2G4, K2G3 and K2G4, the impact test only or theimpact test and the tensile test shall be carried out on each parent plateor coil.

Option 20

8.5 Verification of chemical composition

8.5.1 For ladle analysis determined for each cast, the values reportedby the manufacturer shall apply.

8.5.2 Product analysis shall be carried out if specified at the time ofthe enquiry and order. The purchaser shall specify the number of samples andthe elements to be determined.

Option 15.

8.6 Mechanical tests

8.6.1 Number of samples

The following samples shall be taken from one sample product of each testunit :

-- one sample for tensile testing (see 8.2.1),

-- one sample sufficient for one set of six impact test pieces for qualityJO, J2G3, J2G4, K2G3 and K2G4 and if required for quality JR (see 8.2.1and 8.2.2 a).

8.6.2 Position of samples (see Annex A)

The samples shall be taken from the thickest product in the test unit exceptfor flat products of quality J2G3 and K2G3, for which the samples

Measurements of H or 1 hot-rolled sections Annex 6 (1/3)

FOR S 460 Page 15 of EN 10113-1:1993

8.1.2 The purchaser shall specify the type of the inspection documentat the time of the enquiry and order (see 4.1 and 8.8).

8.1.3 The specific inspection and testing shall be carried out inaccordance with 8.2 to 8.7.

8.1.4 Unless otherwise agreed at the time of the enquiry and orderinspection of surface condition and dimensions shall be carried out by themanufacturer.

Option 9.

8.2 Sampling

The verification of the mechanical properties shall be by cast.

8.3 Test units

The test unit shall contain products of the same form and grade and of thesame thickness range as given in table 3 of part 2 and table 3 of part 3 ofthis European Standard for the yield strength.

For verifying the mechanical properties the test units specified in parts2 and 3 of this European Standard shall apply.


8.4.1 For ladle analysis determined for each cast, the values reportedby the manufacturer shall apply.

8.4.2 Product analysis shall be carried out if agreed at the time of theenquiry and order. The purchaser shall specify the number of samples and theelements to be determined.

Option 3.


8.5.1 Preparation of samples

8.5.1.1 The following samples shall be taken from one sample product ofeach test unit:

-- one sample for tensile testing ;

-- one sample sufficient for one set of six impact test pieces.

8.5.1.2 The sample product can be any product within the test unit.

8.5.1.3 For plates, sheet, wide strip and wide flats the samples shall betaken approximately midway between the edge and centre line of the products.

Annex 6 (2/3) Measurements of H or 1 hot-rolled sections

Page 8 of

EN 10113-2:1993 FOR S 460 NL

8 Inspection and testing

8.1 General

The products shall be supplied in accordance with 8.1 of EN 10113 part 1.

Option 9.

8.2 Sampling

Sampling shall be in accordance with EN 10113 part 1.

8.3 Test units

8.3.1 The test unit shall contain products of the same form and gradeand of the same thickness range as specified in table 3 for the yieldstrength.

For verifying the mechanical properties the following test unit shallapply:

-- 40 t or part thereof.

8.3.2 If specified at the time of the enquiry and order for flatproducts the impact test only or the impact test and the tensile test shallbe carried out on each parent plate or coil.

Option 19a and 19b.


The verification of the chemical composition shall be in accordance with EN10113 part 1.

Option 3.


The mechanical tests shall be in accordance with EN 10113 part 1.

8.6 Test methods

The test methods shall be in accordance with EN 10113 part 1.

8.7 Retests and resubmission for testing

The retests and resubmission for testing shall be in accordance with EN10113 part 1.

8.8 Inspection documents

The inspection documents shall comply with EN 10113 part 1.

Measurements of H or 1 hot-rolled sections Annex 6 (3/3)

Page 8

EN 10113-3:1993 F O R S 4 6 0 M L

7.7 Internal defects

The internal defects shall be in accordance with EN 10113 part 1.

Option 13 (for flat products).

Option 16 (for long products).

8 Inspection and testing

8.1 General

The products shall be supplied in accordance with 8.1 of EN 10113 part 1.

Option 9.

8.2 Sampling

Sampling shall be in accordance with EN 10113 part 1.

8.3 Test units

8.3.1 The test unit shall contain products of the same form and gradeand of the same thickness range as specified in table 3 for the yieldstrength.

For verifying the mechanical properties the following test unit shallapply:

-- 40 t or part thereof.

8.3.2 If specified at the time of the enquiry and order for flatproducts the impact test only or the impact test and the tensile test shallbe carried out on each parent plate or coil.

Option 19a and 19b.


The verification of the chemical composition shall be in accordance with EN10113 part 1.

Option 3.


The mechanical tests shall be in accordance with EN 10113 part 1.

8.6 Test methods

The test methods shall be in accordance with EN 10113. part 1.

Annex 7 (1/4) Measurements of H or 1 hot-rolled sections

Definition of Eurocode 3 classification of cross-sectionsAccording to chapter 5.3 of Eurocode 3, steel profiles are categorized in section classes(see Table 1) which depend on:

- slenderness of cross-sections members (width/thickness ratios of flange and web)

- yield strength with the factor yf

235=ε

- the internal forces and bending moments applied to the cross-section (Ncompression, My, Mz,... : all inducing normal stresses).

The cross-section of class 1 allows the full plastic strength and a moment redistributiondue to the formation of plastic hinges which have sufficient available inelastic rotation. Forclass 2 cross-sections, the available inelastic rotation becomes so limited that the plasticcross-section capacity Mpl may be taken into account, but the redistribution of momentshas to be neglected. Hence the system is assumed to behave elastically though theplastic capacity Mpl of the cross-section is exploited locally. Classes 3 and 4 concerncross-sections with a distribution of elastic stresses, respectively on full or effectivecross-sections. Tables 2 and 3 summarise the existing rules in Eurocode 3 in loadingcases of Ncompression, My and Mz.

Figure 1 (Note: d = h - 2.tf - 2.r and c = b/2 )

Annex 7 (3/4) Measurements of H or I hot-rolled sections

CHAPTER III - CROSS SECTION RESISTANCE AT ULS (γM0 for HotRolled profiles)

III-1. Introduction

This chapter describes the statistical evaluation (carried out at RWTH) for the measuredproperties of rolled profiles with the aim to re-evaluate the γM0 value by taking into account actualmeasurements of hot-rolled profiles in steel mills.

III-2. Statistical evaluation

The geometric and material properties of profiles are measured in different steel mills and theyare collected in a data bank at RWTH. The actual data bank contains the measured propertiesof 3906 profiles provided by 5 project partners. For the γM0 evaluation, not all of the 3906 profilescould be used because some of the profiles are class 4 cross-sections.

For obvious reasons of confidentiality, the steel producers are not named in the followingpresentation, they are only identified by a simple number (1 to 5)

The analysed production is from:

• Germany

• Italy

• Luxembourg

• Spain

• United Kingdom

Hence the analysed production is representative of Western Europe steel-production for hot-rolled I/H profiles.

Measures were taken in the mills during current industrial production, according to chapter II.

For the statistical evaluation the database was divided into individual subsets so that theinfluence of an individual data set on the statistical results could be detected. The followingsubsets were defined:

Subset 1: All profiles

Subset 2: All steel producers, each type of section

Subset 3: Each steel producer, all types of sections

Subset 4: Each steel producer, each type of section

The statistical procedure which was used in the evaluation was based on the revised draft ofAnnex Z of Eurocode 3 (see chapter II and Annex A to this report) and were processed througha computer programme prepared by CTICM.

The statistical evaluations of the subsets were carried out with the computer programme

according to the following steps:

Step 1: In the first step the number of points for regression was selected as 50 % of all dataof the subset and the γM-value was determined with the appropriate standarddeviation Sδ.

Step 2: In a second step the statistical evaluation was carried out with the lower tail of thefrequency distribution while the number of points for regression was restricted to 20.

Step 3: This step was only necessary when the γM -value according to step 1 was lower thanthe γM -value obtained by step 2. Then, the sensitivity of the γM -value was examinedwhile the number of points for regression were chosen between the 50% - value andthe 20 points.

For all subsets the statistical results are given in Annex B to this report.

III-3. Conclusions for hot rolled I/H profiles

For the actual database the following conclusions can be drawn:

• The value of γM0 =1.0 is justified for all examined sections from all steel producers.

• However, the simplified definition of fy according to EC 3, rather than according to EN 10025and EN 10113, is to be abandoned in order to justify γM0 =1.0.

• The hot rolled sections that were measured performed better in the strong inertia plane (I-sections) than in the weak inertia plane (H-sections) so that γM0 =1.0 is easier to justify forthe y-y plane while γM0 =1.1 would be a safe easy conclusion for the z-z plane.

• However, recalling that the analysis is only based on the yield strength value, and does notaccount for other effects, especially strength hardening effects, our conclusion is that apartial safety factor γM0 equal to 1,0 should be recommended for hot-rolled I/H profiles andfor any type of limit state where no local or member instability effect is governing.

• Those conclusions are dependent on the provisions for future validity, as investigated inChapter V.

CHAPTER IV - OTHER LIMIT STATES OF RESISTANCE AT ULS (γM1

and/or γM1)IV-1. Introduction

This part of the report will describe all the performed studies that were not directly related withthe purpose described in Chapter III, i.e. the γM0 partial safety factor for hot-rolled I or H crosssections not subject to local or global instabilities.

While the reported topics were not the main subject of the research project, it was howeverpossible to gather a lot of information and to highlight some main tendencies, even if theconclusions are not often readily transferable to Eurocode drafters.

The following distinction is made between:

Steel elements (see IV-2)

Composite elements (see IV-3)

Connections (see IV-3)

IV-2 Steel Elements

IV-2-1 Buckling strength for I and H profiles

The main problem with this topic is the gap when passing from the plastic or elastic resistanceof the cross section to the buckling strength of the member. This occurs for a reducedslenderness λ = 0,2. Beneath this value, for cross-section resistance, one is allowed a γM0

safety factor, hence 1,0 from other findings of this research project. Above this value, γM1

(instability) applies, that is 1,1. So a sudden 10% step may occur in practical design.

Otherwise, Eurocode 3 makes use of the well-known ECCS buckling curves, with severalpenalty levels, according to the type of the cross-section.

The buckling tests database (ECCS) was reviewed within the research project. No firmconclusion was drawn from this study because:

When studying the compression buckling alone, one would suggest to modify the strengthformulae in order to make a smooth transition around the λ = 0,2 zone (ENV Eurocode 3presents there a gap of 10% due to the sudden change from γM0 to γM1). However, this wouldroughly mean modifying the ECCS buckling curves, which would go further than the subject ofthis research project.

The subject is complicated by the need to rule out the coexistence of compression and bending,also accounting for the risk of Lateral Torsional Buckling (LTB). This is a very difficult problem,since it is recognised that the present formulation in ENV 1993-1-1 is far from perfect.

Hence the problem cannot be seen as a mere matter of calibration of γM. Presently variousoptions are being presented for the conversion of ENV EC3 into EN, and still subject todiscussion.

IV-2-2 Lateral Torsional buckling

The lateral torsional buckling resistance of elements with I or H sections first safety evaluation

is from 1989 and the results are reported in the relevant EC3 background document [166]. The

method of evaluation used in this background document was according to the preliminary draft

version of the Annex Z of EC3.

Before calibrating the partial safety factor γM1 using the latest version of Annex Z of EC3, adetailed study of the past experimental test reports results was necessary and a critical analysisof this EC3 background document has been done.

This document [169] contains a summary of the lateral torsional buckling EC3 backgrounddocument [166], and remarks that were collected from this critical analysis.

A first study was performed, see [170]. This allowed to recalculate the value of the partial safetyfactor γM1 for the resistance of the members with rolled I or H sections with the same past testsdatabase, but after the requalification of the tests results. New lateral torsional buckling testsresults were not found in order to eventually enlarge the initial database. Also, unfortunately, thisevaluation does not include members with welded I or H sections. The results are summarisedin the following table.

Lateral -torsionnal buckling of members

Summary of statistical results for γM1

Database Recalculated value γM1

All database 105 tests 1.18

105 tests, Adjusted procedure 1.39

105 tests, "Droite de Henry" 1.14

Subset 4.0≤λ LT , 9 tests 1.18

Subset 4.0≤λ LT , "Droite de Henry" 1.13

Subset 14.0 LT ≤λ< , 51 tests 1.13

Subset 14.0 ≤λ< LT , "Droite de Henry" 1.07

Subset 1>λLT , 45 tests 1.06

Subset 1>λLT , "Droite de Henry" 0.97

"Mateescu formula", 14.0 LT ≤λ< 1.18

"Mateescu formula", 1LT >λ 1.06

After some assumptions for these reevaluation, we find a global value of γM1 = 1.18 and few

values of the partial safety factor γM1 that are slightly lower than 1.1. Only the case of the testssubset (45 tests) with the reduced slenderness 1>λLT provides a value γM1 = 1.06. Theseresults indicates that the calibration gives "interesting" values (lower than 1.1) especially whentests subsets are carefully defined. But it seems difficult to make final conclusions based onthese results.

- For example Annex Z is very difficult to use where some basic variables were not measured.And, here, this is indeed the case, since only 50 % of the cross-sections properties have beenmeasured.

- Concerning the database, finally and principally, we have to note that the tests selected in thisdatabase were not realised in the aim to evaluate the partial safety factor γM1. Thus, they havenot been realised with the same tests conditions and so we do not dispose of the sameinformations for every test serials. We can also discuss about the representativity of thisdatabase. We dispose of only 9 tests of profiles of Class 3 cross-section and of no tests ofprofiles of Class 2 cross-section. Most of the tested beams have section depthes lower than 305mm and 42 % of the tests were japanese tests realised with profiles H x 200 x 100 x 5,5 x 8(similar section to IPE 200) and without measured dimensions. The steel grade of the rolledsections was 85 % S235 steel grade.

On another hand, concerning the EC3 ENV 1993-1-1 design model, the results seem to showthat this theoretical model is more distant from the real behaviour when the reduced slenderness

LTλ decrease. The discrepancy of the correction factor is then amplified and the value of thepartial safety factor increased. Elsewhere, we do not dispose of a theoretical model for the caseof the cantilever beams which is a critical case regarding this ultimate limit state. Regarding therecent proposal to use the "Maatescu formula " for the reduced slenderness, see ref [171], itseems that this proposal would not modify the actual partial safety factor value.

In the same time, in a second study, the problem has been addressed through numerical MonteCarlo simulations. A numerical procedure have been used to calibrate the γM1 partial safety factorfor the ultimate limit state of lateral torsional buckling according to the EC3 ENV 1993-1-1 modeland for a wide set of rolled profiles, see ref [172]. The results of this simulation conclude to thevalue γM1 = 1.04. But, it must be noted that the results refer to a well precise production,characterised by a small variation coefficient, so that the following conclusions are based on thisproduction statistical parameters and are not valid for other productions whose parameters areless favourable.

IV-2-3 Welded sections bending resistance

This subject is treated in IV-2-5-2 where the presentation of test data is given as well as resultsfor Class 4 hot-rolled sections.

The reason for this paragraph is only to stress that no study could be made on welded sectionsof class 1 to 3 for lack of any test data.

IV-2-4 Buckling of Hollow Sections

IV-2-4-1 Previous studies

The buckling resistance of Hollow Structural Sections have been evaluated in 1989 and theresults are reported in EC3 background document [183]. The method of evaluation used in thisbackground document is according to the preliminary draft version of the Annex Z of EC3.

IV-2-4-2 Results and conclusions

Before to recalibrate the partial safety factor γM1 using the latest version of Annex Z of EC3 andfor the buckling resistance under pure compression ultimate limit state, a detailed study of thepast twenty years research test reports results has been necessary and a critical analysis of theEC3 background document have been done, see ref [185].

This document [185] contains a summary of the flexural buckling tests of hollow sections chosenin the EC3 background document [183], essentials remarks that were collected from the criticalanalysis and a database of the past flexural buckling tests of hollow sections complemented withother recent tests that were collected in order to produce an updated hollow sections flexuralbuckling tests database. The main comments on the database are reported in the document[185], [186], [187] and are summarised hereafter.

- Database representativity : - Though all the 600 tests are not recent, they are representativeof the various types of fabrication, sections steel grade and slenderness that are commonlyavailable on the market. The main drawback is that all the CHS and SHS are Class 1 cross-sections. The EC3 background document is not representative of the Class 2 and 3 HSS cross-sections. The EC3 cross-section classification for SHS does not make differences betweenClass 1,2 and 3 limit slenderness.

- HSS of Class 4 are not considered in EC3 ENV 1993-1-1 despite past research wotks.

- High strength steel : High strength steel (fy = 690 MPa) HSS buckling tests have been includedin the background document evaluation, but for HSS and contrary to the I section profiles, amore favourable curve is not allowed in Annex D for high strength steels.

- Yield strength : - All the buckling tests data of CHS from CIDECT 2A have not been includedin the EC3 background document evaluation due to fy measurement data missing.

- Few tests include measured data of the base material yield strength fyb, and full measured dataof the yield strength of tensile coupon of the tested specimen.

- Recent HSS buckling tests : Many other buckling tests results from other countries (Finland,Italy) or recent research (CIDECT 2R, etc.) are not included in the EC3 background documentand could now be used in the reevaluation.

- Slenderness : The radius of the corner of the SHS is not measured and we generally refer toa nominal slenderness value. The slenderness limits for the subsets are different for eachresearch program.

The recalibration of the partial safety factor have been done using various methods of evaluationrelated to the type of section (SHS, CHS) and fabrication process (cold formed, cold formedwith heat treatment, hot rolled). The diagram hereafter summarise the methods.

methodcurve c

type of fabrication

Heattreatment

section

f mesya

( )( )

( )

r g X f

r g X f

r f X

t Rt mes y mes

N Rt nom y nom

d moy

=

=

=

,

,

( )( )

( )

r g X f

r g X f

r f X

t Rt mes yb mes

N Rt nom yb nom

d moy

=

=

=

,

,

( )( )

( )

r g X f

r g X f

r f X

t Rt mes ya mes

N Rt nom ya nom

d moy

=

=

=

,

,

( )( )f f knt A f fya nom yb nom nom g nom u nom yb nom= + −2 /

( )( )f f knt A f fya mes yb mes mes g mes u mes yb mes= + −2 /

HotCold

yes

noSHS CHS

noyes

curve b curve a

γ RN

d

rr

* =

Am Ac B C

formed Rolled

methodmethod method

The detailed results of the recalibration of γM1 for the cold formed profiles of the CIDECT 2R(1995) research are reported in the following table :

Buckling of cold formed hollow structural sections


HSS γM1 ProposedRecalculated

Producer Ac Am B γM1 values

T 1.09 1.10 1.11 1.22 1.11

1.10 1.11 1.12 1.24

1.06 1.08 1.12 1.12 1.10

M 1.06 1.09 1.13 1.13

1.07 1.10 1.14 1.14

1.08 1.10 1.15 1.15

R 1.03 1.06 1.06 1.13 1.06

1.02 1.05 1.05 1.12

VA 1.05 1.05 1.07 1.13 1.06

1.05 1.05 1.06 1.13

1.05 1.06 1.07 1.13

1.06 1.06 1.08 1.14

TSR 1.10 1.11 1.12 1.22 1.11

1.09 1.10 1.11 1.21

VA2 1.09 1.09 1.10 1.18 1.09

1.08 1.08 1.09 1.17

1.09 1.08 1.10 1.17

1.09 1.09 1.11 1.18

min 1.02 1.05 1.05 1.12 1.06

max 1.10 1.11 1.15 1.24 1.11

The profiles are well suited for the present value of the partial safety factor of the EC3-ENV1993-1-1. The theoretical model Am satisfactorily predict the buckling load. The evaluation with the« Henry line » method is not acceptable due to the lower number of tests results and thetheoretical model B under-estimates the experimental resistance.

The detailed results of the recalibration of γM1 for the cold formed profiles of the Niemi &Rinnevalli Finland research (1990) are reported in the following table :


Global analysis

Summary ofstatistical results for

γM1

Analysis withsubsets

Reference Ac Am B B Henry

1:3 1.09 1.12 1.24 0.97 0.99

4:6 1.08 1.11 1.24 0.97 0.99

7:9 1.08 1.10 1.24 0.96 0.99

10:12 1.07 1.09 1.24 1.09 1.11

13:15 1.07 1.08 1.24 1.08 1.10

16:18 1.06 1.08 1.25 1.08 1.10

19:21 1.07 1.08 1.25 1.12 1.14

22:24 1.07 1.08 1.26 1.13 1.14

25:27 1.07 1.09 1.27 1.13 1.14

28:30 1.08 1.09 1.28 1.13 1.15

31:33 1.08 1.09 1.28 1.14 1.15

34:36 1.08 1.10 1.29 1.14 1.16

37:39 1.09 1.10 1.29 1.14 1.16

min 1.06 1.08 1.24 0.96 0.99

max 1.09 1.12 1.29 1.14 1.16

The results of the recalibration are the same for the two methods :

- a global analysis for the Am model

- an analysis with slenderness subsets for the B model

The final results of the recalibration of the γM1 for the cold formed profiles are summarised inthe following table

Buckling of cold formed hollow structural sections


Research Database Type of methodRecalculated

γM1 values

GLOBAL 1.11CIDECT 2R

(1995) SUBSETS 1.06 < <1.11

GLOBAL all 1.12

f(λ)

Niemi

SHS

(1990)SUBSETS

Henry (subsets)

AllGLOBAL

Henry 0.97

CIDECT 2E

SHS

(1976) SUBSETS subsets f(λ)

allGLOBAL

minus 1 test

f(section) 1.06

CIDECT 2C

CHS

(1974) SUBSETSHenry

allGLOBAL

minus 1 test 1.08

f(λ)SHS

SUBSETSf(t)

CIDECT 2B-CHS SUBSETS f(fy) 1.15

all 1.02GLOBAL

Henry

f(fy) 1.04

SHS

(1969)SUBSETS

Henry

The final results of the recalibration of γM1 for cold formed profiles with heat treatment aresummarised in the following table

Buckling of cold formed heat treated hollow structural sections Summary of statisticalresults for γM1

Research Database Type of method Recalculated γM1 values

all 0.94 < < 0.95 0.95CIDECT 2R (1995)SHS GLOBAL

Henry 0.97

all 1.13 < < 1.16

Henry 1.21 < < 1.24

minus 1 test 1.05 < <1.08 1.08

KEY

SHS

(1986)GLOBAL

Henry (-1 test) 1.08 < < 1.10

all 1.25

minus 1 test 1.14 < < 1.15GLOBAL

Henry (-1 test) 1.20

BIRKEMOE

SHS

(1978)SUBSETS f(λ) 1.09 1.09

The global number of tests (35 tests) taken into account is too small. These profiles have beenconsidered as hot rolled profiles and the use of the EC3 ENV 1993-1-1 buckling curve “a” isconservative.

The more recent research CIDECT 2R tests gives the better value of γM1 , but the number oftests (8) is too small.

• The final results of the recalibration of γM1 for hot rolled profiles are summarised in thefollowing table.

Buckling of hot rolled hollow structural sections Summary of statistical results for γM1

Research Database, type of method and γM1Recalculated

γM1 valuesall 1.11 < < 1.13

GLOBALHenry 1.09 < < 1.11 1.11f(weld) 1.09 < < 1.12

f(λ) 1.07 < < 1.12

CIDECT 2DCHS

(1976) SUBSETSf(λ) Henry 1.08 < < 1.12

all 1.01 1.01C.S.C.M (1975)CHS-HLE GLOBAL

Henry 1.03

all 1.19 < < 1.21GLOBAL

Henry 1.19 < < 1.21f(λ) 1.01 < < 1.17 1.17

CIDECT 2ASHS

(1968) SUBSETSf(λ) Henry 1.04 < < 1.18

all 1.11 < < 1.14GLOBAL

Henry 1.09 < < 1.13f(λ) 1.00 < < 1.14 1.14

CRIFCHS-SHS

(1964) SUBSETSf(λ) Henry 1.01 < < 1.16

Except for the 12 tests of the C.S.C.M, it is difficult to justify a partial safety factor γM1 lower than1.1.

The partial safety factor γM1 in the case of hot rolled sections was evaluated with the a and a0

buckling curves, for comparison. With the a0 curve, the partial safety factor γM1 remains closeto 1.1

The final conclusions of this study ( recalibration of the buckling resistance partial safety factorγM1 for the HSS ) are :

- On the whole, the values of the partial safety factor γM1 are close to 1.1. This is due to thesmall difference between theoretical and experimental resistances. The theoretical bucklingmodel of hollow structural sections, particularly the theoretical model based on the yield strengthof finished products seems realistic and correctly approximates the experimental resistances.On the other hand, the theoretical model based on the yield strength of the base materialprovides values of γM1 greater than 1.1. As a matter of fact, this one underestimates theexperimental resistance, and the re / rt ratio is lower than one. So, for the buckling resistanceunder pure compression, it is not possible to justify a value of γM1 lower than 1.1 for all the typeof sections.

- The main parameters which influence the evaluation are the type of fabrication (cold formed,cold formed heat treated, hot rolled), the type of section (CHS, RHS), the yield stress and theslenderness λ.

- The yield stress is the most sensible parameter that influences the value of the partial safetyfactor γM1 and the thickness is not a very sensible parameter.

- The sensibility of the residual stresses have not been quantified due to the lack of measuredvalues in the available database.

The reevaluation was made with the values of the coefficients of variation of the randomvariables as previously adopted in the EC3 background documents, and based on past studies.With these usually accepted statistical parameters for fy, the present partial safety factor γM1 of EC3 ENV 1993-1-1 is correct. Accounting for lower scatter in fy values would lead to smaller γM1

values. It should then be useful to re-evaluate the values of these coefficients based on recentmills measurement campaigns both for geometrical and mechanical hollow sections properties.

IV-2-5 Plate buckling

IV-2-5-1 Previous studies

Local buckling and Class 4 cross- section resistance (γM1) for EC3

The two background documents [175] and [176] to EC3 ENV 1993-1-1 that refer to Class 4cross-sections were studied. The first one appears to be entirely based on cold-formedsections. The second one covers local buckling and web buckling (shear buckling and patchloading) ultimate limit states. It appears in these documents that only local buckling of beamflanges and of beam webs under compression and bending, for which the background document[176] refer to only seven test specimens with Class 4 webs are within the scope of the present

research project.

Buckling of plates with or without stiffeners

In the case of building structures, the following ultimate limit states of plates buckling werestudied in the background document [178] to EC3 ENV 1993-1-1 :

• ultimate limit state of shear buckling

• ultimate limit state of I beam when large concentrated loads are introduced in unstiffenedwebs, i.e. patch-loading

For the first ULS, the Rockey Model (called "Tension Field Method" in EC3-ENV 1993-1-1) wasshown to be the most accurate method of calculation for transversely stiffened beams, as it besttakes into consideration all of the components which make up the shear strength model. Thestatistical evaluation, by Annex Z to EC3, for the Rockey Model resulted in a value of the partialsafety factor γM1 = 1.25. If the tension zone part is reduced by the correlation factor 0.9, then thepartial safety factor γM1 = 1.10 is sufficient. If the applied moment exceeds the capacity Mf.Rd,then an interaction should be carried out and for this, the same safety factor γM1 =1.10 shouldapply as for the case MSd < Mf.Rd

For the second ULS, the Roberts model (called “crippling” strength function in EC3-ENV 1993-1-1) which is based on a failure model that corresponds to the true failure mechanism, can beused for welded, thin-walled beams as well as rolled profiles. The comparison from tests withthe Roberts formula yields, with a statistical evaluation method according to the Annex Z to EC3,in a partial safety factor γM1 = 1.10. In the case of important bending action, a tri-linear interactionrelationship is conservative and the proposal of γM1 = 1.10 has been adopted in the EC3 ENV1993-1-1.

In the case of bridges structures, the following ultimate limit states of plates buckling werestudied in the background documents [179], [180] and [181] for the drafting of EC3 ENV 1993-2(bridges):

• ultimate limit state of shear buckling of stiffened and unstiffened webs

• ultimate limit state of unstiffened or stiffened web loaded by a transverse force

• ultimate limit state of longitudinal stiffened plate loaded in pure compression

For the first ULS, which is reported in the background document [179], the design rules for theshear buckling resistance of stiffened and unstiffened webs from the chapter 5.6 of the draft ofEC3 ENV 1993-2 are evaluated with test results according to the draft version of Annex Z of EC3 in order to determine the partial safety factor γM1

A summary of the statistical results reported in the background document [179] is given in thefollowing table.

Buckling of plates with or without stiffeners - First ultimate limit state Summary of statisticalresults for γM1

Support conditions Test members γM1

steel welded sections withstiffeners at the supports only 0.92

Non-rigid end poststeel welded sections with

transversal stiffeners 1.01

steel welded sections withstiffeners at the supports only 1.04

steel welded sections withtransversal stiffeners

0.89 < < 1.17

mean value 0.99Rigid end post

longitudinal stiffened steel weldedsections 1.07

Interaction shear force &bending moment

steel welded sections withtransversal stiffeners max value 1.10

In conclusion, for this ULS, the partial safety factor γM1 = 1.10 can be applied to all the strengthfunctions.

For the second ULS, which is reported in the background document [180], the design rules (the"Johansson and Lagerqvist" Model ) for the buckling resistance of unstiffened or stiffened webloaded by a transverse force from chapter 5.7 of the draft of EC3 ENV 1993-2 are evaluatedwith test results according to the draft version of Annex Z of EC3 in order to determine partialsafety factor γM1.


Buckling of plates with or without stiffeners - Second ultimate limit state


Type of load application γM1

Opposite patch loading0.95 < < 1.11

mean value 1.05

Patch loading0.73 < < 1.23 max value

mean value 0.97

End patch loading0.79 < < 1.12

mean value 1.03

For the third ULS, which is reported in the background document [181], the design rules for theresistance of Class 4 cross-sections with longitudinal stiffeners which are loaded in purecompression from the chapter 5.3.6 of the draft of EC3 ENV 1993-2 are evaluated with testresults according to the draft version of Annex Z of EC3 in order to determine partial safetyfactor γM1.


The value of the partial safety factor are 0.72 < γM1 < 1.12. The mean value is γM1 = 0.98.

In conclusion, for this ULS, the partial safety factor γM1 = 1.10 can be applied to all the strengthfunctions.

IV-2-5-2 Results and conclusions

Local buckling & Class 4 cross section resistance γM1 for EC3 ENV 1993-1-1

A first study (UK) has been performed, see ref [173]. This study has considered the value ofthe partial safety factor for resistance of Class 4 cross-sections to local buckling, (γM1 in EC3ENV 1993-1-1), subject to pure axial loading as well as to combined axial / bending. The Class4 cross sections considered are hot-rolled sections or sections fabricated from plates by welding,e.g. welded or box sections. Cold formed sections are not considered.

The tolerances of hot rolled sections are well defined by the mills measurements being reportedin this report. Tolerances for sections made by welding flat elements together depend on thedifferent cutting and welding equipment and procedures in the different fabrication works. Thisvariability of tolerances is addressed in the report [173]. It is very difficult to have confidence inthe partial safety factors without assessing test results. Unfortunately, very few sets with suitabletest data have been found. Reports from Centre de Recherches Scientifiques et Techniques del'Industrie des Fabrications Métalliques (C.R.I.F) (J.Janss, 1993) and Cambridge University(G.H. Little, 1976), have formed the basis for this project. The value of γM1 derived from thesetests has been established according to Annex Z of EC3 - ENV 1993.1.1 and checked by agraphical method. The partial safety factor γM1 have been calculated for both cases using arelatively small population. The two test series used different strengths of steel. The table ofresults shows the importance of a large sample population in order to get consistent results.

Local buckling and Class 4 cross- section resistance Summary of statistical results for γM1

Cross-section&

slendernessTests Loading Number

of tests

Annex Zrecalculated value

γM1

Graphical methodrecalculated value

γM1

Box sectionsb / t = 40

UniversityCambridge Axial / Bending 6 0.85 0.86 - 1.08

Box sectionsb / t = 55

UniversityCambridge Axial / Bending 6 1.04 0.89 - 1.13

IPE sectionsC.R.I.F Pure axial 8 1.07 0.92 - 0.96

This first study has demonstrated that for the methods of calculating the cross-sectionalresistance of Class 4 cross-sections given in the EC3-ENV1993-1-1 there is a possibility tolower the partial safety factor γM1 from 1.1 (which is the actual value) to 1.05 or 1,0, especiallyif a larger population of data could be created. However, the current rules for calculating effective

sections need to be checked for axial load for b / t greater than 40.

In the same time, in a parallel study (Italy), see ref [177], the problem has been addressedthrough numerical simulations. A numerical procedure has been used to calibrate the γM1 partialsafety factor for the ultimate limit state of bending resistance for a wide set of welded profiles.The test results for the bending resistance of fabricated I profiles were replaced with simulatedvalues obtained as follow :

- for fy, according to a distribution derived from a large statistical analysis performed on areal set of laminated plates, representative of a past 3 years production of an Europeanproducer (correlated with plate thickness); S235, S275 and S355 steel grades wereconsidered.

- for the dimensions : - plate thickness tolerances according to EN 10029 class A

- beam total depth and flange width according to a specific ILVA’s welded beams fabrication standard

- for ε coefficient, using the value calculated with the nominal value for fy instead of theactual one (because EC3 strength formulae are calibrated this way).

The cross-sections that have been used for this bending resistance simulation are deep ones(from 690 to 1680 mm total depth), with equal or unequal flanges. A total of 34 differentsymmetrical and unsymmetrical I cross-sections with various geometrical slenderness wereanalysed.

The results of this second research show bending resistance partial safety factors γM1 lower than1.0. But these results depend to the level of internal control and of the quality level of this steelproduction used for these simulations. Thus it could be not valid for others productions.

Buckling of plates with or without stiffeners

In the case of building and bridges structures, the evaluations as reported in the backgrounddocuments were done with the preliminary draft version of the Annex Z to EC3. Recalibrationwith the latest version of the Annex Z to EC3 have given very similar results, for lack of recentplate measurements databases.

IV-3 Composite Elements

IV-3-1 Composite members

The work on calibration of composite beams and columns is described in a series of reports bythe University of Warwick to the SCI and to the UK Department of the Environment, see ref [161]to [165].

This recent work has been based on the EC3 ENV 1993-1-1 values for partial safety factors (1,1)for structural steel and EC2 ENV 1992-1-1 values for partial safety factors for concrete andreinforcing bars. The conclusions are that the γM values for composite beams and columnsdesign with EC4 ENV 1994-1-1 are about right.

However, it is doubtful whether the introduction of 1,0 instead of 1,1 for steel would significantly

change the resistance of the composite section. Anyway, time as well as lack detailed statisticaldata (i.e. individual correlated data for dimensions and yield strength) did not allow too gofurther.

The question has moreover to be re-examined by Eurocode drafters in the light of the possiblymodified safety format for concrete and composite construction (several materials).

IV-3-2 Composite floor slabs

This subject has been investigated from the point of view of the shear connection. Hence, referto IV-4-2.

IV-4 Connections

IV-4-1 Bolted connections

Bolted connections have first been evaluated in 1989 and the results are reported in EC3background documents [188], [189] and [190]. The method used in these backgrounddocuments is described in [191], which is a preliminary draft version of the Annex Z of EC3[192].

Within the present project :

Recalibrations were performed using the latest version of Annex Z of EC3.

Recalibrations have been considered for bolts in tension and/or shear, with improvements onstrength formulae in some cases. The following studies were finalised for the ten following limitstates (the numbering of the ten limit states is accordingly to EC3 1989 background documents).

• 1- simple tensile failure (TNO)

• 2- simple shear failure in the shank part (TNO)

• 3- simple shear failure in the threaded part (LABEIN)

• 4- combined shear and tensile failure in the threaded part (LABEIN)

• 5- combined shear and tensile failure in the shank part (TNO)

• 6- plate bearing failure (TNO)

• 7- failure in net section of attached plates (LABEIN)

• 8- failure in net section of angles connected with one bolt (LABEIN)

• 9- failure in net section of angles connected with two bolts (LABEIN)

• 10- failure in net section of angles connected with three bolts or more (TNO)

The results of the statistical evaluation of the 1st to 5th limit states (bolts strength) aresummarised in the following table, the strength functions are calibrated with the γMb partial safetyfactor, the second column indicates the recalculated value of the γMb partial safety factor ( γMb*

as noted below ) , the third column indicates the ratio between the actual γMb = 1.25 value andthe recalculated value.

Resistance of bolts Summary of statistical results for γMb

γMb* 1.25 / γMb*

Simple tensile failure(ULS 1)

calibrated from1.0 fub As

instead of 0.9 fub As

All grades 1,273

Grade 4.6 1,293

Grade 5.6 1,238

Grade 8.8 1,194

Grade 10.9 1,231

0.982

0.967

1.009

1.047

1.016

Simple shear failure inthe shank of bolts

(ULS 2)

0.7 fub As for 4.6, 5.6 and8.8 grades

0.6 fub As for 10.9 grade

All grades 1.220

Grade 4.6 1.205

Grade 5.6 1.218

Grade 8.8 1.273

Grade 10.9 1.205

1.025

1.037

1.027

0.982

1.038

Simple shear failure inthe threaded part

(ULS-3)

- All Grades 1.11

- Grade 4.6 0.97

- Grade 5.6 0.93

- Grade 8.8 1.16

- Grade 10.9 1.33

1.125

1.289

1.342

1.076

0.938

Combined shear andtensile failure in the

threaded part

(ULS 4)

- All Grades, all angles φ 1.01

- Grade 4.6, all angles φ 0.94


- All Grades, angle φ = 15° 1.17




- All grades, angle φ = 75° 1.13

1.235

1.327

1.209

1.065

1.259

0.869

1.338

1.109


shank part

(ULS 5)

see hereafter proposalon strength formulae

leading to thosecalibration results

- All Grades, all angles φ 1.155




- All Grades, angle φ = 15° −



1.082

1.142

1.053

1.162

-

1.022

1.072

1.076

All Grades, angle φ = 60° 1.162

- All grades, angle φ = 75° 1.278

0.978

The results of the statistical evaluation of the 7thto 10th limit states are summarised in thefollowing table, the strength functions are calibrated with the γM2 partial safety factor. The secondcolumn of the table indicates the recalculated value of the γM2 partial safety factor ( γM2* asnoted below ), the third column indicates the ratio between the actual γM2 = 1.25 value and therecalculated value.

Resistance of bolted plates


γM2* 1.25 / γM2*

Plate bearing failure

(ULS 6)

Fbs=2.5 fu d t (α1 +(n-1)α2)

α1=1.15 e1 / (3 d1) ≥ 1,0

α2= p / (3 d1) – 1 / 4 ≥ 1,0

Plates, angles, 1 to 3 bolts,

grades from S235 to S 355

Ranging from 0.988 to 1.331

Values above 1,25 are for whole testpopulation

Ranging from :

0.939 to 1.266

Failure in net section ofattached plates

ULS 7

- All steel grades 1.19

- FeE235 1.18

- A43 1.08

- StE460 1.65

1.055

1.056

1.157

0.755

Failure in net section ofangles connected with

one bolt

ULS 8


- FeE235 1.12

1.114

1.114


two bolts

ULS 9


- FeE235 1.25

- FeE355 1.47

0.991

0.997

0.852


three or more bolts

ULS 10


- FeE235 1.262

- FeE355 1.210

1.031

0.991

1.033

The proposal of revision of the strength functions which presently includes so-called "modelcoefficients" is summarised in the following table. The proposals are based keeping the actualvalues of the partial safety factors of the EC3 - ENV 1993-1-1: the actual values are γMb = 1.25and γM2 = 1.25 .

Strength functions EC3 - ENV 1993-1-1 Proposal of revisionSimple tensile failure

ULS 1All grades Ft,Rd =

Af 0.9

Mb

sub

γFt,Rd =

Mb

subAfγ

Simple shear failure inthe shank part of bolt

ULS 2All grades Fv.Rd =

Mb

shubAf6.0γ

Fv.Rd = Mb

shubAf6.0γ

Simple shear failure inthe threaded part of bolt

ULS 3

EC3 Table 5.6.3

Grade 4.6 and 5.6 Fv.Rd = Mb

subAf6.0

Grade 8.8 Fv.Rd = Mb

subAf6.0

Grade 10.9 Fv.Rd = Mb

subAf5.0

Fv.Rd = Mb

subAf65.0

Fv.Rd = Mb

subAf6.0

Fv.Rd = Mb

subAf45.0


threaded part of bolt

ULS 4

EC3 § 6.5.5(5)Rd.v

Sd.v

Rd.t

Sd.t

FF

F4.1F

+ ≤ 1

Rd.t

Sd.tFF

≤ 1 & Rd.v

Sd.v

FF

≤ 1

Rd.v

Sd.v

Rd.t

Sd.t

FF

F3.1F

+ ≤ 1

Rd.t

Sd.tFF

≤ 1 & Rd.v

Sd.v

FF

≤ 1

Combined shear andtensile failure in the shank

partULS 5

Interaction :

1FpF

FqF

vs

v

ts

t ≤+

p = 1.1q =1.7

Plate bearing failureULS 6

Fbs=2.5 fu d t (α1 +(n-1) α2)α1=1.15 e1 / 3 d1

α2= p / 3 d1

Failure in net section ofattached plates

ULS 7

Present formula valid for steel S235 butquestionable for other steel grades

EC3 § 5.4.3(b) Nu.Rd = 0.9 Anet fu / γM2no proposal


one bolt ULS 8EC3 § 6.5.2.3(2) Nu.Rd =

2γ

− u02 tf)d5.0e(2Nu.Rd =

2γ

− u02 tf)d5.0e(2.2


two bolts ULS 9

Present formula valid for steel S235

EC3 § 6.5.2.3(2) Nu.Rd = 2M

unet2 fAγ

β

(For steel S355 γM2 * = 1.47 instead of γM2 =1.25)

no proposal


three or more boltsULS 10

EC3 § 6.5.2.3(2) Nu.Rd = 2M

unet3 fAγ

β

β3 = 0,50 (p/d1 < 2.5)β3 = 0,70 (p/d1 > 5.0)+ linear interpolation

Same formatβ3 = 0,55 (p/d1 < 2.5)β3 = 0,70 (p/d1 > 5.0)+ linear interpolation

IV-4-2 Steel-concrete shear connectors

The initial calibration of the partial safety factor γM for shear studs was performed in 1991 andthe results are available in the report [199] .

Within this project, the recalibrations were performed using the latest version of Annex Z of EC3,and the test data contained in [199].

A preliminary calibration is reported in the report [198] and the final calibration and conclusionsare reported in the report [201].

The reports concludes the following :

- The partial safety factor γM = 1.25 is clearly appropriate for shear studs in solid concrete slabsand re-entrant composite decking with through welded studs.

- There appears to be no possibility for reducing γM if one unique value is required for all formsof slab and decking.

- The data collected and summarised in [199] forms a large number of separate statisticalpopulations which are difficult to combine without creating unrepresentative scatter but are toosmall for statistical evaluation as individual populations. This is especially true for compositedecking.

- The simplicity of the EC4 - ENV resistance equations is helpful for designers. but the absenceof terms which reflect the actual behaviour, e.g. the plateau of fu < 500 N/mm2 instead of a moreexact function. means that the calculated reliability is always pessimistic.

- Excepting through-welded studs in re-entrant decking, studs in composite decking have lowerreliability than required by Annex Z, but the extensive use of this form of construction withoutwell-known failure suggests that there is no real problem. The Annex Z reliability level of αR β= 3.04 probably is not appropriate for the calculation of reliability of studs, which are generallyused in large numbers on a given beam. This point needs addressing but was felt to lie beyondthe scope of this project.

- A major test effort using uniform test specimen. uniform test methods and uniform failurecriteria is required if the resistance equations and factors for studs in composite decking is tobe properly understood.

The report [201] on shear studs was checked and the problems in some particular cases werepresented, such as the cases of the trapezoidal decks shear stud locations or the situation ofthe re-cut holes. Some conclusions to solve these problems as proposed are to draw specificrules for shear connectors design. Additional test work with specific shear studs failure wouldbe necessary, because existing steel-concrete tests with these failure modes seem to be poor.

CHAPTER V – FUTURE USE AND FUTURE VALIDITY OF RESULTSV-1. Introduction

The present chapter focuses on :

• How the results of the project will be made useful to the industry via structural designcodes;

• How the results concerning gM0 (see chapter III of this report) will be deemed to be longterm-valid.

Results about other limit states (see chapter IV of this report) are a) less conclusive, and b) oftenstrongly dependant on future studies, quality level of fabrication, etc. So we can onlyrecommend to examine the proposed evidence on a case by case basis.

V-2. Use of the results

The research project schedule was in line with the process of transferring Eurocode 3 andEurocode 4 from ENV status to EN status (with modifications). The respective CEN Projectteams have started work at the beginning of 1999, aiming to produce a final draft within twoyears. Moreover:

Several partners are involved in this Eurocode drafting process, through some of their highscientific level staff:

• For ARBED, chairmanship of the EC3 conversion project team

• For CTICM, chairmanship of CEN TC 250 SC3 (Eurocode 3)

• For RWTH, technical secretariat or participation in CEN TC 250 SC3, SC4 and SC1, andchairmanship of EC3 Conversion Validation Group

• For SCI, technical secretariat in CEN TC 250 SC3, and representation in ECISS TC 10

• For TNO, chairmanship of CEN TC 250 SC4, chairmanship of EC3 Conversion AdvisoryCommittee, vice-chairmanship of CEN TC 250 SC3,

Thus, and owing to the strong tissue of continuous relations between all members of the steelconstruction research and Eurocodes fields, the spreading of this project’s findings should bea natural process.

However, this in not only, of course, a matter of steel and composite Eurocodes. This researchand the present report are intended for presentation to the Eurocodes coordination group, whichhas presently on its agenda the problem of safety format and factors. Again, the abovementioned partners are in a suitable position for such an action.

V-3. Future (long term) validity of conclusions for γM0

The results on γM0 have been derived from in mill measurements which are representative ofthe present production of five important Western Europe steel producers for hot rolled I/H

beams.

Hence it is necessary to investigate the conditions for this production to retain the same qualitylevel, regarding the investigated performances, in the future. However, only proposals can bemade, since this is a matter of steel products standards (harmonized, with CE mark), or ofstructural codes (Eurocodes). It is also possible to consider a situation where an ETA (EuropeanTechnical Agreement) would coexist with steel product standards, however this does not seemrealistic for standard construction products such as steel beams

Several ways have been discussed :

• To issue direct requirements for production performance criteria

• To issue guidelines for the kind of testing requirements that would be necessary in linewith an attestation of conformity procedure (according to the future CEN harmonized productstandard)

• To transfer a set of conclusions to Eurocodes conversion groups and leave it to them totreat the question.

Most probably the best technical way would be for the steel producers to do again, at intervals,a campaign of correlated (yield strength, dimensions) in mill measurements of strength andgeometric properties, followed by an analysis similar to what has been done within this project.A logical process would include an initial assessment (such as the records proceeded withinthis research project) followed with a periodic (e.g. yearly) production conformity assessment.

Several meetings between the main hot rolled beams producers (some of them involving highlevel representatives from Eurocode 3 authorities) allowed an exchange of ideas, theidentification of parameters and problems, and the consideration of the different options.

A partial study from one producer (based on its production) suggested that controlling thesection area could be a way to ensure the conclusion of a safety factor of 1,0. Later on, anotherproposal was made, which considers the target safety index, related with a one year statisticalanalysis of production. This proposal has been checked by other steel producers by the end ofthe project and has been noted as a possible way for introduction of adequate productionrequirements within the future Mandate M120 (harmonised product standards, e.g. EN 10 025),CE mark). This proposal is given in Annex C to this report.

So, in the end, it is expected that the results of this research project will be duly taken intoaccount by CEN TC 250 and ECISS TC 10 in the near future.

CHAPTER VI – CONCLUSIONS

1) Concerning the first part of the project, it is concluded that the partial safety factor γM0 for hotrolled steel sections may be safely taken as 1,0.

This conclusion is valid if adequate procedures are adopted for the production quality to be andto remain similar to the tested production, as discussed in chapter IV. No definite proposal ismade regarding this point.

2) Concerning other limit states, involving γM1 or other components (connections), it isconcluded in some specific cases that modified (generally slightly lower) safety factor valueswould be adequate, or in an equivalent way, modified strength formulae are proposed.However, this analysis has been possible only for bolted connections, where the existingtests are quite numerous and cover well the various situations. For the remaining limit statesthat have been studied, it is either concluded that γM1 = 1,1 is quite satisfactory, or that itwould seem possible to reduce it but for certain specific design situations like interactionbetween axial force and bending.

Indeed it is regretted that a large proportion of existing tests are insufficiently documented forstatistical exploitation, and also that all the design situations can hardly be covered by tests. Toovercome this situation would require very important research efforts in the future.

Finally, this research project conclusions are coming at the right moment for the project teamsin charge of converting ENV 1993 and ENV 1994 into EN to take advantage of them.

CHAPTER VII - LIST OF REFERENCE DOCUMENTS AND WORKREPORTS

VII-1 Documents elaborated during the research works

(Note that all work documents may remain subject to confidentiality rules from author company.However, all documents listed above have been examined and discussed within coordinationmeetings and hence their conclusions have been adopted as they appear in the present finalreport)

1st full meeting - 12th october 19941. « Gamma M proposal draft at 7th oct 1994 »

SCI, C.King2. " Stability aspects for hollow section columns, beams and beam-column "

RWTH, D.Grotmann, G.Sedlacek3. « Present values of Partial safety factors in NADs »

(from ECCS publication N°65)CTICM, B.Chabrolin

4. « Proposed selection of products for testing at B.S »BST, Ph.Wells

5. « List of Background documents for Eurocode 3, part 1 »RWTH Aachen, G.Sedlacek

1st « statistic working group » meeting 16th february 19956. « Application of Annex Z »

Lateral torsional buckling - Working paper - february 1995CTICM, A.Bureau

7. « Partial safety factors for resistance » - calibration exercice - february/march 1995University of Pisa

8. « Lateral torsional buckling » - calibration exercice - march 1995University of Pisa

9. « Measurements carried out by ProfilArbed on I or H hot rolled profiles »Arbed - 14.12.1994

2nd « statistic working group » meeting 27th march 199510. « Procedure to evaluate Npl, Mpl and Mel of H or I hot-rolled sections »

Arbed, Ph.Chantrain11. « Draft list of content of the report on γM factor for the resistance of steel structures to

structural design »RWTH, G.Sedlacek

12. « Evaluation of the results with reference to plastic values »RWTH, M.Feldmann

13. « Determination of ultimate load using moment-rotation characteristics »RWTH, M.Feldmann

14. Evaluation background document on bolted connections »TNO draft report 94-CON-R1668 - 12th dec 1994TNO, O.D.Dijkstra

2nd full meeting 19th may 199515. « List of partial safety factors (γ factors) »

Arbed, Ph.Chantrain16. Measurements in steel mills :

« Procedure to evaluate Npl, Mpl and Mel of H or I hot-rolled sections »

(2nd version - 11 may 1995 - First & Second proposal)Arbed, Ph.Chantrain

17. « Critical analysis of the background document for the lateral torsional bucklingresistance »; Document 5.03 (partim)CTICM, Ph.Lequien

3rd full meeting 22nd september 199518. « Gamma M from mills results » Draft 12th sept 1995

SCI, C.King19. Measurements in steel mills

"Procedure to evaluate partial safety factors γM for H/I hot-rolled sections"

(3rd version - 13 june 1995 )Arbed, Ph.Chantrain

20. « Campaign of measurements on H or I hot-rolled profiles » 21st sept 1995and Disk of the database spread sheet.Arbed, Ph.Chantrain

21. "Critical analysis of the background document for buckling resistance of hollow sectionsand database for the buckling tests of hollow sections" Document 5.03CTICM, Ph.Lequien

22. "Evaluation of partial safety factor for the lateral torsional buckling resistance to Eurocode3 of rolled I profiles"Report CTICM N°8.009-6 - juin 1995CTICM, A.Hollinger

23. Semestrial report / january-june 1995SCI, C.King

24. Semestrial report / january-june 1995CREA, P.Croce

3rd « statistic working group » meeting 2nd february 199625. « Evaluation of the partial safety factors from measurements» + floppy disk

CTICM, A.Bureau26. Statistical procedure clarifications

RWTH, MM Sedlacek & Feldman27. ENV 1993-1-1 : Eurocode 3 Teil 1-1

Annex ZDetermination of design resistance from tests

RWTH, MM Sedlacek & Feldman

4th full meeting 4th march 199628. « Evaluation of the partial safety factors from measurements »

Software for the evaluation of γM0 from measurementsCTICM / 4-3-96

29. « Evaluation of partial safety factors from measurements and tests »Draft - RWTH / 4-3-96

30. « γM Tail of distribution »Diagram - BST / 4-3-96

31. « Minutes of the meeting held on 02.02.1996 at Aachen »RWTH / 15-2-96

32. « Minutes of the meeting working group on bolted and shear connections »22nd February 96TNO / 28-2-96

33. « Sigma Plot » software documentation.

5th full meeting 21st june 199634. « Evaluation of the partial safety factors from measurements »

Program for the evaluation of γM0 from measurementsCTICM / 21-6-96

35. « Evaluation of partial safety factors from measurements and tests »2nd Draft - RWTH / 21-6-96

36. Report 21/6/96A.Cecconi - CREA

37. « Partial Safety Factor for Class 4 Cross-section Resistance »Draft - SCI / 21-6-96

38. Transparency of the Presentation« Pilot study for the evaluation of partial safety factor for bolted connection »TNO / 21-6-96

39. « British Steel γM database » - 13th June 1996BST

40. Background document to Eurocode 3, N°II.5.1Evaluation of test results for the design rules of shear buckling resistance for stiffened andunstiffened websRWTH / 21-3-96

41. Background document to Eurocode 3, N°II.5.2Evaluation of test results for the design rules of stiffened and unstiffened webs, which areloaded by transverse forcesRWTH / 11-3-96

42. Background document to Eurocode 3, N°II.5.3Evaluation of test results for the design rules of longitudinal stiffened steel plates incompressionRWTH / 1-12-95

43. Transparency of the Presentation

« Evaluation of partial safety factor for the buckling resistance to Eurocode 3 of hollowstructural sections »CTICM / 21-6-96

44. CUST Report , Z’Hour Bekkouche« Evaluation du coefficient partiel de sécurité pour la résistance au flambement des profilscreux »Juin 1996

45. Transparency of the Presentation« Issues arising from composite connectors »SCI / 21-6-96

6th full meeting 23rd september 199646. Report 23/9/96

A.Cecconi - CREA47. « Class 4 Cross-section »

« Fabricated beams »« Effect of strain hardening on gamma M0 »SCI

8. « Preliminary results of gamma M0 - Subsets of the statistical evaluation »RWTH

49. « Survey on statistical data from test evaluations for the determination of characteristicvalues in Eurocode 3 - Part 1 »CEN - TC250/SC3CTICM

50. Background document to Eurocode 3 Part 2 - Bridges - Chapter 5, N°II.5.1Evaluation of test results for the design rules of shear buckling resistance for tiffened andunstiffened webs.RWTH / sixth draft, 14-9-96

51. Background document to Eurocode 3 Part 2 - Bridges - Chapter 5, N°II.5.2Evaluation of test results for the design rules of stiffened and unstiffened webs which areloaded by transverse forces.RWTH / sixth draft, 13-9-96

52. Background document to Eurocode 3 Part 2 - Bridges - Chapter 5, N°II.5.3Evaluation of test results for the design rules of longitudinal stiffened steel plates incompression.RWTH / sixth draft, 13-9-96

53. Background document to Eurocode 3 Part 3.1 - Towers and Masts - Chapter 5, N°.3.5.1Evaluation of test results for the design rules of buckling strength for angle struts intransmission towers.RWTH / fourth draft, October 96

7th full meeting 9th December 199654. « Summary of the statistical results for all subsets »

RWTH55. « Summary of the γM values for the re-evaluated subsets »

RWTH

56. Report to ECSC« Ultimate moment of resistance of restrained I-beams »Document RT618 - Version 01 - December 1996SCI

57. Harmonized European StandardCE MarkingVoluntary product certificationBNS

58. Product certificationTHE KEYMARK

8th full meeting 17th February 199759. « Gamma M for shear studs »

Document RT609 - Version 01 Draft 01 - November 1996SCI

60. « Partial safety factors for the resistance of fabricated beams »Document RT620 - Version 01 - February 1997SCI

61. « Partial safety factors γR for bolted connections »Labein 1997 - 01 - 28Document 94/254-IN-CL-002Labein

62 « Strength function revision for bolted connections - Labein Provisional Conclusions »Labein

9th full meeting 29th April 199763. Interim report N°5 - July 1996-December 1996

CTICM64. Evaluation of Partial Safety Factors γM from measurements and tests

Plate material - April 1997RWTH

65. Draft pre-conclusive reportCREA - University of Pisa

VII-2 General references

STANDARDS (S)

66 CENEurocode 3 : Design of steel structures. Part 1.1 : General rules and rules for buildings. Ref.No ENV 1993-1-1 : 1992 E

67 CENEurocode 4 : Design of composite steel and concrete structures. Part 1.1 : General rules andrules for buildings. Ref. No ENV 1994-1-1 : 1992 E

68 CENEurocode 1 : Basis of design and actions on structures. Part 1 : Basis of design. Ref. No ENV1991-1-1 : 1994 E

69 CENEN 10002-1 : Metallic materials - Tensile testing - Part 1 : method of test (at ambienttemperature)

70 CENAnnexe Z : Determination of design resistance from tests. ENV 1993-1-1 : 1992/prA2 : 1994.

71 CENSurvey on statistical data from test evaluations for the determination of characteristic valuesin EC3 part 1 : Aachen may 1993. Doc. CEN/TC : 250/SC 3 N 330 E

72 ISOISO 8930 : Principes généraux de la fiabilité des constructions - Liste des termeséquivalents - Edition trilingue(General principles on reliability for Structures -List of equivalent terms)

73 ISOISO 3898 : Bases de calcul des constructions - Notations - Symboles généraux.

(Basis of design for structures - Notations - General symbols)

74 ISOGeneral Principles on Reliability for Structures - Revision of IS 2394. DocISO/TC98/SC2/WG1.

75 AFNOR (Association Française de NORmalisation)Eurocode 3 "Calcul des structures en acier" et Document d'application Nationale - Partie1.1 Règles générales et règles pour les bâtiments. Norme expérimentale P22-311.

76 AFNOR (Association Française de NORmalisation)

Règlement particulier de la marque NF Acier. Doc P22 A N40. 02/10/92

(Specific rules of product identification mark "NF Acier")

77 CNR 10011/85Costruzioni in acciaio - Istruzioni per il calcolo, l'esecuzione, il collaudo, la manutenzione.

78 CNR 10012/85Istruzioni per la valutazione delle azioni sulle costruzioni

79 BSINational Application Document for use in the UK with ENV 1993-1-1 : 1992.

OTHER GENERAL REFERENCES

80 P. Thoft-Christensen, M.J. BakerStructural reliability theory and its applications. Springer-Verlag, Berlin, Heidelberg, NewYork, 1982.

81 P. Thoft-Christensen, Y. MurotsuApplication of structural system reliability theory. Springer-Verlag, Berlin, Heidelberg, NewYork, 1982.

82 H. Madsen, S. Krenk, N. C. LindMethods of structural safety. Prentice Hall, Inc., Englewood Cliffs N.J. 1986

83 Augusti, Baratta, CasciatiProbabilistic methods in structural engineering - Chapman and Hall

84 E. J. GumbelStatistics of extremes - Columbia University Press, New York 1958

85 A. Vrouwenvelder, A. J. M. SiemensProbabilistic calibration procedure for the derivation of safety factors for the netherlandsbuilding codes. Revue HERON, TNO, Institute for building materials and structures. Vol. 32,9-29, n°4 - 1987.

86 D. O'Leary, C. Moum, J. BrekelmansComparative study of composite slab tests. IABSE Symposium, Mixed structures, includingNew Materials, Brussels 1990.

87 R.P. Johnson, Dongjie HuangCalibration of safety factors γM for composite steel and concrete beams in bending.Proceedings of the Institution of civil Engineers, Structures and Buildings, May 1994.

88 J. M. AribertAspects actuels sur le dimensionnement plastique des assemblages en ConstructionMétallique. Revue Construction Métallique n°2-1992.(Present aspects about the plastic design of connections in constructional steelwork)

89 J. Goyet, B. RémyFiabilité des structures - Méthodologie d'ensemble et application aux structures à barres.Revue Construction Métallique n°4 - 1988. CTICM.(Structural reliability - Global methodology and application to frames)

90 P. Bernard, M. FogliUne méthode de Monte-Carlo performante pour le calcul de la probabilité de ruine. RevueConstruction Métallique n°4 - 1987. CTICM.(An efficient Monte-Carlo method for the evaluation of the failure probability)

91 J. P. Muzeau, M. Lemaire, K. TawilMéthode fiabiliste des surfaces de réponse quadratique (SRQ) et évaluation des réglements.Revue Construction Métallique n°3 - 1992(Reliability method of quadratic response surfaces and evaluation of codes)

92 B. ChabrolinDétermination des coefficients partiels de sécurité à prendre en compte pour la vérificationà la fatigue d'un élément de structure. Revue Construction Métallique n°4 - 1988.(Determination of partial safety factors for fatigue check of a structural member)

93 J. Goyet, A. BureauSécurité probabiliste des structures - Evaluation de coefficients partiels de sécurité pourl'élaboration des nouveaux règlements. Revue Construction Métallique n°1-1990. CTICM.(Probabilistic safety of structures - Evaluation of partial safety factors for the new regulation)

94 J. Goyet, A. BureauDétermination d'une valeur de calcul pour la résistance au flambement des tubes creuxcirculaires - Revue Construction Métallique n °1 - 1990. CTICM.(Determination of a design value for the buckling resistance of Circular Hollow Sections)

95 J. BerthellemySécurité des assemblages dans les structures calculées en plasticité. Revue ConstructionMétallique n°1 - 1990.(Safety of connections in structures designed with plastic analysis)

96 A. M. HasoferProblème de statistiques des valeurs extrêmes - Revue Construction Métallique n°1 - 1993.CTICM.(Problem of extreme values statistics)

97 D. Grotmann, G. SedlacekStability aspects for hollow section columns, beams and beam-columns. Institute of SteelConstruction, RWTH Aachen, Germany.

98 Basic notes on actions.JCSS - Lisbon 1976

99 Definizione dei coefficienti parziali di sicurezza γm per i collegamenti da introdurre nellaversione italiana dell'EC3 - Università di Pisa - Istituto di Scienza delle Costruzioni(Preliminare)

100 Urbano, Castiglioni, PoggiLa Normativa Europea per le strutture in Acciaio - EC3 - Confronti con le norme CNR10011/85 - Diparmento Ingegneria Strutturale - Politecnico di Milano.

101 Casciati, Favarelli, ZanonValutazione probabilistica dei coefficienti di ponderazione dei carichi agenti sulle strutturemetalliche - CTA Torino 1979.

102 Castiglioni, Poggi, UrbanoSui coefficienti "incasellati" EC3 - CTA Abano Terme 1991.

103 Casciati, Favarelli, ZanonCriteri di combinazione di carichi accidentali di strutture metalliche in zona sismica - CTAVerona 1977.

104 Del Corso, SanpaolesiIl codice europeo sulle azioni : le problematiche del carico neve - CTA Abano Terme 1991.

105 De Luca, Faella, PilusoL'approcio dell'EC3 per la verifica di telai a nodi spostabili - CTA Abano Terme 1991.

106 C. Floris, C. GiommiOn stochastic load combination modelling and algorithmy for calculating probability of failure.Proceedings of ICASP & ... , Mexico City 1991.

107 C. Floris, A. Colombo, M. MorelloStochastic and non stochastic load combination analysis. Proceedings of ICASP & ..., MexicoCity 1991.

108 Casciati, FavarelliLa sicurezza strutturale nei confronti degli stati limite descrivibili come problemi diottimizzazione vincolata. Costruzioni Metalliche n°3 - 1977.

109 G. Ballio, F. CasciatiLa sicurezza strutturale nella costruzione metallica : approcci probabilistici e considerazioniprogettuali. Costruzioni Metalliche n°4 - 1977.

110 A. Migliacci, F. Mola, S. Cristini, G. MirabellaValutazione della sicurezza di sezioni rettangolari in c.a. sogette a pressoflesione retta conil metodo di livello 2 e confronti con i risultati del metodo di livello 1. Studi e Ricerche Vol. 71985, Corso di Perfezionamenti Costruzioni in C.A.F.lli Pesenti, Politecnico di Milano.

111 C. Floris, A. MazzicchelliReliability assessment of column under stochastic stresses. Journal of structural engineeringn°11 - 1991.

112 Ballio, SolariThe new italian recommendation for wind load on structures : basic assumptions and criticalconsiderations. Journal of Wind Engineering and Industrial Aerodynamics n°30 - 1980.

113 Second International Colloqium on stability - Introductory report - European Convention forStructural Steelwork.

114 R. NarayananAxially compressed structure. Stability and strength. Applied Science Publishers.

115 E.S. VentselTeoria della Probabilita - Ed MIR

116 Ballio, MazzolaniCostruzioni in Acciaio

117 DemidovicFondamenti di analisi numerica - Ed MIR

118 H. H. Snijder et al.Evaluation of test results on welded connections in order to obtain strength functions andsuitable model factors. TNO report BI-88-139, October 1988.

119 M. Kersken-Bradley, W. Maier, R. Rackwitz, A. VrouwenvelderEstimation of structural properties by testing for use in limit state design. JCSS, WorkingDocument, November 1990.

120 J. BrekelmansEvaluatie van de proefresultaten uit het SPRINT-project RA31. TNO report BI-89-138,November 1989 (in Dutch)

121 J.W.B. Stark, B.W.E.M. Van HoveStatistical analysis of push-out tests on stud connectors in composite steel and concretestructures. TNO report BI-90-038, 1990

122 J.W.B. Stark, B.W.E.M. Van HoveStatistical analysis of push-out tests on stud connectors in composite steel and concretestructures. TNO report BI-91-163, September 1991

123 F. S. K. Bijlaard et al.Procedure for the determination of design resistance from tests. TNO report BI-87-112,November 1988.

124 Rationalisation of safety and serviceability factors in structural codes, CIRIA Report 63,October 1976.

125 Beeby, Johnson, Nethercot and BeckettBackground document for the National Application Document (NAD) of Eurocode ENV EC1:Relative levels of safety in Eurocodes, March 1993. Report to the department of theenvironment.(from SCI)

126 Evaluation des coefficients partiels de sécurité pour la vérification de la résistance en sectiondes profilés métalliques de la gamme UNIMETAL. Analyse de la campagne de mesures.Rapport CTICM n°8.009-2 Avril 1993.Evaluation of partial safety factors for resistance of cross-sections of UNIMETAL steelprofiles. Analysis of measured values. Report CTICM n°8.009-2 April 1993.

127 Evaluation des coefficients partiels de sécurité pour la vérification de la résistance en sectiondes profilés métalliques de la gamme UNIMETAL. Analyse de la campagne d'essais. RapportCTICM n°8.009-3 Avril 1993.Evaluation of partial safety factors for resistance of cross-sections of UNIMETAL steelprofiles. Analysis of test results. Report CTICM n°8.009-3 April 1993.

VII-3 Background documents to eurocode

The documents listed in this section are “background documents to Eurocode (3) “ , which havebeen drafted under ENV Eurocodes mandates..

128 Background document for chapter 2 of Eurocode 3129 Design against brittle fracture130 Background document of the relation between the nominal value of the yield strength in

Eurocode 3 and the specification in material standards.131 Background document for chapter 4 of Eurocode 3132 Background document for the justification of a safety factor γM* = 1,0 for beams in bending

about the strong axis made of rolled section133 The b/t - ratios controling the applicability of analysis models in Eurocode 3.134 Evaluation of test results on columns, beams and beam-columns with cross-sectional classes

1-3 in order to obtain strength functions and suitable model factors135 (partim)

Evaluation of test results on beams with cross-sectional classes 1-3 in order to obtainstrength functions and suitable model factors

136 Evaluation of test results on columns and beam-columns with cross-sectional class IV inorder to obtain strength functions and suitable model factors

137 Design rules for thin-walled plate girders for the ultimate and serviceability limit state takingaccount of the buckling phenomena

138 Evaluation of test results on hollow section lattice girder connections(Background document for Annex K)

139 Imperfections for compressed members and sway framesEvaluation of test results on bolted connections in order to obtain strength functions andsuitable model factors

140 Part A : Results141 Part B : Evaluations142 Part C : Test Data143 Part C : Data sheets144 Comparison of bolt strength according to Eurocode n°3 with bolt strength according to

national standards145 Part A : Results146 Part B : Evaluations147 Part C : Test Data148 Comparison of weld strength according to Eurocode n°3 with weld strength according to

national standards149 Beam to column connections150 Evaluation of test results on beam to column connections in order to obtain strength functions

and suitable model factors "In preparation"151 Procedure for the determination of design resistance from tests152 Background document for chapter 9 of Eurocode 3153 Report on the comparison of classification tables in existing national codes for fatigue in

Europe and statistical evaluation of large and small scale specimen test dataBackground information on fatigue design rules for hollow sections; statistical evaluation

154 Part A : Classification method Background document for annex AEvaluation of test results on connections in thin walled sheetings and members in order toobtain strength functions and suitable model factors

155 Part A : Evaluations and results156 Part B : Test data Background document for annex D157 Background document for design rules specific for high strength steels according to EN

10113158 Statistical evaluations of the results of bolted connections159 Evaluations of test results on welded connections made from FeE 460 in order to obtain

strength functions and suitable model factors160 Statistical analysis of strength functions for welded H-sections joints with respect to available

experimental data

VII-4 References for Chapter IV

Composite members161 Johnson R.P. and Huang D.J.

"Partial safety factors γM for composite beams in bending, found from test data"University of Warwick - Department of EngineeringResearch report CE 38February 1992

162 Johnson R.P. and Huang D.J."Reliability analysis for composite beams with ductile partial shear connection"University of Warwick - Department of EngineeringResearch report CE 40March 1992

163 Johnson R.P. and Huang D.J."Reliability analysis for composite beams with non-ductile shear connection"University of Warwick - Department of EngineeringResearch report CE 42March 1993

164 Johnson R.P."Coefficients of variation of areas of flanges and webs of rolled steel I and H sections"University of Warwick - Department of EngineeringResearch report CE 43January 1993

165 Johnson R.P. and Huang D.J."Partial safety factors for resistance of encased composite columns to compression and uniaxial

bending"University of Warwick - Department of EngineeringResearch report CE 49September revised October 1994

Lateral - torsional buckling of members166 Eurocode 3 - Design of steel structures - Part 1 - General Rules and Rules for Buildings

Background Documentation ; Chapter 5 ; Document 5.03 (partim)"Evaluation of test results on beams with cross-sectional Class 1-3 in order to obtain strength

functions and suitable model factors"167 « Application of Annex Z »

Lateral torsional buckling - Working paper - February 1995CTICM, A.Bureau

168 « Lateral torsional buckling » - calibration exercice - March 1995University of Pisa

169 « Critical analysis of the background document for the lateral torsional buckling resistance »Document 5.03 (partim)CTICM, Ph.Lequien

170 "Evaluation of partial safety factor for the lateral torsional buckling resistance to Eurocode 3 of rolledI profiles"Report CTICM N°8.009-6 - Juin 1995CTICM, A.Hollinger

171 D.Mateescu"Considération sur la valeur du coefficient de réduction pour le déversement des éléments fléchis"Revue Construction Métallique, n°1 - 1994.

172 Draft pre-conclusive reportCREA - University of Pisa

Plate buckling

Local buckling and Class 4 cross-section resistance (γM1) for EC3173 « Partial Safety Factor for Class 4 Cross-section Resistance »

Draft - SCI / 21-6-96174 « Class 4 Cross-section »

« Fabricated beams »« Effect of strain hardening on gamma M0 »SCI

175 Eurocode 3 - Design of steel structures - Part 1 - General Rules and Rules for BuildingsBackground Documentation ; Chapter 5 ; Document 5.04"Evaluation of test results on columns and beam-columns with cross-sectional Class IV in order toobtain strength functions and suitable model factors"

176 Eurocode 3 - Design of steel structures - Part 1 - General Rules and Rules for BuildingsBackground Documentation ; Chapter 5 ; Document 5.05"Design rules for thin-walled plate girders for the ultimate and serviceability limit state taking accountof the buckling phenomena"

177 Draft pre-conclusive reportCREA - University of Pisa

Buckling of plates with or without stiffeners178 Eurocode 3 - Design of steel structures - Part 1 - General Rules and Rules for Buildings

Background Documentation ; Chapter 5 ; Document 5.05"Design rules for thin-walled plate girders for the ultimate and serviceability limit state taking accountof the buckling phenomena"

179 Background documentation to Eurocode 3 - Design of Steel Structures - Part 2 - BridgesChapter 5. Document N°II.5.1Evaluation of test results for the design rules of shear buckling resistance for stiffened andunstiffened webs.RWTH / sixth draft, 14-9-96

180 Background documentation to Eurocode 3 - Design of Steel Structures - Part 2 - BridgesChapter 5. Document N°II.5.2Evaluation of test results for the design rules of stiffened and unstiffened webs which are loaded bytransverse forces.RWTH / sixth draft, 13-9-96

181 Background documentation to Eurocode 3 - Design of Steel Structures - Part 2 - BridgesChapter 5. Document N°II.5.3Evaluation of test results for the design rules of longitudinal stiffened steel plates in compression.RWTH / sixth draft, 13-9-96

182 Evaluation of partial safety factors γM from measurements and testsPlate material - April 1997RWTH

Buckling of Hollow sections183 Eurocode 3 - Design of steel structures - Part 1 - General Rules and Rules for Buildings

Background Documentation ; Chapter 5 ; Document 5.03"Evaluation of test results on columns, beams and beam-columns with cross-sectional Class 1 - 3in order to obtain strength functions and suitable model factors"April 1989

184 " Stability aspects for hollow section columns, beams and beam-column "RWTH, D.Grotmann. G.Sedlacek

185 "Critical analysis of the background document for buckling resistance of hollow sections anddatabase for the buckling tests of hollow sections" Document 5.03CTICM, Ph.Lequien

186 Transparency of the Presentation« Evaluation of partial safety factor for the buckling resistance to Eurocode 3 of hollow structuralsections »CTICM / 21-6-96

187 « Evaluation du coefficient partiel de sécurité pour la résistance au flambement des profils creux »Rapport CUST, Z’Hour BekkoucheJuin 1996

Resistance of connections

Bolted connections188 Eurocode 3 - Design of steel structures - Part 1 - General Rules and Rules for Buildings

Background Documentation ; Chapter 6 ; Document 6.01Evaluation of test results on bolted connections in order to obtain strength functions and suitablemodel factors.Part A : ResultsMarch 1989

189 Eurocode 3 - Design of steel structures - Part 1 - General Rules and Rules for BuildingsBackground Documentation ; Chapter 6 ; Document 6.02Evaluation of test results on bolted connections in order to obtain strength functions and suitablemodel factors.Part B : Evaluations

190 Eurocode 3 - Design of steel structures - Part 1 - General Rules and Rules for BuildingsBackground Documentation ; Chapter 6 ; Document 6.03Evaluation of test results on bolted connections in order to obtain strength functions and suitable

model factors.Part A : Test DataApril 1989

191 Bijlaard. F.S.K.. et al. :Procedure for the determination of design resistance from testsTNO report BI-87-112. November 1988

192 Draft Annex Z (Informative) : Determination of design resistance from testsDocument prENV 1993-1-1 / A2 (94 / 185226) with corrections 960201

193 Evaluation background document on bolted connectionsTNO draft report 94-CON-R1668 - 12th dec 1994TNO. O.D.Dijkstra

194 « Minutes of the meeting working group on bolted and shear connections »22nd February 96TNO / 28-2-96

195 Transparency of the Presentation« Pilot study for the evaluation of partial safety factor for bolted connection »TNO / 21-6-96

196 « Partial safety factors γR for bolted connections »Labein 1997 - 01 - 28Document 94/254-IN-CL-002Labein

197 « Partial safety factors γR for bolted connections » (final report)TNO 1997 - 12 - 04Document 96-CON-R1222TNO

Shear connections198 Calibration of Gamma M for Shear Studs

Document RT 580 - Preliminary CalculationsSCI

199 Stark. J.W.B. and Hove. B.W.E.M. van :Statistical analysis of push-out tests on stud connectors in composite steel and concrete structuresTNO report BI-91-163, Parts 1, 2 and 3, September 1991

200 Transparency of the Presentation« Issues arising from composite connectors »SCI / 21-6-96

201 « Gamma M for shear studs »Document RT 609 - Version 01 Draft 01 - November 1996SCI

ANNEX A

This Annex reproduces Eurocode 3 Annex Z « Determination of design resistance from tests.

This document has been published by CEN as part of ENV 1993-1-1 :1992/A2 :1998(Amendment 2) in 1998.

Annex Z [informative]Determination of design resistance from tests

Z.1 General

Z.1.1 Scope(1) This annex gives guidance on evaluating the results of tests in accordance with Section 8, carried out inconnection with the design of steel structures.

(2) This annex gives specific guidance that supplements the more general information on the determination of designresistance from tests given in annex D of ENV 1991-1.

(3) This annex covers cases where there is no structural redundancy.

Z.1.2 Symbols

(1) In this annex the following symbols are used:

b is the mean value correction factor;bi is the correction term for test specimen i ;b is the estimator for the mean value correction factor b ;b (r) is the realisation of the estimator b ;Ed is the design value of an effect of actions;E(...) is the mean value of (...) ;E(∆) is the mean value of ∆ ;grt(X) is the resistance function (of the basic variables X ) used as the design model;kc is the ratio of the nominal resistance rn to the characteristic resistance rk ;n is the number of experiments;P(.) = p is the probability p that ... (with p in %) ;Q is the standard deviation of the variable ℓn(r) [Q = σ�n(r) ] ;Rd is the design value of the resistance;r is the resistance value;rd is the design value of the resistance;re is the experimental resistance value;ree is the extreme (maximum or minimum) value of the experimental resistance [i.e. the value of re that

deviates most from the mean value rem ];rei is the experimental resistance for specimen i ;rem is the mean value of the experimental resistance;rk is the characteristic value of the resistance;rm is the resistance value calculated using the mean values Xm of the basic variables;rn is the nominal value of the resistance;rt is the theoretical resistance determined from the resistance function grt (X) ;rti is the theoretical resistance determined using the measured parameters X for specimen i ;s is the estimator for the standard deviation σ;s∆ is the estimator for σ∆ ;sδ(r) is the realisation of the standard deviation estimator sδ ;u is the value of the standardized normal distribution;ud is the design fractile factor for the standardized normal distribution;uk is the characteristic fractile factor for the standardized normal distribution;V is the coefficient of variation [V (standard deviation) / (mean value)] ;Vδ is the estimator for the coefficient of variation of the error term δ ;Vδ(r) is the realisation of the estimator Vδ ;X is an array of j basic variables X1 ... Xj ;Xm is the array of mean values of the basic variables;Xn is the array of nominal values of the basic variables;α is a weighting factor;β is the reliability index;γF is the partial factor for actions, combining the uncertainties included in γf and γSd ;

γf is the partial factor for actions, taking account of possible deviations of values of actions from therepresentative values;

γm is the partial factor for resistances, taking account of possible deviations of the material propertiesand of manufacturing tolerances from the characteristic values;

γR is the partial factor for resistances, combining the uncertainties included in γm and γRd [γR = rk/rd];γR

* is the corrected partial factor [γR* = rn/rd so γR

* = kc γR] ;γRd is the partial factor for resistances, taking account of model uncertainties;γSd is the partial factor for actions or effects of actions, taking account of model uncertainties;∆ is the logarithm of the error term δ [∆i ℓn(δi )] ;∆ is the estimator for E(∆);δ is the error term;δi is the observed error term for test specimen i obtained from a comparison of the experimental

resistance rei and the mean value corrected theoretical resistance brti ;ηK is the reduction factor applicable in the case of prior knowledge;σ is the standard deviation [σ variance 1];σ∆2 is the variance of the term ∆ .

(2) In the examples the following symbols are also used:

do is the hole diameter;di is the diameter of bolt i ;e1 is the end distance;fui is the ultimate tensile strength of plate i ;fu is the ultimate tensile strength of the bolt;ti is the thickness of plate i .

Z.2 Basis

(1) In ENV 1991-1 the design format adopted for ultimate limit states is:

Ed ≤ Rd

where:

Ed is the design value of an effect of actions;

Rd is the design value of the resistance.

(2) In ENV 1993-1-1, for internal forces and moments, the design format generally adopted is:

Sd ≤ Rd

where:

Sd is the design value of the internal force or moment.

(3) The partial factors used in ENV 1993 (see also annex A of ENV 1991-1) are indicated in figure Z.1.

Note: In ENV 1993-1-1 γM is used in place of γR for the partial factors for resistance

Figure Z.1: Partial factors used in ENV 1993-1-1

(4) This annex describes a standard procedure for determining characteristic values, design values and partial factorsfor resistance γR from the results of tests. This procedure complies with the basic safety assumptions outlined in ENV1991-1.

(5) Based on observation of actual behaviour in tests and on theoretical considerations, a “design model” is selected,leading to a resistance function. The efficiency of this model is then checked by means of a statistical interpretation ofall available test data. If necessary the design model is adjusted until sufficient correlation is achieved between thetheoretical values and the test data.

(6) The variation in the prediction of the design model is also determined from the tests (that is, the variation of the“error” term δ). This variation is combined with the variations of the other variables in the resistance function. Theseinclude:

- variation in material strength and stiffness;

- variation in geometrical properties.

(7) The characteristic resistance is determined taking account of the variations of all the variables.

(8) The design value is also determined from the test data and hence the γ-factor to be applied to the characteristicresistance function is obtained.

(9) For clarity, the standard procedure is presented in Z.3 as a number of discrete steps. The assumptions regardingthe test population and data are also explained.

Z.3 Standard evaluation procedure

Z.3.1 General

(1) For the standard evaluation procedure the following assumptions are made:

a) The resistance function is a function of a number of independent variables;

b) A sufficient number of test results is available;

c) All actual geometrical and material properties are measured;

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

e) All variables follow a log-normal distribution.

NOTE: Adopting a log-normal distribution for all variables has the advantage that no negative values can occurfor the geometrical and resistance variables, which is physically correct.

(2) The standard procedure comprises the nine steps given in Z.3.2.1 to Z.3.2.9.

NOTE: As an example, the procedure is illustrated for the resistance function for bolts in bearing.

(3) If the characteristic resistance is not required, the relevant portions of steps 7, 8 and 9 may be omitted.

Z.3.2 Standard procedure

Z.3.2.1Step 1: Develop a design model

(1) Develop a design model for the theoretical resistance rt of the member or structural detail considered,represented by the resistance function:

rt = ( ) X grt ... (Z.1)

(2) The resistance function should include all relevant basic variables X that affect the resistance at the relevant limitstate.

(3) All basic parameters should be measured for each test specimen i (assumption (c)) and should be available foruse in the evaluation.

Z.3.2.2Step 2: Compare experimental and theoretical values.

(1) Put the actual measured properties into the resistance function to obtain theoretical values rti for comparison withthe experimental values rei from the tests.

EXAMPLE: For bolts in bearing:

When e1 ≥ 3 do: rti = 2,5 di ti fui

(2) The points representing pairs of corresponding values ( rti, rei ) should be plotted on a diagram, as indicated infigure Z.2.

(3) If the resistance function is exact and complete, all points ( rti, rei ) will lie on the bisector of the angle betweenthe axes of the diagram (i.e. θ π/4). In general the points (rti, rei) will show some scatter.

Figure Z.2: re rt diagram

Z.3.2.3Step 3: Estimate the mean value correction factor b .

(1) Represent the probabilistic model of the resistance r in the format:

r = b rt δ ... (Z.2a)

in which the error term δ is such that the mean value E(δ) is given by:

E(δ) = 1,0 ... (Z.2b)

(2) The estimator b for the mean value correction factor b should be obtained by comparing the theoretical values rti of the resistance function with the corresponding experimental values rei .

(3) For each specimen i (where i 1 to n ) the correction term bi should be determined from:

bi = rei / rti ... (Z.3a)

(4) The estimator b for the mean value correction factor b should be obtained from:

b = ∑=

n

1iib

n1 ... (Z.3b)

(5) From the tests a realisation ( )rb of the estimator b should be calculated from:

( )rb = ∑=

n

1iib

n1 ... (Z.4)

EXAMPLE: For the case of bolts in bearing:

b (r) = 1,0

(6) In the (re , rt) diagram the mean value correction factor (r) may be represented by the slope of a straight linepassing through the origin, showing the mean value of the test results as a correction of the theoretical values,see figure Z.3.

Figure Z.3: (re , rt) diagram with the mean value correction line re (r) rt

NOTE: We have: E(r) = b rt E(δ) = b rt

and we also have: E( b rt ) = E( b ) rt = b rt

Therefore b rt is a good estimator for E(r).

(7) The theoretical resistance function, calculated using the mean values Xm of the basic variables, may be obtainedfrom:

rm = b (r) rt(X,_m) b (r) grt(X,_m) ... (Z.5)

Z.3.2.4Step 4: Estimate the coefficient of variation Vδ of the error term δ.

(1) The error term δi for each experimental value rei relative to the corresponding mean value corrected theoreticalresult b rti should be determined for i 1 to n from:

δi =r b

r

i t

i e ... (Z.6)

(2) From the values of δi an estimator for Vδ should be determined by defining:

∆i = ( ) n i δl ... (Z.7)

(3) The estimator ∆ for E(∆) should be obtained from:

∆ = ∑=

∆n

1iin

1 ... (Z.8)

(4) The estimator s∆2 for σ∆2 should be obtained from:

s∆2 = ( )2n

1ii1n

1∑=

∆−∆−

... (Z.9)

(5) The estimator Vδ2 should be obtained from:

Vδ2 = ( ) 1 - s exp 2

∆ ... (Z.10)

(6) The realisation Vδ(r) of Vδ may be used as the coefficient of variation Vδ of the error term δ.

EXAMPLE: For the example of bolts in bearing Vδ(r) = 0,08.

(7) Alternatively, for small values of sδ(r) the approximation Vδ(r) ≈ sδ(r) may be used.

Z.3.2.5Step 5: Analyse the compatibility

(1) The compatibility of the test population should be analysed with regard to the assumptions made in the resistancefunction.

(2) If the scatter of the (rei , rti) values is too high to give economic characteristic resistance functions, this scattermay be reduced in one of the following ways:

a) by correcting the resistance functions, such that additional parameters not adequately represented in theresistance functions are taken into account;

b) by modifying the estimators for b (r) and Vδ(r).

(3) To ascertain which parameters have most influence on the scatter, the test results may be split into sub-sets withrespect to these parameters.

EXAMPLE: As an illustration, the results of shear tests on bolts are shown in figure Z.4, split into sub-sets accordingto the bolt grade. Clearly in this case the resistance function can be improved if the coefficient 0,7 in the resistancefunction is replaced by a function of the bolt strength fub .

Figure Z.4: Shear failure of bolts with the shear plane in the threaded portion

(4) The purpose in such cases should be to improve the resistance function per sub-set by analysing each sub-setusing the standard procedure.

NOTE: The disadvantage of splitting the test results into sub-sets is that the number of test results in each sub-setcan become rather small.

(5) In determining the fractile factors uk (see step 7) the uk value for the sub-sets may be determined on the basisof the total number of the tests in the original series.

(6) In this way, an improved resistance function may be obtained consisting of the original resistance functionmultiplied by a factor dependent on the variation of a few additional parameters.

NOTE: It is often found that the frequency distribution for resistance from tests cannot be described by a uni-modal function, because it represents two or more sub-sets which result in a bi-modal or multi-modal function. This can be checked by plotting on Gaussian paper, see figures Z.5 and Z.6. When plotted with the horizontalaxis to a linear scale, a uni-modal function should give a straight line (if normally distributed) or a monotonicallycurved line (if log-normal). It is more convenient to plot log-normally distributed functions with a logarithmichorizontal axis because this gives a linear plot.

If no other way is found to separate the sub-sets, a uni-modal function can be extracted from bi-modal or multi-modal functions using the procedure outlined in figure Z.7. The statistical data for the uni-modal function canbe taken from a tangent to the actual distribution. Thus b m(r) and smb(r) are obtained instead of b (r) and sb(r)

and hence smδ(r) instead of sδ(r). The evaluation procedure for uni-modal functions described hereafter can thenbe used.

Commonly it is difficult to construct a representative tangent, in which case a linear regression of the lower endof the data can be carried out and the regression line used in place of the tangent. Generally it is advisable to useat least 20 data points for this regression.

Figure Z.5: Uni-modal distribution

Figure Z.6: Bi-modal or multi-modal distribution

Figure Z.7: Extraction of a uni-modal function from a bi-modal or multi-modal distribution by construction ofa tangent, or alternatively by linear regression

Z.3.2.6Step 6: Determine the coefficients of variation VXi of the basic variables.

(1) Unless it can be shown that the test population is fully representative of the variation in reality, the coefficientsof variation VXi of the basic variables in the resistance function should not be determined from the test data. As thisis not generally the case, the coefficients of variation VXi should normally be determined on the basis of priorknowledge.

EXAMPLE: For the resistance function considered for the bearing resistance of bolts, the following values have beendetermined from studies on the variability of bolt dimensions and material properties:

Vdn = 0,005

Vt = 0,05

Vfu = 0,07

Z.3.2.7Step 7: Determine the characteristic value rk of the resistance.

(1) For a log-normal distribution the characteristic resistance rk should be obtained from:

rk = E(r) exp(-uk Q - 0,5 Q2 ) ... (Z.11)

with:

Q = σℓn(r) = ( ) 1 + V n r2l ... (Z.12)

where:

-uk is the characteristic value [with uk > 0] of the standard normal distribution:

P(u < -uk) = p [e.g. p 5 % for uk 1,64]

Vr is the coefficient of variation of the random variable r

σ�n(r) is the standard deviation of the variable ℓn(r)

(2) If the resistance function for j basic variables is a product function of the form:

r = b rt δ = b {X1 x X2 ... Xj }δ

the mean value E(r) may be obtained from:

E(r) = b {E(X1) x E(X2) ... E(Xj) }E(δ) =b grt (Xm) ... (Z.13a)

and the coefficient of variation Vr may be obtained from the product function:

Vr2 = (Vδ

2 + 1) ( ) 11Vj

1i

2Xi −

+∏

=... (Z.13b)

(3) Alternatively, for small values of Vδ2 and VXi

2 the following approximation for Vr may be used:

Vr2 = V + V rt

22δ ... (Z.14a)

with:

Vrt2 = ∑

=

j

1i

2XiV ... (Z.14b)

EXAMPLE: In the case of bolts in bearing (with e1/do > 3 ):

grt(Xm) = 2,5 dm tm fum

Vrt = 0,086 = 070, + 050, + 0050, = V + V + V 222fu2

t2

dn2

Vrt = 0,118 = 080, + 0860, = V + V 222rt

2δ

(4) If the resistance function is a more complex function of the form:

r = b rt δ = b grt (X1, ..., Xj) δ

the mean value E(r) may be obtained from:

E(r) = b grt (E(X1), ..., E(Xj)) E(δ) = b grt(Xm) x 1,0 ... (Z.15a)

and the coefficient of variation Vrt may be obtained from:

Vrt2 =

2j

1i i

rt

mrt2

mrt2

rt LiXg

)X( g1 =

)X( g

)]X(g[ VAR∑=

σ×

∂∂

× ... (Z.15b)

EXAMPLE: The method is illustrated for the following fictitious resistance function:

grt(X) = bo0,5 to1,5 fu

Assume:

Vbo = 0,005 from prior knowledge;

Vto = 0,05 from prior knowledge;

Vfu = 0,07 from prior knowledge;

Vδ = 0,09 from the evaluation of tests.

Substitute mean values for the variables in calculating VAR [grt] in expression (Z.15b) and thus calculate:

Vrt2 =

)X( g

fs

+ ts1,5 +

bs0,5 )X( g

= )X( g

)]X(g[ VAR

mrt2

um

fu2

om

to2

om

bo2

mrt2

mrt2

rt

Vrt2 = 0,25 Vbo

2 + 2,25 Vto2 + Vfu

2

Vr2 = Vrt

2 + Vδ2 = 0,25 Vbo

2 + 2,25 Vto2 + Vfu

2 + Vδ2

Vr2 = 0,25 (0,005)2 + 2,25 (0,05)2 + (0,07)2 + (0,09)2 = 0,019

Vr = 0,14

(5) If a large number of tests (say n 100) is available, the characteristic resistance rk may be obtained by replacing b by the realisation )r(b of b and using the realisation Vδ(r) of Vδ . Thus in this case the characteristic resistance rk may be obtained from:

rk = ( ) Q 0,5 - Q u-exp )X( g b 2,kmrt)r( ∞ ... (Z.16)

with:

Q = ( ) 1 + V n r2l ... (Z.17)

(6) If the number of tests is limited to a smaller number n allowance should be made in the distribution of ∆ forstatistical uncertainties. The distribution should be considered as a central t-distribution with the parameters ∆ , V∆(r) and n.

(7) In this case the characteristic resistance rk should be obtained from:

rk = ( ) Q 0,5 - Q u - Q u-exp )X( g b 2n,krtrtk,mr)r( δδ∞ αα ... (Z.18)

with:

Qrt = σ (rt) n l = ( ) 1 + V n rt2l ... (Z.19a)

Qδ = σ δ )( n l = ( ) 1 + V n 2δl ... (Z.19b)

Q = σ (r) n l = ( ) 1 + V n r2l ... (Z.19c)

αrt =Q

Qrt ... (Z.20a)

αδ =QQδ ... (Z.20b)

where:

uk,n is the characteristic fractile factor from table Z.1;

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

αrt is the weighting factor for Qrt

αδ is the weighting factor for Qδ

Table Z.1: Factor uk,n for determining 5% characteristic fractile values

Total number of available test results n 1 2 3 4 5 6 8 10 20 30 ∞

Factor uk,n for the case where Vδ isunknown (see Note 2) - - - 2,63 2,33 2,18 2,00 1,92 1,76 1,73 1,64

Notes:

1) This table is an extract from table D.1 in annex D of ENV 1991-1.

2) The value of Vδ is to be estimated from the test sample under consideration.

EXAMPLE: For the case of bolts in bearing and a large number of tests: [here Q ≈ Vr]

rk = rtm exp(-1,64 x 0,118 - 0,5 x 0,1182 )

rk = rtm x 0,818

Z.3.2.8Step 8: Determine the design value rd of the resistance

(1) The procedure for determining the characteristic value rk of the resistance may be extended by replacing thecharacteristic fractile factor uk by the design fractile factor ud related to a value of the reliability index β 3,8 to obtainthe design value rd of the resistance.

(2) For the case of a large number of tests the design value rd may be obtained from:

rd = ( ) Q 0,5 - Q u-exp )X( g b 2dmrt ... (Z.21)

(3) According to annex A of ENV 19911, for a large number of tests the value of ud may be taken as:

ud = αR β = 0,8 β = 3,04

(4) For the case of a limited number of tests the design value rd should be obtained from:

rd = ( ) Q 0,5 - Q u - Q u-exp )X( g b 2n,drtrtk,mrt δδ∞ αα ... (Z.22)

where:

ud,n is the design fractile factor from table Z.2;

ud,∞ is the value of ud,n for n → ∞ [ud, ∞ 3,04].

Table Z.2: Factor ud,n for determining design fractile valuesTotal number of available test results n 1 2 3 4 5 6 8 10 20 30 ∞Factor ud,n for the case where Vδ isunknown (see Note 2) - - - 11,40 7,85 6,36 5,07 4,51 3,64 3,44 3,04

Notes:1) This table is an extract from table D.1 in annex D of ENV 1991-1.2) The value of Vδ is to be estimated from the test sample under consideration.

(5) The initial estimate for the partial factor γR may be obtained from:

γR = rk / rd ... (Z.23)

EXAMPLE: For the case of bolts in bearing and a large number of tests:

γR = exp((3,04 - 1,64) Q ) = exp(1,40 x 0,118) = 1,18

Z.3.2.9Step 9: Final choice of characteristic values and γR values

(1) The design resistance functions may contain basic variables defined as nominal values Xn. The nominal valueof the material strength may be adopted as the characteristic value and the nominal values for the geometrical variablesmay be adopted as mean values. However in such cases a suitable adjustment should be made in the final choice of the γR values.

(2) The ratio kc between the nominal resistance rn and the characteristic resistance rk should be obtained from:

kc =rr

k

n =( )r

X g

k

nrt ... (Z.24)

(3) The corrected partial factor γR* for use with the nominal resistance function may be obtained from:

γR* = γRc k = ( )( ) r / r r / r dkkn = r / r dn ... (Z.25)

EXAMPLE: For the case of bolts, the nominal values t and d are assumed to represent mean values, whereas thenominal value of the ultimate tensile strength fu is assumed to be equal to the characteristic value defined by the fractilefactor uk,fu = 2.

Thus:

fu = exp(2 x 0,07 - 0,5 x 0,072 ) fum = 0,867 fum

Hence:

kc =0,8180,867 = 1,06

and:

γR* = 1,06 x 1,18 = 1,25

(4) In order to avoid γR* values that vary too widely between one resistance function and another, the classes of

γRi values given in table Z.3 have been established for use in ENV 1993.

Table Z.3: Classes for γRi

Resistance criterion Strength parameter Class Numerical value

Yielding of cross-section fy γR0 1,00 *)

Stability failure fy γR1 1,10

Fracture fu γR2 1,25

*) In ENV 1993-1-1 both γR0 and γR1 are set to 1,10.

(5) The final choice of γRi should be made according to the relevant class and the nominal resistance function grt(Xn) should be modified to give the final resistance function r such that:

r = ( ) X r nt = ( ) X g nrtγ

γ

R* i R = rn

γ

γ

R* i R = γ i Rd r ... (Z.26)

EXAMPLE: In the case of bolts in bearing:

γR* = γR2 = 1,25 and therefore r = 2,5 dn t fu

Z.3.3 Simplified standard procedure

(1) A simplified version of the standard procedure for the determination of design resistances from a limited numberof tests, with small variability both in the test results and in the basic variables, may be carried out as summarized in the

following step-by-step procedure:

Step 1: Develop a design model: rt = grt (X).

Step 2: Compare theory with tests: Plot re against rt .

Step 3: Estimate mean value correction factor b :

Mean value corrected resistance: rm= ( )rb rt

Calculate ( ) ∑=

=n

1iir b

n1b

Step 4: Estimate variation Vδ of the error term δ :

Vδ = Vδ(r) = ( ) 1 - s exp 2∆

with:

s∆2 = ( )2n

1ii1n

1∑=

∆−∆−

∆ = ∑=

∆n

1iin

1

∆i = ( ) n iδl

r br n

i t

i el

Step 5: Check compatibility of the test population.

Step 6: Determine the coefficients of variation VXi of the basic variables Xi from prior knowledge.

Step 7: Determine the characteristic resistance:

rk = ( ) Q 0,5 - Q u - Q u-exp )X( g b 2nk,rtrtk,mrt δδ∞ αα

Qrt ≈ Vrt = V i X2∑

Qδ ≈ Vδ

Q ≈ Vr = V + V 2rt

2δ

αrt =Q

Qrt

αδ =QQδ

Step 8: Determine the design resistance:

rd = ( ) Q 0,5_ Q u - Q u_exp )X( g b 2nd,rtrtd,mrt δδ∞ αα

Calculate initial value of partial factor:

γR = r / r dk

Step 9: Final choice of characteristic values and γR values:

kc =rr

k

n =r

)X( g

k

nrt

Calculate corrected value of partial factor:

γR* = γRc k = r / r dn

Select final value of partial factor γRi from γR0 , γR1 or γR2

Adopt final resistance function:

r = ( ) X r nt =γ

γ

R*i R

n

r = rd γR i

Z.4 Simplified procedure for the case of prior knowledge

(1) If the validity of the resistance function rt and an upper bound for the coefficient of variation Vr are alreadyknown from a significant number of previous tests, the following simplified procedure may be adopted when further testsare carried out.

(2) If only one further test is carried out, the characteristic value rk may be determined from the result re of thistest by applying:

rk = ηk re ... (Z.27)

where:

ηk is the reduction factor applicable in the case of prior knowledge.

(3) In the case of only one further test, the reduction factor ηk may be obtained from:

ηk = 0,9 exp(2,31 Vr 0,5 Vr2 ) ... (Z.28)

where:

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

(4) If two or three further tests are carried out, leading to a mean value rem , the reduction factor ηk may be obtainedfrom:

ηk = exp(2,0 Vr 0,5 Vr2 ) ... (Z.29)

provided that each extreme (maximum or minimum) value ree satisfies the condition:

r 0,10 r - r ememee ≤ ... (Z.30)

(5) The values of the coefficient of variation Vr given in table Z.4 may be assumed for the types of failure specified,leading to the listed values of ηk according to expressions (Z.28) and (Z.29).

Table Z.4: Reduction factor ηk

Reduction factor ηkType of failure observed in tests Coefficient of

variation Vr For 1 test For 2 or 3 tests

Excessive yielding or gross deformation 0,05 0,80 0,90

Local buckling 0,11 0,70 0,80

Overall buckling 0,17 0,60 0,70

ANNEX B

CALIBRATION OF γM0 FOR I/H HOT ROLLED SECTIONS

DATA SET 1 : All SECTIONS

DATA SET 2 : ALL STEEL PRODUCERS, EACH TYPE OF SECTION

DATA SET 3 : EACH STEEL PRODUCER, ALL TYPES OF SECTIONS

DATA SET 4 : EACH STEEL PRODUCER AND EACH TYPE OF SECTION

Data set 1:

All profiles

Table : γM -values

1-5 Npl Mel.y Mpl.y Mel.z Mpl.zProfil EC 3 EN EC 3 EN EC 3 EN EC 3 EN EC 3 EN

all n = 2639nr = 1320Ud =3.040Sδ =0.06γM =1.035

n = 2717nr = 1358Ud =3.040Sδ =0.05γM =1.008

n = 98nr = 49Ud =3.040Sδ =0.03γM =0.981

n = 95nr = 48Ud =3.040Sδ =0.03γM =0.984

n = 3755nr = 1878Ud =3.040Sδ =0.06γM =1.037

n = 3758nr = 1878Ud =3.040Sδ =0.06γM =1.018

n = 98nr = 49Ud =3.040Sδ =0.03γM =0.990

n = 95nr = 48Ud =3.040Sδ =0.04γM =0.995

n = 3755nr = 1878Ud =3.040Sδ =0.06γM =1.065

n = 3758nr = 1878Ud =3.040Sδ =0.07γM =1.053

n = 2639nr = 20Ud =3.040Sδ =0.06γM =1.021

n = 2717nr = 20Ud =3.040Sδ =0.05γM =0.991

n = 98nr = 20Ud =3.040Sδ =0.03γM =0.982

n = 95nr = 20Ud =3.040Sδ =0.03γM =0.973

n = 3755nr = 20Ud =3.040Sδ =0.07γM =1.025

n = 3758nr = 20Ud =3.040Sδ =0.08γM =1.010

n = 98nr = 20Ud =3.040Sδ =0.03γM =0.994

n = 95nr = 20Ud =3.040Sδ =0.03γM =0.990

n = 3755nr = 20Ud =3.040Sδ =0.09γM =1.061

n = 3758nr = 20Ud =3.040Sδ =0.09γM =1.052

Data set 2: All steel producer, each type of profile

Table : γM -values

1-5 Npl Mel.y Mpl.y Mel.z Mpl.zProfil EC 3 EN EC 3 EN EC 3 EN EC 3 EN EC 3 EN

HEA n = 820nr = 410Ud =3.040Sδ =0.06γM =1.022

n = 820nr = 410Ud =3.040Sδ =0.06γM =1.004

n = 72nr = 36Ud =3.040Sδ =0.03γM =0.991

n = 69nr = 34Ud =3.040Sδ =0.03γM =0.987

n = 812nr = 406Ud =3.040Sδ =0.06γM =1.024

n = 815nr = 408Ud =3.040Sδ =0.06γM =0.998

n = 72nr = 36Ud =3.040Sδ =0.04γM =1.001

n = 69nr = 34Ud =3.040Sδ =0.04γM =1.005

n = 812nr = 806Ud =3.040Sδ =0.07γM =1.046

n = 815nr = 408Ud =3.040Sδ =0.07γM =1.020

n = 820nr = 20Ud =3.040Sδ =0.05γM =1.005

n = 820nr = 20Ud =3.040Sδ =0.05γM =0.983

n = 72nr = 20Ud =3.040Sδ =0.03γM =0.984

n = 69nr = 20Ud =3.040Sδ =0.03γM =0.976

n = 812nr = 20Ud =3.040Sδ =0.05γM =1.009

n = 815nr = 20Ud =3.040Sδ =0.05γM =0.984

n = 72nr = 20Ud =3.040Sδ =0.03γM =0.993

n = 69nr = 20Ud =3.040Sδ =0.03γM =0.991

n = 812nr = 20Ud =3.040Sδ =0.05γM =1.023

n = 815nr = 20Ud =3.040Sδ =0.04γM =0.995

HEB n = 781nr = 390Ud =3.040Sδ =0.05γM =1.042

n = 794nr = 397Ud =3.040Sδ =0.05γM =1.011

n = 822nr = 411Ud =3.040Sδ =0.05γM =1.046

n = 822nr = 411Ud =3.040Sδ =0.05γM =1.016

n = 822nr = 411Ud =3.040Sδ =0.06γM =1.076

n = 822nr = 411Ud =3.040Sδ =0.06γM =1.048

1-5 Npl Mel.y Mpl.y Mel.z Mpl.z

Profil EC 3 EN EC 3 EN EC 3 EN EC 3 EN EC 3 ENn = 781nr = 285Ud =3.040Sδ =0.05γM =1.040

n = 794nr = 290Ud =3.040Sδ =0.05γM =1.009

n = 822nr = 300Ud =3.040Sδ =0.05γM =1.044

n = 822nr = 300Ud =3.040Sδ =0.05γM =1.015

n = 822nr = 300Ud =3.040Sδ =0.06γM =1.076

n = 822nr = 300Ud =3.040Sδ =0.06γM =1.050

n = 781nr = 143Ud =3.040Sδ =0.05γM =1.039

n = 794nr = 145Ud =3.040Sδ =0.05γM =1.006

n = 822nr = 150Ud =3.040Sδ =0.05γM =1.041

n = 822nr = 150Ud =3.040Sδ =0.05γM =1.013

n = 822nr = 150Ud =3.040Sδ =0.06γM =1.076

n = 822nr = 150Ud =3.040Sδ =0.06γM =1.051

n = 781nr = 20Ud =3.040Sδ =0.06γM =1.039

n = 794nr = 20Ud =3.040Sδ =0.05γM =1.007

n = 822nr = 20Ud =3.040Sδ =0.06γM =1.042

n = 822nr = 20Ud =3.040Sδ =0.05γM =1.014

n = 822nr = 20Ud =3.040Sδ =0.07γM =1.085

n = 822nr = 20Ud =3.040Sδ =0.07γM =1.056

HEM n = 215nr = 108Ud =3.040Sδ =0.06γM =1.070

n = 215nr = 108Ud =3.040Sδ =0.06γM =1.024

n = 216nr = 108Ud =3.040Sδ =0.06γM =1.069

n = 216nr = 108Ud =3.040Sδ =0.06γM =1.023

n = 216nr = 108Ud =3.040Sδ =0.06γM =1.066

n = 216nr = 108Ud =3.040Sδ =0.05γM =1.021

n = 215nr = 20Ud =3.040Sδ =0.03γM =1.032

n = 215nr = 20Ud =3.040Sδ =0.03γM =0.989

n = 216nr = 20Ud =3.040Sδ =0.03γM =1.026

n = 216nr = 20Ud =3.040Sδ =0.03γM =0.983

n = 216nr = 20Ud =3.040Sδ =0.05γM =1.051

n = 216nr = 20Ud =3.040Sδ =0.05γM =1.010

1-5 Npl Mel.y Mpl.y Mel.z Mpl.zProfil EC 3 EN EC 3 EN EC 3 EN EC 3 EN EC 3 ENHP n = 46

nr = 23Ud =3.040Sδ =0.03γM =1.005

n = 46nr = 23Ud =3.040Sδ =0.03γM =0.961

n = 46nr = 23Ud =3.040Sδ =0.04γM =1.005

n = 46nr = 23Ud =3.040Sδ =0.04γM =0.961

n = 46nr = 23Ud =3.040Sδ =0.04γM =1.032

n = 46nr = 23Ud =3.040Sδ =0.04γM =0.987

n = 46nr = 20Ud =3.040Sδ =0.03γM =1.002

n = 46nr = 20Ud =3.040Sδ =0.03γM =0.959

n = 46nr = 20Ud =3.040Sδ =0.03γM =1.003

n = 46nr = 20Ud =3.040Sδ =0.03γM =0.959

n = 46nr = 20Ud =3.040Sδ =0.04γM =1.027

n = 46nr = 20Ud =3.040Sδ =0.04γM =0.983

IPEn = 449nr = 224Ud =3.040Sδ =0.06γM =1.018

n = 514nr = 257Ud =3.040Sδ =0.06γM =1.022

n = 673nr = 336Ud =3.040Sδ =0.05γM =1.024

n = 673nr = 336Ud =3.040Sδ =0.06γM =1.026

n = 673nr = 336Ud =3.040Sδ =0.06γM =1.069

n = 673nr = 366Ud =3.040Sδ =0.07γM =1.072

n = 449nr = 20Ud =3.040Sδ =0.03γM =0.981

n = 514nr = 20Ud =3.040Sδ =0.03γM =0.980

n = 673nr = 20Ud =3.040Sδ =0.03γM =0.991

n = 673nr = 20Ud =3.040Sδ =0.03γM =0.989

n = 673nr = 20Ud =3.040Sδ =0.07γM =1.060

n = 673nr = 20Ud =3.040Sδ =0.07γM =1.060

UBP n = 37nr = 20Ud =3.040Sδ =0.01γM =0.955

n = 37nr = 20Ud =3.400Sδ =0.02γM =0.940

n = 7nr = 7Ud =7.715Sδ =0.03γM =1.105

n = 7nr = 7Ud =7.715Sδ =0.03γM =1.105

n = 30nr = 20Ud =3.440Sδ =0.01γM =0.951

n = 30nr = 20Ud =3.440Sδ =0.01γM =0.910

n = 7nr = 7Ud =7.715Sδ =0.03γM =1.143

n = 7nr = 7Ud =7.715Sδ =0.03γM =1.143

n = 30nr = 20Ud =3.440Sδ =0.01γM =0.946

n = 30nr = 20Ud =3.440Sδ =0.01γM =0.905

1-5 Npl Mel.y Mpl.y Mel.z Mpl.z

Profil EC 3 EN EC 3 EN EC 3 EN EC 3 EN EC 3 ENUB n = 180

nr = 90Ud =3.040Sδ =0.05γM =1.023

n = 180nr = 90Ud =3.040Sδ =0.04γM =1.008

n = 1046nr = 523Ud =3.040Sδ =0.06γM =1.032

n = 1046nr = 523Ud =3.040Sδ =0.06γM =1.026

n = 1046nr = 523Ud =3.040Sδ =0.07γM =1.065

n = 1046nr = 523Ud =3.040Sδ =0.07γM =1.063

n = 180nr = 77Ud =3.040Sδ =0.05γM =1.024

n = 180nr = 77Ud =3.040Sδ =0.05γM =1.009

n = 1046nr = 450Ud =3.040Sδ =0.08γM =1.030

n = 1046nr = 450Ud =3.040Sδ =0.08γM =1.024

n = 1046nr = 450Ud =3.040Sδ =0.09γM =1.064

n = 1046nr = 450Ud =3.040Sδ =0.09γM =1.062

n = 180nr = 52Ud =3.040Sδ =0.04γM =1.019

n = 180nr = 52Ud =3.040Sδ =0.04γM =1.004

n = 1046nr = 300Ud =3.040Sδ =0.06γM =1.027

n = 1046nr = 300Ud =3.040Sδ =0.06γM =1.023

n = 1046nr = 300Ud =3.040Sδ =0.06γM =1.063

n = 1046nr = 300Ud =3.040Sδ =0.07γM =1.064

n = 180nr = 26Ud =3.040Sδ =0.04γM =1.004

n = 180nr = 26Ud =3.040Sδ =0.04γM =0.998

n = 1046nr = 150Ud =3.040Sδ =0.05γM =1.025

n = 1046nr = 150Ud =3.040Sδ =0.06γM =1.023

n = 1046nr = 150Ud =3.040Sδ =0.07γM =1.065

n = 1046nr = 150Ud =3.040Sδ =0.07γM =1.066

n = 180nr = 20Ud =3.040Sδ =0.03γM =1.003

n = 180nr = 20Ud =3.040Sδ =0.03γM =0.994

n = 1046nr = 20Ud =3.040Sδ =0.08γM =1.040

n = 1046nr = 20Ud =3.040Sδ =0.08γM =1.038

n = 1046nr = 20Ud =3.040Sδ =0.09γM =1.080

n = 1046nr = 20Ud =3.040Sδ =0.09γM =1.080

1-5 Npl Mel.y Mpl.y Mel.z Mpl.zProfil EC 3 EN EC 3 EN EC 3 EN EC 3 EN EC 3 ENUC n = 95

nr = 48Ud =3.069Sδ =0.06γM =1.072

n = 95nr = 48Ud =3.069Sδ =0.04γM =1.000

n = 8nr = 8Ud =5.070Sδ =0.04γM =1.080

n = 8nr = 8Ud =5.070Sδ =0.04γM =1.080

n = 87nr = 44Ud =3.114Sδ =0.05γM =1.050

n = 87nr = 44Ud =3.114Sδ =0.03γM =0.986

n = 8nr = 8Ud =5.070Sδ =0.04γM =1.088

n = 8nr = 8Ud =5.070Sδ =0.04γM =1.088

n = 87nr = 44Ud =3.114Sδ =0.07γM =1.129

n = 87nr = 44Ud =3.114Sδ =0.05γM =1.043

n = 95nr = 20Ud =3.069Sδ =0.04γM =1.041

n = 95nr = 20Ud =3.069Sδ =0.03γM =0.983

n = 8nr = 8Ud =3.114Sδ =0.04γM =1.080

n = 8nr = 8Ud =5.070Sδ =0.04γM =1.080

n = 87nr = 20Ud =5.070Sδ =0.04γM =1.030

n = 87nr = 20Ud =3.114Sδ =0.03γM =0.974

n = 8nr = 8Ud =5.070Sδ =0.04γM =1.088

n = 8nr = 8 Ud =5.070Sδ =0.04γM =1.088

n = 87nr = 20Ud =3.114Sδ =0.04γM =1.077

n = 87nr = 20Ud =3.114Sδ =0.04γM =1.033

n = 95nr = 20Ud =3.040Sδ =0.04γM =1.039

n = 95nr = 20Ud =3.040Sδ =0.03γM =0.982

n = 8nr = 8Ud =3.040Sδ =0.04γM =1.002

n = 8nr = 8Ud =3.040Sδ =0.04γM =1.002

n = 87nr = 20Ud =3.040Sδ =0.04γM =1.027

n = 87nr = 20Ud =3.040Sδ =0.03γM =0.973

n = 8nr = 8Ud =3.040Sδ =0.04γM =1.005

n = 8nr = 8 Ud =3.040Sδ =0.04γM =1.005

n = 87nr = 20Ud =3.040Sδ =0.04γM =1.074

n = 87nr = 20Ud =3.040Sδ =0.04γM =1.030

Data set 3: Each steel producer, all types of profiles

Table : γM -values

1 Npl Mel.y Mpl.y Mel.z Mpl.zProfil EC 3 EN EC 3 EN EC 3 EN EC 3 EN EC 3 EN

all n = 838

nr = 419

Ud =3.040

Sδ =0.07

γM =1.049

n = 868

nr = 434

Ud =3.040

Sδ =0.06

γM =1.009

n = 40

nr = 20

Ud =3.383

Sδ =0.02

γM =0.977

n = 40

nr = 20

Ud =3.383

Sδ =0.03

γM =0.988

n = 910

nr = 455

Ud =3.040

Sδ =0.07

γM =1.049

n = 910

nr = 455

Ud =3.040

Sδ =0.06

γM =1.008

n = 40

nr = 20

Ud =3.383

Sδ =0.02

γM =0.986

n = 40

nr = 20

Ud =3.383

Sδ =0.03

γM =0.989

n = 910

nr = 455

Ud =3.040

Sδ =0.07

γM =1.043

n = 910

nr = 455

Ud =3.040

Sδ =0.06

γM =1.008

n = 838nr = 20Ud =3.040Sδ =0.03γM =1.011

n = 868nr = 20Ud =3.040Sδ =0.02γM =0.966

n = 40nr = 20Ud =3.383Sδ =0.02γM =0.977

n = 40nr = 20Ud =3.383Sδ =0.03γM =0.988

n = 910nr = 20Ud =3.040Sδ =0.03γM =1.009

n = 910nr = 20Ud =3.040Sδ =0.02γM =0.964

n = 40nr = 20Ud =3.383Sδ =0.02γM =0.986

n = 40nr = 20Ud =3.383Sδ =0.03γM =0.989

n = 910nr = 20Ud =3.040Sδ =0.04γM =1.012

n = 910nr = 20Ud =3.040Sδ =0.03γM =0.969

2 Npl Mel.y Mpl.y Mel.z Mpl.zProfil EC 3 EN EC 3 EN EC 3 EN EC 3 EN EC 3 ENAll n = 957

nr = 478Ud =3.040Sδ =0.06γM =1.032

n = 1005nr = 502Ud =3.040Sδ =0.05γM =0.995

n = 32nr = 20Ud =3.429Sδ =0.05γM =1.028

n = 30nr = 20Ud =3.440Sδ =0.06γM =1.044

n = 1096nr = 548Ud =3.040Sδ =0.05γM =1.032

n = 1098nr = 549Ud =3.040Sδ =0.05γM =0.997

n = 32nr = 20Ud =3.429Sδ =0.05γM =1.035

n = 30nr = 20Ud =3.440Sδ =0.06γM =1.047

n = 1096nr = 548Ud =3.040Sδ =0.06γM =1.047

n = 1098nr = 549Ud =3.040Sδ =0.06γM =1.011

n = 957nr = 20Ud =3.040Sδ =0.04γM =1.015

n = 1005nr = 20Ud =3.040Sδ =0.04γM =0.977

n = 32nr = 20Ud =3.429Sδ =0.05γM =1.028

n = 30nr = 20Ud =3.440Sδ =0.06γM =1.044

n = 1096nr = 20Ud =3.040Sδ =0.04γM =1.016

n = 1098nr = 20Ud =3.040Sδ =0.04γM =0.987

n = 32nr = 20Ud =3.429Sδ =0.05γM =1.035

n = 30nr = 20Ud =3.440Sδ =0.06γM =1.047

n = 1096nr = 20Ud =3.040Sδ =0.05γM =1.036

n = 1098nr = 20Ud =3.040Sδ =0.05γM =1.000


nr = 32Ud =3.246Sδ =0.07γM =1.093

n = 64nr = 32Ud =3.246Sδ =0.06γM =1.054

n = 6nr = 6Ud =6.360Sδ =0.04γM =1.207

n = 5nr = 5Ud =7.850Sδ =0.04γM =1.269

n = 58nr = 29Ud =3.280Sδ =0.09γM =1.107

n = 59nr = 30Ud =3.274Sδ =0.07γM =1.064

n = 6nr = 6Ud =6.360Sδ =0.04γM =1.181

n = 5nr = 5Ud =7.850Sδ =0.04γM =1.264

n = 58nr = 29Ud =3.280Sδ =0.09γM =1.150

n = 59nr = 30Ud =3.274Sδ =0.07γM =1.099

n = 64nr = 20Ud =3.246Sδ =0.06γM =1.073

n = 64nr = 20Ud =3.246Sδ =0.05γM =1.039

n = 6nr = 6Ud =6.360Sδ =0.04γM =1.207

n = 5nr = 5Ud =7.850Sδ =0.04γM =1.269

n = 58nr = 20Ud =3.280Sδ =0.07γM =1.098

n = 59nr = 20Ud =3.274Sδ =0.07γM =1.067

n = 6nr = 6Ud =6.360Sδ =0.04γM =1.181

n = 5nr = 5Ud =7.850Sδ =0.04γM =1.264

n = 58nr = 20Ud =3.280Sδ =0.08γM =1.139

n = 59nr = 20Ud =3.274Sδ =0.07γM =1.100


nr = 224Ud =3.040Sδ =0.05γM =1.031

n = 447nr = 224Ud =3.040Sδ =0.04γM =1.009

n = 14nr = 14Ud =4.162Sδ =0.03γM =0.999

n = 14nr = 14Ud =4.162Sδ =0.03γM =0.999

n = 1335nr = 668Ud =3.040Sδ =0.06γM =1.030

n = 1335nr = 668Ud =3.040Sδ =0.05γM =1.021

n = 14nr = 14Ud =4.162Sδ =0.03γM =1.009

n = 14nr = 14Ud =4.162Sδ =0.03γM =1.009

n = 1335nr = 668Ud =3.040Sδ =0.06γM =1.067

n = 1335nr = 668Ud =3.040Sδ =0.06γM =1.058

n = 447

nr = 20Ud =3.040Sδ =0.03γM =1.005

n = 447nr = 20Ud =3.040Sδ =0.03γM =0.994

n = 14nr = 14Ud =4.162Sδ =0.03γM =0.999

n = 14nr = 14Ud =4.162Sδ =0.03γM =0.999

n = 1335nr = 20Ud =3.040Sδ =0.07γM =1.034

n = 1335nr = 20Ud =3.040Sδ =0.08γM =1.032

n = 14nr = 14Ud =4.162Sδ =0.03γM =1.009

n = 14nr = 14Ud =4.162Sδ =0.03γM =1.009

n = 1335nr = 20Ud =3.040Sδ =0.08γM =1.074

n = 1335nr = 20Ud =3.040Sδ =0.09γM =1.073


nr = 166Ud =3.040Sδ =0.05γM =1.042

n = 333nr = 166Ud =3.040Sδ =0.05γM =1.019

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.186

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.186

n = 356nr = 178Ud =3.040Sδ =0.05γM =1.047

n = 356nr = 178Ud =3.040Sδ =0.05γM =1.027

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.208

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.208

n = 356nr = 178Ud =3.040Sδ =0.06γM =1.096

n = 356nr = 178Ud =3.040Sδ =0.05γM =1.079

n = 333nr = 112Ud =3.040Sδ =0.05γM =1.042

n = 333nr = 112Ud =3.040Sδ =0.05γM =1.016

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.186

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.186

n = 356nr = 120Ud =3.040Sδ =0.05γM =1.048

n = 356nr = 120Ud =3.040Sδ =0.04γM =1.024

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.208

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.208

n = 356nr = 120Ud =3.040Sδ =0.06γM =1.094

n = 356nr = 120Ud =3.040Sδ =0.05γM =1.075

n = 333nr = 65Ud =3.040Sδ =0.06γM =1.049

n = 333nr = 65Ud =3.040Sδ =0.05γM =1.015

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.186

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.186

n = 356nr = 70Ud =3.040Sδ =0.05γM =1.048

n = 356nr = 70Ud =3.040Sδ =0.04γM =1.024

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.208

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.208

n = 356nr = 70Ud =3.040Sδ =0.06γM =1.096

n = 356nr = 70Ud =3.040Sδ =0.05γM =1.077

n = 333nr = 20Ud =3.040Sδ =0.06γM =1.053

n = 333nr = 20Ud =3.040Sδ =0.06γM =1.027

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.186

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.186

n = 356nr = 20Ud =3.040Sδ =0.06γM =1.056

n = 356nr = 20Ud =3.040Sδ =0.05γM =1.026

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.208

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.208

n = 356nr = 20Ud =3.040Sδ =0.06γM =1.104

n = 356nr = 20Ud =3.040Sδ =0.06γM =1.085

Data set 4: Each steel producer, each type of profile

Data set 4.1: Steel producer 1

Table : γM -values (S235)1 Npl Mel.y Mpl.y Mel.z Mpl.zProfil EC 3 EN EC 3 EN EC 3 EN EC 3 EN EC 3 EN

HEA100

n = 30nr = 20Ud =3.440Sδ =0.10γM =1.022

n = 30nr = 20Ud =3.440Sδ =0.10γM =1.022

n = 30nr = 20Ud =3.440Sδ =0.10γM =1.033

n = 30nr = 20Ud =3.440Sδ =0.10γM =1.033

n = 30nr = 20Ud =3.440Sδ =0.09γM =0.998

n = 30nr = 20Ud =3.440Sδ =0.09γM =0.998

HEA200

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.879

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.879

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.886

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.886

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.892

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.892

HEA240

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.998

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.998

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.008

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.008

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.009

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.009


HEA450

n = 30nr = 20Ud =3.440Sδ =0.06γM =0.948

n = 30nr = 20Ud =3.440Sδ =0.06γM =0.907

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.949

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.909

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.966

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.925

HEA600

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.921

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.882

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.924

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.885

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.941

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.901

HEB120

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.953

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.953

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.964

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.964

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.959

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.959

HEB180

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.962

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.962

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.976

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.976

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.946

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.946

1 Npl Mel.y Mpl.y Mel.z Mpl.z

Profil EC 3 EN EC 3 EN EC 3 EN EC 3 EN EC 3 EN

HEB240

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.041

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.996

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.040

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.995

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.038

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.994

HEB500

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.986

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.944

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.990

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.948

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.996

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.954

HEB700

n = 30nr = 20Ud =3.440Sδ =0.07γM =1.070

n = 30nr = 20Ud =3.440Sδ =0.07γM =1.024

n = 30nr = 20Ud =3.440Sδ =0.08γM =1.075

n = 30nr = 20Ud =3.440Sδ =0.08γM =1.029

n = 30nr = 20Ud =3.440Sδ =0.07γM =1.079

n = 30nr = 20Ud =3.440Sδ =0.07γM =1.033

HEM180

n = 30nr = 20Ud =3.440Sδ =0.07γM =1.160

n = 30nr = 20Ud =3.440Sδ =0.07γM =1.111

n = 30nr = 20Ud =3.440Sδ =0.07γM =1.163

n = 30nr = 20Ud =3.440Sδ =0.07γM =1.113

n = 30nr = 20Ud =3.440Sδ =0.07γM =1.150

n = 30nr = 20Ud =3.440Sδ =0.07γM =1.101


HEM240

n = 28nr = 20Ud =3.440Sδ =0.04γM =1.095

n = 28nr = 20Ud =3.440Sδ =0.04γM =1.049

n = 28nr = 20Ud =3.440Sδ =0.04γM =1.094

n = 28nr = 20Ud =3.440Sδ =0.04γM =1.048

n = 28nr = 20Ud =3.440Sδ =0.04γM =1.080

n = 28nr = 20Ud =3.440Sδ =0.04γM =1.034

HEM300

n = 30nr = 20Ud =3.440Sδ =0.10γM =1.190

n = 30nr = 20Ud =3.440Sδ =0.10γM =1.140

n = 30nr = 20Ud =3.440Sδ =0.10γM =1.200

n = 30nr = 20Ud =3.440Sδ =0.10γM =1.149

n = 30nr = 20Ud =3.440Sδ =0.12γM =1.271

n = 30nr = 20Ud =3.440Sδ =0.12γM =1.217

HEM550

n = 30nr = 20Ud =3.440Sδ =0.06γM =1.098

n = 30nr = 20Ud =3.440Sδ =0.06γM =1.052

n = 30nr = 20Ud =3.440Sδ =0.06γM =1.103

n = 30nr = 20Ud =3.440Sδ =0.06γM =1.056

n = 30nr = 20Ud =3.440Sδ =0.06γM =1.104

n = 30nr = 20Ud =3.440Sδ =0.06γM =1.057

HEM600

n = 30nr = 20Ud =3.440Sδ =0.09γM =1.141

n = 30nr = 20Ud =3.440Sδ =0.09γM =1.092

n = 30nr = 20Ud =3.440Sδ =0.09γM =1.139

n = 30nr = 20Ud =3.440Sδ =0.09γM =1.090

n = 30nr = 20Ud =3.440Sδ =0.08γM =1.137

n = 30nr = 20Ud =3.440Sδ =0.08γM =1.089



IPE 180 n = 30nr = 20Ud =3.440Sδ =0.03γM =0.860

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.860

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.879

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.879

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.893

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.893

IPE 220 n = 30nr = 20Ud =3.440Sδ =0.06γM =0.959

n = 30nr = 20Ud =3.440Sδ =0.06γM =0.959

n = 30nr = 20Ud =3.440Sδ =0.06γM =0.966

n = 30nr = 20Ud =3.440Sδ =0.06γM =0.966

n = 30nr = 20Ud =3.440Sδ =0.06γM =0.994

n = 30nr = 20Ud =3.440Sδ =0.06γM =0.994

IPE 300 n = 30nr = 20Ud =3.440Sδ =0.03γM =0.909

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.909

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.925

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.925

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.948

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.948

IPE 450 n = 30nr = 20Ud =3.440Sδ =0.05γM =0.978

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.978

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.994

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.994

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.030

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.030


IPE 500 n = 30nr = 20Ud =3.440Sδ =0.05γM =0.870

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.870

n = 30nr = 20Ud =3.440Sδ =0.06γM =0.886

n = 30nr = 20Ud =3.440Sδ =0.06γM =0.886

n = 30nr = 20Ud =3.440Sδ =0.06γM =0.897

n = 30nr = 20Ud =3.440Sδ =0.06γM =0.897

IPE 600 n = 30nr = 20Ud =3.440Sδ =0.04γM =0.861

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.902

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.864

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.909

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.870

HEA240

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.989

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.989

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.990

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.990

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.994

n = 30nr = 20Ud =3.440Sδ =0.03γM =0.994

HEA600

n = 30nr = 20Sδ =0.03γM =0.942

n = 30nr = 20Sδ =0.03γM =0.915

n = 30nr = 20Sδ =0.03γM =0.952

n = 30nr = 20Sδ =0.03γM =0.926

HEB300

n = 30nr = 20Ud =3.440Sδ =0.04γM =1.042

n = 30nr = 20Ud =3.440Sδ =0.04γM =1.013

n = 30nr = 20Ud =3.440Sδ =0.04γM =1.040

n = 30nr = 20Ud =3.440Sδ =0.04γM =1.010

n = 30nr = 20Ud =3.440Sδ =0.04γM =1.046

n = 30nr = 20Ud =3.440Sδ =0.04γM =1.016



HEB450

n = 30nr = 20Ud =3.440Sδ =0.04γM =1.014

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.986

n = 30nr = 20Ud =3.440Sδ =0.04γM =1.021

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.992

n = 30nr = 20Ud =3.440Sδ =0.04γM =1.031

n = 30nr = 20Ud =3.440Sδ =0.04γM =1.002

HEM280

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.081

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.050

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.081

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.051

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.082

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.052

HEM800

n = 30nr = 20Ud =3.440Sδ =0.04γM =1.022

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.994

n = 30nr = 20Ud =3.440Sδ =0.04γM =1.028

n = 30nr = 20Ud =3.440Sδ =0.04γM =0.999

n = 30nr = 20Ud =3.440Sδ =0.04γM =1.036

n = 30nr = 20Ud =3.440Sδ =0.04γM =1.007

IPE 270 n = 30nr = 20Ud =3.440Sδ =0.04γM =1.005

n = 30nr = 20Ud =3.440Sδ =0.04γM =1.005

n = 30nr = 20Ud =3.440Sδ =0.03γM =1.005

n = 30nr = 20Ud =3.440Sδ =0.03γM =1.005

n = 30nr = 20Ud =3.440Sδ =0.03γM =1.005

n = 30nr = 20Ud =3.440Sδ =0.03γM =1.005


IPE 500 n = 30nr = 20Ud =3.440Sδ =0.05γM =0.992

n = 30nr = 20Ud =3.440Sδ =0.05γM =0.992

n = 30nr = 20Ud =3.440Sδ =0.06γM =1.012

n = 30nr = 20Ud =3.440Sδ =0.06γM =1.012

UBP305x305x180

n = 30nr = 20Ud =3.440Sδ =0.01γM =0.955

n = 30nr = 20Ud =3.440Sδ =0.01γM =0.913

n = 30nr = 20Ud =3.440Sδ =0.01γM =0.951

n = 30nr = 20Ud =3.440Sδ =0.01γM =0.910

n = 30nr = 20Ud =3.440Sδ =0.01γM =0.946

n = 30nr = 20Ud =3.440Sδ =0.01γM =0.905


Table : γM -values2 Npl Mel.y Mpl.y Mel.z Mpl.zProfil EC 3 EN EC 3 EN EC 3 EN EC 3 EN EC 3 EN

HEA n = 500nr = 250Ud =3.040Sδ =0.06γM =1.024

n = 500nr = 250Ud =3.040Sδ =0.06γM =0.988

n = 31nr = 20Ud =3.434Sδ =0.05γM =1.029

n = 29nr = 20Ud =3.460Sδ =0.06γM =1.044

n = 503nr = 252Ud =3.040Sδ =0.06γM =1.028

n = 505nr = 252Ud =3.040Sδ =0.06γM =0.991

n = 31nr = 20Ud =3.434Sδ =0.05γM =1.043

n = 29nr = 20Ud =3.460Sδ =0.06γM =1.049

n = 503nr = 252Ud =3.040Sδ =0.06γM =1.049

n = 505nr = 252Ud =3.040Sδ =0.06γM =1.008

n = 500nr = 20Ud =3.040Sδ =0.05γM =1.011

n = 500nr = 20Ud =3.040Sδ =0.05γM =0.986

n = 31nr = 20Ud =3.434Sδ =0.05γM =1.029

n = 29nr = 20Ud =3.460Sδ =0.06γM =1.044

n = 503nr = 20Ud =3.040Sδ =0.05γM =1.014

n = 505nr = 20Ud =3.040Sδ =0.05γM =0.983

n = 31nr = 20Ud =3.434Sδ =0.05γM =1.043

n = 29nr = 20Ud =3.460Sδ =0.06γM =1.049

n = 503nr = 20Ud =3.040Sδ =0.05γM =1.038

n = 505nr = 20Ud =3.040Sδ =0.05γM =0.997

HEB n = 374nr = 187Ud =3.040Sδ =0.05γM =1.039

n = 378nr = 194Ud =3.040Sδ =0.05γM =0.999

n = 415nr = 208Ud =3.040Sδ =0.05γM =1.040

n = 415nr = 208Ud =3.040Sδ =0.05γM =1.002

n = 415nr = 208Ud =3.040Sδ =0.05γM =1.055

n = 415nr = 208Ud =3.040Sδ =0.05γM =1.017

n = 374nr = 20Ud =3.040Sδ =0.04γM =1.028

n = 378nr = 20Ud =3.040Sδ =0.04γM =0.992

n = 415nr = 20Ud =3.040Sδ =0.04γM =1.033

n = 415nr = 20Ud =3.040Sδ =0.05γM =1.005

n = 415nr = 20Ud =3.040Sδ =0.05γM =1.053

n = 415nr = 20Ud =3.040Sδ =0.06γM =1.020


HP n = 46nr = 23Ud =3.349Sδ =0.03γM =1.015

n = 46nr = 23Ud =3.349Sδ =0.03γM =0.971

n = 46nr = 23Ud =3.349Sδ =0.04γM =1.016

n = 46nr = 23Ud =3.349Sδ =0.04γM =0.972

n = 46nr = 23Ud =3.349Sδ =0.04γM =1.045

n = 46nr = 23Ud =3.349Sδ =0.04γM =1.000

n = 46nr = 20Ud =3.349Sδ =0.03γM =1.012

n = 46nr = 20Ud =3.349Sδ =0.03γM =0.968

n = 46nr = 20Ud =3.349Sδ =0.03γM =1.014

n = 46nr = 20Ud =3.349Sδ =0.03γM =0.969

n = 46nr = 20Ud =3.349Sδ =0.04γM =1.040

n = 46nr = 20Ud =3.349Sδ =0.04γM =0.995

IPEn = 18nr = 18Ud =3.814Sδ =0.08γM =1.130

n = 53nr = 26Ud =3.309Sδ =0.04γM =0.939

n = 109nr = 54Ud =3.040Sδ =0.05γM =1.007

n = 109nr = 54Ud =3.040Sδ =0.05γM =1.003

n = 109nr = 54Ud =3.040Sδ =0.05γM =1.012

n = 109nr = 54Ud =3.040Sδ =0.05γM =1.002

n = 18nr = 18Ud =3.814Sδ =0.08γM =1.130

n = 53nr = 20Ud =3.309Sδ =0.04γM =0.937

n = 109nr = 20Ud =3.040Sδ =0.05γM =1.016

n = 109nr = 20Ud =3.040Sδ =0.05γM =0.999

n = 109nr = 20Ud =3.040Sδ =0.05γM =1.020

n = 109nr = 20Ud =3.040Sδ =0.05γM =1.003

HEA(S235)

n = 456nr = 228Ud =3.040Sδ =0.06γM =1.027

n = 456nr = 228Ud =3.040Sδ =0.06γM =0.987

n = 458nr = 229Ud =3.040Sδ =0.06γM =1.029

n = 458nr = 229Ud =3.040Sδ =0.06γM =0.990

n = 458nr = 229Ud =3.040Sδ =0.07γM =1.049

n = 458nr = 229Ud =3.040Sδ =0.06γM =1.007



n = 456nr = 20Ud =3.040Sδ =0.06γM =0.989

n = 458nr = 20Ud =3.040Sδ =0.05γM =1.018

n = 458nr = 20Ud =3.040Sδ =0.06γM =0.989

n = 458nr = 20Ud =3.040Sδ =0.06γM =1.036

n = 458nr = 20Ud =3.040Sδ =0.05γM =0.995

HEA240(S235)

n = 130nr = 65Ud =3.040Sδ =0.08γM =1.026

n = 130nr = 65Ud =3.040Sδ =0.08γM =1.026

n = 130nr = 65Ud =3.040Sδ =0.08γM =1.026

n = 130nr = 65Ud =3.040Sδ =0.08γM =1.026

n = 130nr = 65Ud =3.040Sδ =0.08γM =1.040

n = 130nr = 65Ud =3.040Sδ =0.08γM =1.040

n = 130nr = 45Ud =3.040Sδ =0.08γM =1.032

n = 130nr = 45Ud =3.040Sδ =0.08γM =1.032

n = 130nr = 45Ud =3.040Sδ =0.08γM =1.033

n = 130nr = 45Ud =3.040Sδ =0.08γM =1.033

n = 130nr = 45Ud =3.040Sδ =0.08γM =1.044

n = 130nr = 45Ud =3.040Sδ =0.08γM =1.044

n = 130nr = 20Ud =3.040Sδ =0.08γM =1.036

n = 130nr = 20Ud =3.040Sδ =0.08γM =1.036

n = 130nr = 20Ud =3.040Sδ =0.08γM =1.037

n = 130nr = 20Ud =3.040Sδ =0.08γM =1.037

n = 130nr = 20Ud =3.040Sδ =0.07γM =1.033

n = 130nr = 20Ud =3.040Sδ =0.07γM =1.033

HEA360(S235)

n = 82nr = 41Ud =3.143Sδ =0.05γM =1.013

n = 82nr = 41Ud =3.143Sδ =0.05γM =0.970

n = 82nr = 41Ud =3.143Sδ =0.05γM =1.019

n = 82nr = 41Ud =3.143Sδ =0.05γM =0.975

n = 82nr = 41Ud =3.143Sδ =0.06γM =1.031

n = 82nr = 41Ud =3.143Sδ =0.06γM =0.987


n = 82nr = 20Ud =3.143Sδ =0.05γM =1.014

n = 82nr = 20Ud =3.143Sδ =0.05γM =0.971

n = 82nr = 20Ud =3.143Sδ =0.05γM =1.019

n = 82nr = 20Ud =3.143Sδ =0.05γM =0.975

n = 82nr = 20Ud =3.143Sδ =0.06γM =1.033

n = 82nr = 20Ud =3.143Sδ =0.06γM =0.989

HEA600(S235)

n = 102nr = 51Ud =3.040Sδ =0.05γM =1.025

n = 102nr = 51Ud =3.040Sδ =0.05γM =0.981

n = 102nr = 51Ud =3.040Sδ =0.05γM =1.030

n = 102nr = 51Ud =3.040Sδ =0.05γM =0.986

n = 102nr = 51Ud =3.040Sδ =0.05γM =1.045

n = 102nr = 51Ud =3.040Sδ =0.05γM =1.001

n = 102nr = 20Ud =3.040Sδ =0.05γM =1.034

n = 102nr = 20Ud =3.040Sδ =0.05γM =0.990

n = 102nr = 20Ud =3.040Sδ =0.05γM =1.037

n = 102nr = 20Ud =3.040Sδ =0.05γM =0.993

n = 102nr = 20Ud =3.040Sδ =0.05γM =1.041

n = 102nr = 20Ud =3.040Sδ =0.05γM =0.997

HEA(S355)

n = 39nr = 20Ud =3.389Sδ =0.06γM =1.051

n = 39nr = 20Ud =3.389Sδ =0.06γM =1.033

n = 28nr = 20Ud =3.480Sδ =0.06γM =1.053

n = 28nr = 20Ud =3.480Sδ =0.06γM =1.055

n = 40nr = 20Ud =3.383Sδ =0.06γM =1.071

n = 40nr = 20Ud =3.383Sδ =0.06γM =1.041

n = 28nr = 20Ud =3.480Sδ =0.06γM =1.063

n = 28nr = 20Ud =3.480Sδ =0.06γM =1.064

n = 40nr = 20Ud =3.383Sδ =0.06γM =1.095

n = 40nr = 20Ud =3.383Sδ =0.06γM =1.064

n = 39nr = 20Ud =3.040Sδ =0.06γM =1.030

n = 39nr = 20Ud =3.040Sδ =0.06γM =1.013

n = 28nr = 20Ud =3.040Sδ =0.06γM =1.026

n = 28nr = 20Ud =3.040Sδ =0.06γM =1.027

n = 40nr = 20Ud =3.040Sδ =0.06γM =1.051

n = 40nr = 20Ud =3.040Sδ =0.06γM =1.022

n = 28nr = 20Ud =3.040Sδ =0.06γM =1.035

n = 28nr = 20Ud =3.040Sδ =0.06γM =1.036

n = 40nr = 20Ud =3.040Sδ =0.06γM =1.072

n = 40nr = 20Ud =3.040Sδ =0.06γM =1.042



HEB(S235)

n =303nr = 152Ud =3.040Sδ =0.05γM =1.038

n = 303nr = 152Ud =3.040Sδ =0.05γM =0.991

n = 315nr = 158Ud =3.040Sδ =0.05γM =1.034

n = 315nr = 158Ud =3.040Sδ =0.05γM =0.987

n = 315nr = 158Ud =3.040Sδ =0.05γM =1.049

n = 315nr = 158Ud =3.040Sδ =0.05γM =1.004

n =303nr = 20Ud =3.040Sδ =0.05γM =1.032

n = 303nr = 20Ud =3.040Sδ =0.04γM =0.986

n = 315nr = 20Ud =3.040Sδ =0.04γM =1.026

n = 315nr = 20Ud =3.040Sδ =0.04γM =0.981

n = 315nr = 20Ud =3.040Sδ =0.05γM =1.044

n = 315nr = 20Ud =3.040Sδ =0.05γM =0.998

HEB300(S235)

n = 38nr = 20Ud =3.394Sδ =0.03γM =0.972

n = 38nr = 20Ud =3.394Sδ =0.03γM =0.930

n = 38nr = 20Ud =3.394Sδ =0.03γM =0.981

n = 38nr = 20Ud =3.394Sδ =0.03γM =0.939

n = 38nr = 20Ud =3.394Sδ =0.03γM =0.987

n = 38nr = 20Ud =3.394Sδ =0.03γM =0.945

HEB (S355)

n = 67nr = 34Ud =3.229Sδ =0.05γM =1.059

n = 80nr = 40Ud =3.154Sδ =0.04γM =1.020

n = 95nr = 48Ud =3.069Sδ =0.05γM =1.057

n = 95nr = 48Ud =3.069Sδ =0.04γM =1.025

n = 95nr = 48Ud =3.069Sδ =0.05γM =1.066

n = 95nr = 48Ud =3.069Sδ =0.05γM =1.036

n = 67nr = 34Ud =3.040Sδ =0.05γM =1.049

n = 80nr = 40Ud =3.040Sδ =0.04γM =1.015

n = 95nr = 48Ud =3.040Sδ =0.05γM =1.055

n = 95nr = 48Ud =3.040Sδ =0.04γM =1.023

n = 95nr = 48Ud =3.040Sδ =0.05γM =1.065

n = 95nr = 48Ud =3.040Sδ =0.05γM =1.034


n = 67nr = 20Ud =3.229Sδ =0.04γM =1.049

n = 80nr = 20Ud =3.154Sδ =0.04γM =1.012

n = 95nr = 20Ud =3.069Sδ =0.05γM =1.058

n = 95nr = 20Ud =3.069Sδ =0.05γM =1.027

n = 95nr = 20Ud =3.069Sδ =0.05γM =1.077

n = 95nr = 20Ud =3.069Sδ =0.05γM =1.045

n = 67nr = 20Ud =3.040Sδ =0.04γM =1.040

n = 80nr = 20Ud =3.040Sδ =0.04γM =1.007

n = 95nr = 20Ud =3.040Sδ =0.05γM =1.056

n = 95nr = 20Ud =3.040Sδ =0.05γM =1.026

n = 95nr = 20Ud =3.040Sδ =0.05γM =1.075

n = 95nr = 20Ud =3.040Sδ =0.05γM =1.043

IPE (S235)

n = 18nr = 18Ud =3.814Sδ =0.08γM =1.130

n = 53nr = 26Ud =3.309Sδ =0.04γM =0.939

n = 53nr = 26Ud =3.309Sδ =0.03γM =0.957

n = 53nr = 26Ud =3.309Sδ =0.03γM =0.932

n = 53nr = 26Ud =3.309Sδ =0.03γM =0.931

n = 53nr = 26Ud =3.309Sδ =0.04γM =0.945

n = 18nr = 18Ud =3.814Sδ =0.08γM =1.130

n = 53nr = 20Ud =3.309Sδ =0.04γM =0.937

n = 53nr = 20Ud =3.309Sδ =0.04γM =0.961

n = 53nr = 20Ud =3.309Sδ =0.03γM =0.928

n = 53nr = 20Ud =3.309Sδ =0.02γM =0.934

n = 53nr = 20Ud =3.309Sδ =0.04γM =0.949

IPE (S355)

n = 55nr = 28Ud =3.297Sδ =0.04γM =1.023

n = 55nr = 28Ud =3.297Sδ =0.04γM =1.005

n = 55nr = 28Ud =3.297Sδ =0.04γM =1.030

n = 55nr = 28Ud =3.297Sδ =0.04γM =1.019



n = 55nr = 20Ud =3.297Sδ =0.04γM =1.014

n = 55nr = 20Ud =3.297Sδ =0.05γM =1.039

n = 55nr = 20Ud =3.297Sδ =0.04γM =1.019

Data set 4.3: Steel producer 3Table : γM -values3 Npl Mel.y Mpl.y Mel.z Mpl.zProfil EC 3 EN EC 3 EN EC 3 EN EC 3 EN EC 3 EN

IPE n = 23nr = 20Ud =3.580Sδ =0.07γM =1.102

n = 23nr = 20Ud =3.580Sδ =0.07γM =1.102

n = 23nr = 20Ud =3.580Sδ =0.07γM =1.112

n = 23nr = 20Ud =3.580Sδ =0.07γM =1.112

n = 23nr = 20Ud =3.580Sδ =0.08γM =1.137

n = 23nr = 20Ud =3.580Sδ =0.08γM =1.137



HEA n = 54nr = 27Ud =3.303Sδ =0.04γM =1.031

n = 54nr = 27Ud =3.303Sδ =0.04γM =1.031

n = 54nr = 27Ud =3.303Sδ =0.05γM =1.045

n = 54nr = 27Ud =3.303Sδ =0.05γM =1.045

n = 54nr = 27Ud =3.303Sδ =0.05γM =1.048

n = 54nr = 27Ud =3.303Sδ =0.05γM =1.048

n = 54nr = 20Ud =3.303Sδ =0.05γM =1.037

n = 54nr = 20Ud =3.303Sδ =0.05γM =1.037

n = 54nr = 20Ud =3.303Sδ =0.05γM =1.052

n = 54nr = 20Ud =3.303Sδ =0.05γM =1.052

n = 54nr = 20Ud =3.303Sδ =0.05γM =1.056

n = 54nr = 20Ud =3.303Sδ =0.05γM =1.056

HEB n = 28nr = 20Ud =3.480Sδ =0.04γM =1.019

n = 28nr = 20Ud =3.480Sδ =0.04γM =1.019

n = 28nr = 20Ud =3.480Sδ =0.04γM =1.025

n = 28nr = 20Ud =3.480Sδ =0.04γM =1.025

n = 28nr = 20Ud =3.480Sδ =0.04γM =1.020

n = 28nr = 20Ud =3.480Sδ =0.04γM =1.020

IPE n = 84nr = 42Ud =3.131Sδ =0.05γM =1.039

n = 84nr = 42Ud =3.131Sδ =0.05γM =1.039

n = 122nr = 61Ud =3.040Sδ =0.04γM =1.018

n = 122nr = 61Ud =3.040Sδ =0.04γM =1.018

n = 122nr = 61Ud =3.040Sδ =0.05γM =1.051

n = 122nr = 61Ud =3.040Sδ =0.05γM =1.051


n = 84nr = 20Ud =3.131Sδ =0.03γM =1.003

n = 84nr = 20Ud =3.131Sδ =0.03γM =1.003

n = 122nr = 20Ud =3.040Sδ =0.03γM =0.988

n = 122nr = 20Ud =3.040Sδ =0.03γM =0.988

n = 122nr = 20Ud =3.040Sδ =0.03γM =1.021

n = 122nr = 20Ud =3.040Sδ =0.3γM =1.021

IPE 360 n = 30nr = 20Ud =3.440Sδ =0.02γM =1.013

n = 30nr = 20Ud =3.440Sδ =0.02γM =1.013

n = 30nr = 20Ud =3.440Sδ =0.02γM =1.008

n = 30nr = 20Ud =3.440Sδ =0.02γM =1.008

n = 30nr = 20Ud =3.440Sδ =0.03γM =1.037

n = 30nr = 20Ud =3.440Sδ =0.03γM =1.037

IPE 450 n = 54nr = 27Ud =3.303Sδ =0.04γM =0.995

n = 54nr = 27Ud =3.303Sδ =0.04γM =0.995

n = 92nr = 46Ud =3.086Sδ =0.05γM =1.008

n = 92nr = 46Ud =3.086Sδ =0.05γM =1.008

n = 92nr = 46Ud =3.086Sδ =0.06γM =1.070

n = 92nr = 46Ud =3.086Sδ =0.06γM =1.070

n = 54nr = 20Ud =3.303Sδ =0.04γM =0.993

n = 54nr = 20Ud =3.303Sδ =0.04γM =0.993

n = 92nr = 20Ud =3.086Sδ =0.04γM =0.998

n = 92nr = 20Ud =3.086Sδ =0.04γM =0.998

n = 92nr = 20Ud =3.086Sδ =0.05γM =1.051

n = 92nr = 20Ud =3.086Sδ =0.05γM =1.051

UBP n = 7nr = 7Ud =7.715Sδ =0.03γM =1.093

n = 7nr = 7Ud =7.715Sδ =0.03γM =1.093

n = 7nr = 7Ud =7.715Sδ =0.03γM =1.105

n = 7nr = 7Ud =7.715Sδ =0.03γM =1.105

n = 7nr = 7Ud =7.715Sδ =0.03γM =1.143

n = 7nr = 7Ud =7.715Sδ =0.03γM =1.143



n = 7nr = 7Ud =3.040Sδ =0.03 γM =0.963

n = 7nr = 7Ud =3.040Sδ =0.03γM =0.964

n = 7nr = 7Ud =3.040Sδ =0.03γM =0.964

n = 7nr = 7Ud =3.040Sδ =0.03γM =0.979

n = 7nr = 7Ud =3.040Sδ =0.03γM =0.979

UC n = 94nr = 47Ud =3.074Sδ =0.06γM =1.075

n = 94nr = 47Ud =3.074Sδ =0.04γM =1.001

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.186

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.186

n = 87nr = 44Ud =3.114Sδ =0.05γM =1.050

n = 87nr = 44Ud =3.114Sδ =0.03γM =0.986

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.208

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.208

n = 87nr = 44Ud =3.114Sδ =0.07γM =1.129

n = 87nr = 44Ud =3.114Sδ =0.05γM =1.043

n = 94nr = 20Ud =3.074Sδ =0.04γM =1.041

n = 94nr = 20Ud =3.074Sδ =0.03γM =0.986

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.186

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.186

n = 87nr = 20Ud =3.114Sδ =0.04γM =1.030

n = 87nr = 20Ud =3.114Sδ =0.03γM =0.974

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.208

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.208

n = 87nr = 20Ud =3.114Sδ =0.04γM =1.077

n = 87nr = 20Ud =3.114Sδ =0.04γM =1.033

n = 94nr = 20Ud = 3.040Sδ =0.04γM =1.039

n = 94nr = 20Ud =3.040Sδ =0.03γM =0.985

n = 7nr = 7Ud =3.040Sδ =0.04γM =0.998

n = 7nr = 7Ud =3.040Sδ =0.04γM =0.998

n = 87nr = 20Ud =3.040Sδ =0.04γM =1.027

n = 87nr = 20Ud =3.040Sδ =0.03γM =0.973

n = 7nr = 7Ud =3.040Sδ =0.04γM =1.004

n = 7nr = 7Ud =3.040Sδ =0.04γM =1.004

n = 87nr = 20Ud =3.040Sδ =0.04γM =1.074

n = 87nr = 20Ud =3.040Sδ =0.04γM =1.030

UC203x203x46

n = 64nr = 32Ud =3.246Sδ =0.03γM =0.972

n = 64nr = 32Ud =3.246Sδ =0.03γM =0.972

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.186

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.186

n = 57nr = 28Ud =3.286Sδ =0.03γM =0.980

n = 57nr = 28Ud =3.286Sδ =0.03γM =0.980

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.208

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.208

n = 57nr = 28Ud =3.286Sδ =0.03γM =0.980

n = 57nr = 28Ud =3.286Sδ =0.03γM =0.980


n = 64nr = 20Ud =3.246Sδ =0.03γM =0.968

n = 64nr = 20Ud =3.246Sδ =0.03γM =0.968

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.186

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.186

n = 57nr = 20Ud =3.286Sδ =0.03γM =0.974

n = 57nr = 20Ud =3.286Sδ =0.03γM =0.974

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.208

n = 7nr = 7Ud =7.715Sδ =0.04γM =1.208

n = 57nr = 20Ud =3.286Sδ =0.03γM =0.972

n = 57nr = 20Ud =3.286Sδ =0.03γM =0.972

UC254x254x89

n = 30nr = 20Ud =3.440Sδ =0.03γM =1.049

n = 30nr = 20Ud =3.440Sδ =0.03γM =1.049

n = 30nr = 20Ud =3.440Sδ =0.03γM =1.040

n = 30nr = 20Ud =3.440Sδ =0.03γM =1.002

n = 30nr = 20Ud =3.440Sδ =0.03γM =1.084

n = 30nr = 20Ud =3.440Sδ =0.03γM =1.045

n = 30nr = 20Ud =3.040Sδ =0.03γM =1.037

n = 30nr = 20Ud =3.040Sδ =0.03γM =0.999

n = 30nr = 20Ud =3.040Sδ =0.03γM =1.029

n = 30nr = 20Ud =3.040Sδ =0.03γM =0.991

n = 30nr = 20Ud =3.040Sδ =0.03γM =1.071

n = 30nr = 20Ud =3.040Sδ =0.03γM =1.032

UB n = 180nr = 90Ud =3.040Sδ =0.05γM =1.023

n = 180nr = 90Ud =3.040Sδ =0.04γM =1.008

n = 1044nr = 522Ud =3.040Sδ =0.06γM =1.032

n = 1044nr = 522Ud =3.040Sδ =0.06γM =1.027

n = 1044nr = 522Ud =3.040Sδ =0.07γM =1.066

n = 1044nr = 522Ud =3.040Sδ =0.07γM =1.063

n = 180nr = 78Ud =3.040Sδ =0.05γM =1.024

n = 180nr = 78Ud =3.040Sδ =0.05γM =1.009

n = 1044nr = 450Ud =3.040Sδ =0.06γM =1.030

n = 1044nr = 450Ud =3.040Sδ =0.06γM =1.024

n = 1044nr = 450Ud =3.040Sδ =0.07γM =1.064

n = 1044nr = 450Ud =3.040Sδ =0.07γM =1.062



n = 180nr = 52Ud =3.040Sδ =0.04γM =1.004

n = 1044nr = 300Ud =3.040Sδ =0.06γM =1.027

n = 1044nr = 300Ud =3.040Sδ =0.06γM =1.023

n = 1044nr = 300Ud =3.040Sδ =0.07γM =1.063

n = 1044nr = 300Ud =3.040Sδ =0.07γM =1.064

n = 180nr = 26Ud =3.040Sδ =0.04γM =1.004

n = 180nr = 26Ud =3.040Sδ =0.04γM =0.998

n = 1044nr = 150Ud =3.040Sδ =0.05γM =1.025

n = 1044nr = 150Ud =3.040Sδ =0.06γM =1.023

n = 1044nr = 150Ud =3.040Sδ =0.07γM =1.065

n = 1044nr = 150Ud =3.040Sδ =0.07γM =1.066

n = 180nr = 20Ud =3.040Sδ =0.03γM =1.003

n = 180nr = 20Ud =3.040Sδ =0.03γM =0.994

n = 1044nr = 20Ud =3.040Sδ =0.08γM =1.040

n = 1044nr = 20Ud =3.040Sδ =0.08γM =1.038

n = 1044nr = 20Ud =3.040Sδ =0.08γM =1.080

n = 1044nr = 20Ud =3.040Sδ =0.09γM =1.080

UB254x102x22

n = 285nr = 142Ud =3.040Sδ =0.09γM =1.042

n = 285nr = 142Ud =3.040Sδ =0.09γM =1.042

n = 285nr = 142Ud =3.040Sδ =0.09γM =1.057

n = 285nr = 142Ud =3.040Sδ =0.09γM =1.057

n = 285nr = 20Ud =3.040Sδ =0.06γM =0.998

n = 285nr = 20Ud =3.040Sδ =0.05γM =0.998

n = 285nr = 20Ud =3.040Sδ =0.06γM =1.004

n = 285nr = 20Ud =3.040Sδ =0.06γM =1.004


UB254x102x25

n = 22nr = 20Ud =3.600Sδ =0.05γM =1.008

n = 22nr = 20Ud =3.600Sδ =0.05γM =1.008

n = 46nr = 23Ud =3.349Sδ =0.04γM =0.956

n = 46nr = 23Ud =3.349Sδ =0.04γM =0.956

n = 46nr = 23Ud =3.349Sδ =0.04γM =0.990

n = 46nr = 23Ud =3.349Sδ =0.04γM =0.990

n = 22nr = 20Ud =3.600Sδ =0.05γM =1.008

n = 22nr = 20Ud =3.600Sδ =0.05γM =1.008

n = 46nr = 20Ud =3.349Sδ =0.04γM =0.950

n = 46nr = 20Ud =3.349Sδ =0.04γM =0.950

n = 46nr = 20Ud =3.349Sδ =0.04γM =0.988

n = 46nr = 20Ud =3.349Sδ =0.04γM =0.988

UB254x146x31.1

n = 109nr = 54Ud =3.040Sδ =0.05γM =1.023

n = 109nr = 54Ud =3.040Sδ =0.05γM =1.023

n = 118nr = 59Ud =3.040Sδ =0.05γM =1.017

n = 118nr = 59Ud =3.040Sδ =0.05γM =1.017

n = 118nr = 59Ud =3.040Sδ =0.05γM =1.023

n = 118nr = 59Ud =3.040Sδ =0.05γM =1.023

n = 109nr = 20Ud =3.040Sδ =0.04γM =1.009

n = 109nr = 20Ud =3.040Sδ =0.04γM =1.009

n = 118nr = 20Ud =3.040Sδ =0.04γM =1.000

n = 118nr = 20Ud =3.040Sδ =0.04γM =1.000

n = 118nr = 20Ud =3.040Sδ =0.04γM =1.020

n = 118nr = 20Ud =3.040Sδ =0.04γM =1.020

UB356x127x33

n = 100nr = 50Ud =3.040Sδ =0.05γM =1.070

n = 100nr = 50Ud =3.040Sδ =0.05γM =1.070

n = 100nr = 50Ud =3.040Sδ =0.05γM =1.114

n = 100nr = 50Ud =3.040Sδ =0.05γM =1.114



n = 100nr = 20Ud =3.040Sδ =0.07γM =1.093

n = 100nr = 20Ud =3.040Sδ =0.07γM =1.137

n = 100nr = 20Ud =3.040Sδ =0.07γM =1.137

n = 100nr = 30Ud =3.040Sδ =0.06γM =1.084

n = 100nr = 30Ud =3.040Sδ =0.06γM =1.084

n = 100nr = 30Ud =3.040Sδ =0.06γM =1.127

n = 100nr = 30Ud =3.040Sδ =0.06γM =1.127

n = 100nr = 40Ud =3.040Sδ =0.06γM =1.074

n = 100nr = 40Ud =3.040Sδ =0.06γM =1.074

n = 100nr = 40Ud =3.040Sδ =0.05γM =1.118

n = 100nr = 40Ud =3.040Sδ =0.05γM =1.118

UB406x178x54

n = 36nr = 20Ud =3.406Sδ =0.08γM =1.052

n = 36nr = 20Ud =3.406Sδ =0.08γM =1.052

n = 36nr = 20Ud =3.406Sδ =0.07γM =1.041

n =36nr =20Ud =3.406Sδ =0.07γM =1.041

UB457x152x52

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.012

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.012

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.030

n = 30nr = 20Ud =3.440Sδ =0.05γM =1.030


UB457x191x67

n = 68nr = 34Ud =3.223Sδ =0.04γM =1.010

n = 68nr = 34Ud =3.223Sδ =0.04γM =1.010

n = 68nr = 34Ud =3.223Sδ =0.05γM =1.031

n = 68nr = 34Ud =3.223Sδ =0.05γM =1.031

n = 68nr = 20Ud =3.223Sδ =0.04γM =1.016

n = 68nr = 20Ud =3.223Sδ =0.04γM =1.016

n = 68nr = 20Ud =3.223Sδ =0.05γM =1.039

n = 68nr = 20Ud =3.223Sδ =0.05γM =1.039

n = 68nr = 20Ud =3.040Sδ =0.04γM =1.008

n = 68nr = 20Ud =3.040Sδ =0.04γM =1.008

n = 68nr = 20Ud =3.040Sδ =0.05γM =1.030

n = 68nr = 20Ud =3.040Sδ =0.05γM =1.030

UB533x210x82

n = 41nr = 20Ud =3.377Sδ =0.08γM =1.142

n = 41nr = 20Ud =3.377Sδ =0.08γM =1.142

n = 41nr = 20Ud =3.377Sδ =0.08γM =1.152

n =41nr =20Ud =3.377Sδ =0.08γM =1.152

n = 41nr = 20Ud =3.040Sδ =0.08γM =1.110

n = 41nr = 20Ud =3.040Sδ =0.08γM =1.110

n = 41nr = 20Ud =3.040Sδ =0.08γM =1.121

n =41nr =20Ud =3.040Sδ =0.08γM =1.121



UB610x229x101

n = 92nr = 46Sδ =0.06γM =0.994

n = 92nr = 46Sδ =0.06γM =0.994

n = 92nr = 46Sδ =0.06γM =0.999

n = 92nr = 46Sδ =0.06γM =0.999

n = 92nr = 20Sδ =0.08γM =1.017

n = 92nr = 20Sδ =0.08γM =1.017

n = 92nr = 20Sδ =0.07γM =1.015

n = 92nr = 20Sδ =0.07γM =1.015

UB610x229x113

n = 36nr = 20Ud =3.406Sδ =0.06γM =1.107

n = 36nr = 20Ud =3.406Sδ =0.06γM =1.063

n = 36nr = 20Ud =3.406Sδ =0.06γM =1.120

n = 36nr = 20Ud =3.406Sδ =0.06γM =1.077

n = 36nr = 20Ud =3.040Sδ =0.06γM =1.082

n = 36nr = 20Ud =3.040Sδ =0.06γM =1.040

n = 36nr = 20Ud =3.040Sδ =0.06γM =1.095

n = 36nr = 20Ud =3.040Sδ =0.06γM =1.054

UB686x254x125

n = 32nr = 20Ud =3.429Sδ =0.08γM =1.048

n = 32nr = 20Ud =3.429Sδ =0.08γM =1.010

n = 32nr = 20Ud =3.429Sδ =0.08γM =1.052

n = 32nr = 20Ud =3.429Sδ =0.08γM =1.014



HEA n = 38nr = 20Ud =3.040Sδ =0.04γM =1.024

n = 38nr = 20Ud =3.040Sδ =0.04γM =0.989

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.186

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.186

n = 32nr = 20Ud =3.040Sδ =0.05γM =1.013

n = 32nr = 20Ud =3.040Sδ =0.04γM =0.988

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.208

n = 6nr = 6Ud =3.040Sδ =0.01γM =1.208

n = 32nr = 20Ud =3.040Sδ =0.05γM =1.052

n = 32nr = 20Ud =3.040Sδ =0.04γM =1.030

HEB n = 149nr = 74Ud =3.040Sδ =0.06γM =1.072

n = 149nr = 74Ud =3.040Sδ =0.05γM =1.044

n = 149nr = 74Ud =3.040Sδ =0.06γM =1.081

n = 149nr = 74Ud =3.040Sδ =0.05γM =1.052

n = 149nr = 74Ud =3.040Sδ =0.07γM =1.128

n = 149nr = 74Ud =3.040Sδ =0.06γM =1.102

n = 149nr = 20Ud =3.040Sδ =0.05γM =1.066

n = 149nr = 20Ud =3.040Sδ =0.05γM =1.043

n = 149nr = 20Ud =3.040Sδ =0.05γM =1.070

n = 149nr = 20Ud =3.040Sδ =0.05γM =1.048

n = 149nr =20Ud =3.040Sδ =0.06γM =1.121

n = 149nr = 20Ud =3.040Sδ =0.06γM =1.094



IPE n = 144nr = 72Ud =3.040Sδ =0.04γM =0.995

n = 144nr = 72Ud =3.040Sδ =0.04γM =0.995

n = 173nr = 86Ud =3.040Sδ =0.04γM =1.012

n = 173nr = 86Ud =3.040Sδ =0.04γM =1.012

n = 173nr = 86Ud =3.040Sδ =0.05γM =1.076

n = 173nr = 86Ud =3.040Sδ =0.05γM =1.076

n = 144nr = 50Ud =3.040Sδ =0.03γM =0.986

n = 144nr = 50Ud =3.040Sδ =0.03γM =0.986

n = 173nr = 60Ud =3.040Sδ =0.04γM =1.009

n = 173nr = 60Ud =3.040Sδ =0.04γM =1.009

n = 173nr = 60Ud =3.040Sδ =0.05γM =1.076

n = 173nr = 60Ud =3.040Sδ =0.05γM =1.076

n = 144nr = 33Ud =3.040Sδ =0.03γM =0.976

n = 144nr = 33Ud =3.040Sδ =0.03γM =0.976

n = 173nr = 40Ud =3.040Sδ =0.03γM =1.004

n = 173nr = 40Ud =3.040Sδ =0.03γM =1.004

n = 173nr = 40Ud =3.040Sδ =0.05γM =1.081

n = 173nr = 40Ud =3.040Sδ =0.05γM =1.081

n = 144nr = 20Ud =3.040Sδ =0.02γM =0.969

n = 144nr = 20Ud =3.040Sδ =0.02γM =0.969

n = 173nr = 20Ud =3.040Sδ =0.03γM =1.002

n = 173nr = 20Ud =3.040Sδ =0.03γM =1.002

n = 173nr = 20Ud =3.040Sδ =0.06γM =1.087

n = 173nr = 20Ud =3.040Sδ =0.06γM =1.087

ANNEX C

A Proposal regarding the way to control production of hot rolled beams, to ensure a γM0 of 1,0according to the results of the project

SAFETY INDEX FOR YIELD STRENGTH AND AREAPOPULATIONS

1) GENERAL

A areaeR strength yield

Population(A) (A) prob:

)e(R )e(R prob:g

f=

=

Probability of a product value : B = Re . A

ee

ee

dR . RB ).(R .

R1 (B) prob

∫=∞+

∞−gf

Mean value of this product : A.RB e=

Second order moment of

this product : E2 (B) = E2 (Re) . E2 (A)

Or in general ∫=+∞

∞−dx).x(prob.x)x(E 2

2

and 22

2)x( x)x(E −=σ

therefore with x = B = Re . A

22e2e2

2)B( A.R)A(E.)R(E −=σ

and by taking x = Re resp. A this gives

( ) ( )

2A

2e

2R

22A

2R)B(

2A

2e

2R

22A

2R

22e

22A

2e

2R

2)B(

.R.A.

.R.A.

A.RA.R

ee

ee

e

σ+σ+σσ=σ

σ+σ+σσ=

−+σ+σ=σ

2) SAFETY CONDITION

nommin.eB A.R.kB ≥σ−

This corresponds to plastic loadresistance and for design withfactored loads

For normal service conditions however (uncertainties from loading beingremoved, representing roughly a 1,4 factor), failure is prevented when thefollowing relation is fulfilled !

( ) 4,1/A.R.kB nommin.eB* ≥σ−

k* represents how many times the standard deviation σB is containedbetween B and ( )[ ]/1,4A.R nome.min !

Failure probability is equal to the probability that B gets smaller than( )[ ]/1,4A.R nome.min !!

Hence k* reflects the safety index β

3) Following 1) and 2) we obtain

( ) 4,1/A.R.R.A.kA.R nommin.e2A

2e

2R

22A

2R

*e ee

≥σ+σ+σσ−

or

4,11

A.

RR

R.

AA

A.

Rk

AA.

RR

2nom

2A

2min.e

2e

2min.e

2R

2nom

2

2nom

2A

2min.e

2R*

nommin.e

e ee ≥σ

+σ

+σσ

−

lets assume

σ=σ

σ=σ→

+=

+=→

+=+=

aA

rR

nom

emin.ee

nom

emin.ee ee

aAArRR

aAArRR

which leads to

( ) ( )4,1

1A

.R

RrR

.AAa

A.

Rk

Aa1.

Rr

12nom

2a

2min.e

2min.ee

2min.e

2r

2nom

2nom

2nom

2a

2min.e

2r*

nommin.e

e ee ≥σ+

+σ+

+σσ

−

+

+

and hence gives

+

−≥

++ 1

4,11

Aa.

Rr

Aa

Rr

nommin.e

e

nommin.e

e

2nom

2a

2

min.e

e2

min.e

2r

2

nom2nom

2a

2min.e

2r*

A.

Rr

1R

.A

a1A

.R

k ee σ

++

σ

++

σσ

or

2nom

2a

2

min.e

e2

min.e

2r

2

nom2nom

2a

2min.e

2r

nommin.e

e

nommin.e

e

*

A.

Rr

1R

.A

a1A

.R

4,111

Aa.

Rr

Aa

Rr

k

ee σ

++

σ

++

σσ

−+

++

≤

4)

For a population of yield strength and area corresponding to one year check,we need a safety index β of 4,7!

This corresponds to a failure probability of 1,3. 10-6 as accepted in EC1, Part1 !

Hence we must have

k* = β ≥ 4,7

This may be used in production control

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* This document is also available in an electronic form (PDF)