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ISSN 1018-5593

European Commission

technical steel research Properties and service performance

Simplified version of Eurocode 3 for usual buildings

STEEL RESEARCH

European Commission

technical steel research Properties and service performance

Simplified version of Eurocode 3 for usual buildings P. Chantrain, J.-B. Schleich ARBED recherches BP 141 L-4009 Esch-sur-Alzette

Contract No 7210-SA/513 1 July 1991 to 30 June 1994

Final report

Directorate-General Science, Research and Development

1997

EUR 16839 EN

LEGAL NOTICE Neither the European Commission nor any person acting on behalf of the Commission is responsible for the use which might be made of the following information.

A great deal of additional information on the European Union is available on the Internet. It can be accessed through the Europa server (http://europa.eu.int)

!

Cataloguing data can be found at the end of this publication. Luxembourg: Office for Official Publications of the European Communities, 1997 ISBN 92-828-1485-8 © European Communities, 1997 Reproduction is authorised provided the source is acknowledged. Printed in Luxembourg

[

I

SIMPLIFIED VERSION OF EIIROCODE 3 FOR USUAL BUILDINGS. ECSC Agreement 7210-SA/513 Summary The aim of the following E.C.S.C. research is to elaborate a simple but complete document to design commonly used buildings in steel construction. This document is completely based on Eurocode 3 and each paragraph is totally conform to Eurocode 3. Only the design formulas necessary to design braced or non-sway buildings are taken into account in this document. Tall buildings (skyscrapers) and halls are not treated. The designers and steel constructors are able to calculate and erect a commonly used steel building with this design handbook. Therefore also the important load cases from Eurocode 1 will be included in this document. The working group of the research project was constituted of 10 European engineering offices. Firstly that working group has carried out different examples of calculation of braced or non-sway buildings according to Eurocode 3 Part 1.1: check of existing steel structures and design of new steel buildings. Afterwards thanks to those examples of calculation the needed design formulas of Eurocode 3 was highlighted and general procedure of design was determined. The design handbook "Simplified version of Eurocode 3" is based on that experience. The link of the working group to the drafting panel of Eurocode 3 was guaranteed by the Professor Sedlacek of Aachen University. Liaison has been ensured with both other E.C.S.C. research projects nr SA/312 and nr S A/419 also dealing with Eurocode 3: respectively, "Application software of Eurocode 3: EC3-tools" (CTICM, France) and "Design handbook for sway buildings" (CSM-Italy).

VERSION SIMPLIFIEE DE L'EUROCODE 3 POUR LES BATIMENTS COURANTS Agrément CECA 7210-SA/513 Sommaire Le but de cette recherche est d'élaborer un document simple mais complet pour calculer des bâtiments courants en construction métallique. Ce document est entièrement basé sur l'Eurocode 3 et chaque paragraphe est totalement conforme à VEurocode 3. Il n'a été pris en compte que les formules nécessaires au calcul de bâtiments contreventés et rigides. Les bâtiments très élancés (gratte-ciel) et les halls industriels n'y sont pas traités. Les bureaux d'études et constructeurs métalliques devront être capables de calculer et d'ériger un bâtiment courant en acier avec ce manuel de dimensionnement. Les cas de charges le plus importants issus de l'Eurocode 1 seront également inclus dans ce document. Le groupe de travail du projet de recherche était constitué de 10 bureaux d'études européens. En première partie ce groupe de travail a effectué différents exemples de calculs de bâtiments contreventés et rigides conformément à l'Eurocode 3 Partie 1.1: vérification de structures en acier déjà existantes et dimensionnement de nouveaux bâtiments en acier. Grâce à ces exemples concrets de calcul, les formules de l'Eurocode 3 utiles au dimensionnement ont été mises en évidence et une procédure générale de dimensionnement a été déterminée. Le manuel de dimensionnement "Version simplifiée de l'Eurocode 3" se base sur cette expérience. La jonction entre le groupe de travail et le groupe de rédaction de l'Eurocode 3 a été faite par le professeur Sedlacek de l'Université d'Aix-La-Chapelle. Une collaboration a été assurée avec deux autres projets de recherche CECA N° SA/312 et N° SA/419 qui concernent aussi l'Eurocode 3: respectivement, "Logiciel d'application de l'Eurocode 3: EC3-Tools" (CTICM, France) et "Manuel de dimensionnement de bâtiments souples (à nœuds déplaçables)" (CSM, Italie)

VEREINFACHTE VERSION DES EUROCODE 3 FÜR ÜBLICHE GEBÄUDE. EGKS Zulassung7210-SA/513 Zusammenfassung Dieses EGKS Forschungsprojekt hat zum Ziel, ein einfaches aber vollständiges Dokument für allgemeine (übliche) Stahlbaubemessung auszuarbeiten. Dieses Dokument ist völlig auf Eurocode 3 basiert und jeder Paragraph paßt genau zu Eurocode 3. Nur die Bemessungsformeln, die notwendig sind für ausgesteifte oder unverschiebliche Tragwerke , werden berücksichtigt. Hochhäuser (Wolkenkratzen) oder Hallen werden nicht behandelt. Die Ingenieurbüros und Stahlkonstrukteuren haben die Möglichkeit mit diesem DesignHandbuch einen einfachen Stahlbau zu berechnen und zu bauen. Dafür sind die wichtigsten Lastfälle von Eurocode 1 in diesem Dokument beinhaltet. Die Arbeitsgruppe des Forschungssprojekt bestand aus 10 europäischen Ingenieurbüros. Die Arbeitsgruppe hat, im ersten Teil dieses Forschungsvorhabens, verschiedene Berechnungsbeispiele mit ausgesteiften oder unverschieblichen Tragwerken nach Eurocode 3 Teil 1.1 durchgefühlt : Berechnungs-Nachweis einer existierenden Stahlstruktur und Dimensionierung eines neuen Stahlbaus. Anschließend an diese konkreten Beispiele, wurden die benutzten Bemessungsformeln nach Eurocode 3 hervorgehoben und ein allgemeines Bemessungsverfahren wurde festgelegt. Das Design-Handbuch "Vereinfachte Version des Eurocode 3" basiert auf dieser Erfahrung. Die Verbindung zwischen der Arbeitsgruppe und dem technischen Komitee wurde von Professor Sedlacek der Aachener Universität hergestellt. Eine Zusammenarbeit bestand mit zwei anderen EGKS Forschungesprojekten N° SA/312 und N° SA/419, die auch Eurocode 3 behandeln : "Application software of Eurocode 3: EC3-tools" (CTICM, France) und "Design handbook for sway buildings" (CSM-Italy).

Contents Summary

3

Sommaire

4

Zusammenfassung

5

Contents

7

1. Introduction

9

2. Working group

10

3. Part 1 : Worked examples 3.1. Exercise 1 : Verification of an existing braced or non-sway structure 3.2. Exercise 2: Verification of a non-sway wind bracing in a building 3.3. Exercise 3: Design of a braced or non-sway structure

11

4. Part 2 : Design handbook ·

12

11 12 12

FIGURES (Ito 8 ) APPENDICES List of symbols List of tables List of

flow-charts

(6 pages) (3 pages) (1 page)

"Design handbook according to Eurocode 3 for braced or non-sway steel buildings" (short title : "EC3 for non-sway buildings") (196 pages)

15 23 29 32 33

1. Introduction The research was divided into different parts: - in the first part worked examples of braced or non-sway structures has been carried out by European engineering offices according to Eurocode 3 and Eurocode 1. Different contacts have been taken with different engineering offices in Europe and professional organisations (E.C.C.S. and C.T.I.C.M.). The working group of this research project has been constituted with 10 engineering offices. - in the second part the needed formulae for simple design of braced or non-sway structures have been selected thanks to the exercises about check and design of steel buildings. The design handbook has been elaborated on the basis of that experience. The present final report of this research project presents the design handbook called "Design handbook according to Eurocode 3 for braced or non-sway steel buildings" (short title : "EC3for non-sway buildings").

2. Working group The research project was fully managed and carried out by ProfilARBED-Research (RPS Department), with the active support of the following working group which is particularly thanked for the fruitful collaboration : - the following 10 engineering offices which were involved to perform 3 worked examples : Reference Number

Engineering office

City

Country

2

Adem

Mons

Belgium

3

Bureau Delta

Liège

Belgium

4

Varendonck Groep / Steelrrack

Gent

Belgium

6

Ramboll & Hanneman

Copenhagen

Denmark

7

Bureau Veritas

Courbevoie

France

9

Socotec

Saint-Quentin-Yvelines

France

10

Sofresid

Montreuil

France

13

Danieli Ingegneria

Livorno

Italy

14

Schroeder & Associés

Luxembourg

Luxemburg

16

D3BN

Nieuwegein

The Netherlands

- Professor Sedlacek and assistant from Aachen University (Germany) which guaranteed the link of this working group to the drafting panel of Eurocode 3 and Eurocode 1, - some other engineering offices which participated to the meetings of the full working group : Reference number

City

Country

5

Engineering office Verdeyen & Moenart Associate Partner

Bruxelles

Belgium

12 18

Ingenieur gruppe Bauen Ove Arup & Partners

Karlsruhe London

19

ECCS-TCll

Kiel

Germany United Kingdom Germany

10

-some members of CTICM (France) and SIDERCAD (Italy) involved in complementary research projects about simplified approaches of Eurocode 3 (respectively, "Application software of Eurocode 3 : EC3-tools" and "Design handbook for sway buildings") : . which participated to the meetings of the full working group, . and with which a general flow-chart (FC1) about elastic global analysis of steel frame according to EC3 has been established.

3. Part 1 : Worked examples In order to find the needed formulae and to familiarise the engineering offices to the Eurocodes, it has been decided to perform 3 different exercises (check and design of a steel structure), - exercise 1: verification of an existing braced or non-sway steel structure, - exercise 2: verification of a non-sway steel wind bracing in a building, - exercise 3: design of a braced or non-sway steel structure, Different drawings issued from the exercises of the offices are enclosed in the technical report n° 4 (TR4) showing the type of the calculated buildings and some details : - office building with bracing system (engineering offices n° 2, 9 and 16), (Annex 1 of TR4); - car park (engineering office n° 3), (Annex 2 of TR4); - residential building with bracing system (engineering office n° 7), (Annex 3 of TR4); - office building with bracing system (engineering office n° 10), (Annex 4 of TR4); - industrial building with catalytic reactors (engineering office n° 13), (Annex 5 of TR4); - office building with concrete core (engineering office n° 14), (Annex 6 of TR4); - office building with concrete core (engineering office n° 4), (Annex 7 of TR4); - office building with bracing system (engineering office n° 6), (Annex 8 of TR4).

3.1. Exercise 1 : Verification of an existing braced or non-sway structure The flow-chart of figure 1 shows the procedure followed for the verification of an existing building with the Eurocodes 1 and 3. This first exercise aimed to find the needed formulae given by the Eurocodes in order to check the safety of the different limit states. This exercise was not an iterative processes, but was only a verification procedure of an existing braced or non-sway building. The flow-chart of figure 1 is divided into 3 subjects: a. The "Keywords" representing the different steps of a check procedure. 1. conceptional type of structure. 2. occupancies. 3. shape. 4 structural concept. 5 action effects. 6. design and verification. b. The "Requirements and References" of each step of the verification. The references are Eurocode 1, Eurocode 3 and the product standards EN 10025 and EN 10113. c. The "Object" describing each step of the verification.

11

3.2. Exercise 2: Verification of a non-sway wind bracing in a building The non-sway wind bracing consisted of a latticed steel structure. The flow-chart of figure 2 gives the procedure of the verification of this wind bracing. This exercise was also not an iterative process. The description of the present flow-chart (figure 2) is the same than in the first example presented in the chapter 3.1 (figure 1).

3.3. Exercise 3: Design of a braced or non-sway structure After the two first exercises, the engineering offices were familiarised with the Eurocodes 1 and 3. They were able to perform a complete design of a structure by using an iterative procedure. The aim of this exercise was to analyse the way to find a good solution. This exercise allowed us to follow step by step the calculation of a structure in practice. The practical design handbook about the simplified version of the Eurocode 3 follows an improved way than the one defined in the initial design procedure. The figure 3 shows the different data for the design and the type of chosen optimisation. The Figure 4 gives the type of building to be designed. 4. Part 2 : Design handbook A list of the needed formulae taken from the Eurocode 3 has been established following the initial procedure defined for the exercises (see figures 5 to 8). This initial design procedure nearly corresponds to the sequence of the chapters of Eurocode 3. It had to be adapted to common practice. The solved exercises E3 (design of a building) and the experience of each engineering office allowed to determine a more suitable design procedure which constitutes the frame of the design handbook. About that practical design procedure reference may be made to the enclosed design handbook which is called "Design handbook according to Eurocode 3 for braced or nonsway steel buildings" (short title : "EC3for non-sway buildings") : - table of contents - general flow-chart FC1 about elastic global analysis of steel frames according to Eurocode 3 (see chapter I of the design handbook); this flow-chart FC1 constitutes the link with the 2 other researches about simplified approaches of EC3 : from CTICM and SIDERCAD (see chapter 2 of the present report), - flow-chart FC3.1 and FC3.2 about general procedures to study structures submitted to actions (see chapter ΠΊ of the design handbook), with load cases which are respectively defined : . by relevant combinations of characteristic values of load arrangements, (g, q, s, w, ...), in general cases, . or, by relevant combinations of characteristic values for the effects of actions (N, V, Μ; δ, f,...), in case of first order elastic global analysis. - flow-chart FC4 about elastic global analysis of braced or non-sway steel frames according to Eurocode 3 (see chapter IV of the design handbook), - flow-chart FC 12 about elastic global analysis of bracing system according to Eurocode 3 (see chapter ΧΠ of the design handbook)

12

In general, for the design of buildings we need to : - define the analysis model of frames (assumptions of plane frames, bracing systems, connections, members,...) - characterise the load arrangements and load cases, - carry out the elastic global analysis of frames in order to determine the effects of actions : . deformations (δ), vibrations (f) for Serviceability Limit States (SLS) and, . internal forces and moments (N, V, M) for Ultimate Limit States (ULS). - check the members at SLS (vertical and horizontal displacements, eigenfrequencies) and at ULS (resistance of cross-sections, stability of members and stability of webs) for : . members in tens on (braces,...) . members in compression (columns,...) . members in bending (beams,...) . members with combined axial load force and bending moment (beam-columns,...) - check the local effects of transverse forces on webs at ULS (resistance and stability of webs), - check the connections at SLS and at ULS. Especially for members to be checked at ULS specific tables are given in the concerned chapters of the handbook, with list of checks according to different types of loading (separate or combined internal forces and moments : N, V, M). The design handbook which is enclosed to this final report of the research project, intends to be a design aid in supplement to the complete document Eurocode 3 - Part 1.1 in order to facilitate the use of Eurocode 3 for the design of such steel structures which are usual in common practice : braced or non-sway steel structures. Although the present design handbook has been carefully established and intends to be selfsufficient it does not substitute in any case for the complete document Eurocode 3 - Part 1.1, which should be consulted in conjunction with the NAD, in case of doubt or need for clarification. All references to Eurocode 3 - Part 1.1 which appear systematically, are made in [...]. Any other text, tables or figures not quoted from Eurocode 3 are considered to satisfy the rules specified in Eurocode 3 - Part 1.1. The lists of all symbols, tables and flow-charts included in the "Design Handbook" are enclosed to the present appendices.

13

1. conceptional rype of structure different braced non sway structures Chapter 5.2.6.2 clause (2) 7.3.2. lateral-torsional buckling of beams. -> Chapter 5.5.2 clause (1) formula (5.48) clause (2) formula (5.49) clause (3) clause (5) clause (6) Annex F clause (7) limit condition clause (8) 7.3.3. bending and axial tension. -> Chapter 5.5.3 7.3.4. bending and axial compression. -> Chapter 5.5.4 -without lateral-torsional buckling: clause (1) formula (5.51) class 1 and 2 cross-sections clause (3) formula (5.53) class 3 cross-sections - with lateral-torsional buckling: clause (2) formula (5.52) class 1 and 2 cross-sections clause (4) formula (5.54) class 3 cross-sections clause (7) figure 5.5.3 7.4. Resistance of connections. 7.4.1. boltedjoints. -> Chapter 6.5 7.4.1.1. Positioning of holes. -> Chapter 6.5.1 figures 6.5.1 to 6.5.4 (ECCSpublication n°65: table 62 ) 7.4.1.2. Design shear rupture resistance. -> Chapter 6.5.2.2 clause (2) formula (6.1) clause (3) figure 6.5.5 Figure 7

21

Eurocode 3 Formulae References 7.4.1.3. Angles. -> Chapter 6.5.2.3

clause (2) formulae (6.2) to (6.4) clause (3) figure 6.5.6 7.4.1.4. Categories of bolted connections. -> Chapter 6.5.3 and table 6.5.2 7.4.1.5. Distribution offorces between fasteners. -> Chapter 6.5.4 figure 6.5.7 7.4.1.6. Design resistance of bolts. -> Chapter 6.5.5 clause (2) table 6.5.3 clause (3) clause (4) formula (6.5) clause (5) formula (6.6) clause (9) clause (10) (ECCSpublication n°65: tables 6.6, 6.7and6.8) 7.4.1.7. High strength bolts in slip-resistant connections -> Chapter 6.5.8 -> Chapter 6.5.9 Annex J -> Chapter 6.5.10 clause (1) formula (6.11) and figure 6.5.10 [-> Chapter 6.5.11 clause (2) formula (6.12)7 [-> Chapter 6.5.12 clause (1) formula (6.13)7 -> Chapter 6.5.13. tables 6.5.6 and 6.5.7, figure 6.5.12 [7.4.2 Joints with rivets. -> Chapter 6.5.67 -> Chapter 6.6 7.4.3 Welded connections. clause (3)7 [-> Chapter 6.6.3 clause (1) -> Chapter 6.6.4 clause (4) clause (7) -> Chapter 6.6.5.1 clause (2) -> Chapter 6.6.5.2 clause (2) -> Chapter 6.6.5.3 clause (1) Annex M clause (3) formula (6.14) clause (4) formula (6.15) clause (5) -> Chapter 6.6.8 clause (2) formula (6.16) clause (3) [-> Chapter 6.6.9 clause (1)7 [ clause (3) formula (6.18)7 -> Chapter 6.6.10 clause (2) clause (3) 7.4.4 Beam-to-column connections. -> Chapter 6.9 and Annex J 7.4.5. Column bases. -> Chapter 6.11 and Annex L 7.5. Frame stability. -> Chapter 5.2.6.1 clause (1) clause (3) clause (4) 7.6. Static equilibrium. -> Chapter 2.3.2.4 clauses (1) to (12) Figure 8

22

1. List of symbols in the "Design Handbook" 1.

List of symbols (1/6)

Latin symbols

a a aVsd>Msd) LX.f. 1.1 Uniaxial bending of class 1 or 2 cross-section LX.f. 1.2 Biaxial bending of class 1 or 2 cross-section LX.f. 1.3 Bending of class 3 cross-section LX.f. 1.4 Bending of class 4 cross-section LX.f.2 Stability of web to (Nx.Sd, Vz.Sd, My.Sd)

161 167 167 167 167 167 1 ^7 167 170 170 171 171 171 172

X.a Generalities X.b Classification of cross-section X.c Resistance of webs to (F,N,V,M) X.C.1 Yield criterion to (F,N,V,M) X.c.2 Crushing resistance to F X.d Stability of webs to (F ; (F, M)) X.d.l Crippling resistance to (F;(F, M)) X.d. 1.1 Crippling resistance to F X.d. 1.2 Crippling resistance to (F,M) X.d.2 Buckling resistance to F X.e Stability of webs to compression flange buckling

184 185 I8 5 185 187 188 188 188 188 189 190

TRANSVERSE FORCES ON WEBS (F ; (F, N, V, M))

CONNECTIONS

XLa Generalities XI.b Bolted connections XLb. 1 Positioning of holes XI.b.2 Distribution of forces between bolts XI.b.3 Prying forces XI.b.4 Categories of bolted connections XI.b.5 Design ULS resistance of bolts XI.b.5.1 Bearing resistance XI.b.5.2 Shear resistance XI.b.5.2.1 General case

38

176

I77

177

^7^ 178 180 180 181 182

184

191

191 191 191 191 193 193 194 194 196 196

TABLE OF CONTENTS

XI.b.5.2.2 Long joints XI.b.5.3 Tension resistance XI.b.5.4 Punching shear resistance XI.b.5.5 Shear and tension interaction XI.b.6 ULS resistance of element with bolt holes XI.b.6.1 Net section ULS resistance XI.b.6.2 ULS resistance of angle with a single row of bolt XI.b.6.3 Block shear ULS resistance XI.b.7 High strength bolts in slip-resistant connections at SLS XI.c Welded connections XI.c. 1 Type of weld XI.C.2 Fillet weld XI.C.3 Design resistance of fillet weld XI.C.3.1 Throat thickness XI.c.3.2 Design resistance XI.C.4 Design resistance of butt weld XI.c. 5 Joints to unstiffened flanges Xl.d Pin connections XI.e Beam-to-column connections Xl.f Design of column bases

196 197 197 197 198 198 198 198 198 199 199 199 200 200 201 201 202 202 202 202

XII DESIGN OF BRACING SYSTEM

203 203 203 203 203 206 212 212 212 213 216 216 216 216 216 216 216

APPENDIX A :

List of symbols

217

APPENDIX Β

List of tables List of flow-charts

223

List of references to Eurocode 3 Part 1.1 related to all check formulas at ULS

227

XILa Generalities XILa. 1 Flow-chart FC 12:Elastic global analysis of bracing system according to EC 3 XILa. 1.1 Flow-chart FC 12: general XD.a.1.2 Flow-chart FC 12: details XILa. 1.3 Comments on flow-chart FC 12 Xll.b Static equilibrium XII.c Load arrangements and load cases XII.c.l Generalities XII.C.2 Global imperfections of the bracing system XILd Bracing system stability XILe First order elastic global analysis XILf Verifications at SLS Xll.g Verifications at ULS Xll.g. 1 Classification of the bracing system Xll.g. 1.1 Non-sway bracing system XII.g.2 ULS checks

APPENDIX C APPENDIX D

226

39

PRELIMINARIES O.a

Foreword

0-a.l

Generalities

(1) The Eurocodes are being prepared to harmonize design procedures between countries which are members of CEN (European Committee for Standardization). (2) Eurocode 3 - Part 1.1 "Design of Steel Structures ¡General Rules and Rules for Buildings' has been published initially as an ENV document (European pre-standard - a prospective European Standard for provisional application). (3) The national authorities of the members states have issued National Application Documents (NAD) to make Eurocode 3 - Part 1.1 operative whilst it has ENV-status (ENV 1993-1-1). 0.a.2

Objective of this design handbook

(1) The present publication is intended to be a design aid in supplement to the complete document Eurocode 3 - Part 1.1 in order to facilitate the use of Eurocode 3 for the design of such steel structures which are usual in common practice : braced or non-sway steel structures. (2) Therefore, the "Design handbook according to Eurocode 3 for braced or non-sway steel buildings" presents the main design formulas and rules extracted from Eurocode 3 - Part 1.1, which are needed to deal with : - elastic global analysis of buildings and similar structures in steel, - checks of structural members and connections at limit states, - in case of braced or non-sway structures, - according to the european standard Eurocode 3 - Part 1.1 (ENV 1993-1-1). 0-a.3

Warning

(1) Although the present design handbook has been carefully established and intends to be self-sufficient it does not substitute in any case for the complete document Eurocode 3 Part 1.1, which should be consulted in conjunction with the NAD, in case of doubt or need for clarification. (2) All references to Eurocode 3 - Part 1.1 are made in [...]. (3) Any other text, tables or figures not quoted from Eurocode 3 are considered to satisfy the rules specified in Eurocode 3 - Part 1.1.

41

O.a.4 How to read this design handbook (1) Example of numbering of chapters and paragraphs : VIE . a . 1 . 2 (2) Layout of pages : EC 3 for non-sway buildings - VI Members in tension

| Ref.

f

\

left column short title for references of the handbook

k

References

t

Page 68

t

concerned chapter

number of the page

Main text with a following example about layout of chapters: (...)

Π

STRUCTURAL CONCEPT OF THE BUILDING

(...)

ILh

Material properties

(...)

n.h.3 (...)

Connecting devices

II.h.3.2

Welding consumables

(...)

(3) In the left column of each page (Ref.): references to Eurocode 3 are always included between brackets [...]; the other references are specified without brackets; the word "form." means "formula" (4) References to Eurocode 3 are also given in the text between brackets [...] O.a. 5

Acknowledgements

(1) Particular thanks for fruitful collaboration are addressed to: . 15 engineering offices : Adem (Belgium), Bureau Delta (Belgium), Varendonck Groep/Steeltrak (Belgium), VM Associate Partner (Belgium), Rambøll, Hannemann & Højlund (Denmark), Bureau Veritas (France), Socotec (France), Sofresid (France), CPU Ingenieurbüro (Germany), IGB-Ingenieurgrappe Bauen (Germany), Danieli Ingegneria (Italy), Schroeder & Associés (Luxemburg), D3BN (the Netherlands), Ove Arup & Partners (United Kingdom), ECCS / TC 11 (Germany), . RWTH : Steel Construction Department from Aachen University with Professor SEDLACEK G. and GROTMANN D., . SIDERCAD (Italy) with MM. BANDINIM. and CATTANEO F., . CnCM (France) with MM. CHABROLIN B., GALEA Y. and BUREAU A. (2) Grateful thanks are also expressed to : . the ECSC which supported this work in the scope of the european research n° P2724(contract n° 7210 - SA/513), . the F6 executive committee which has followed and advised the working group of the research, . anyone who has contributed to the work: MM. CONAN Yves, MAUER Thierry, GERARDY LC.

42

Ή

O.b

References

- in the left column of each page (Ref.): references to Eurocode 3 are always included between brackets [...]; the other references are specified without brackets. - references to Eurocode 3 are also given in the text between brackets [...] - the reference "i" given in this chapter is designated in the text by IM. / l / Eurocode 1, draft version, Basis of Design and Actions on Structures (Parts 1, 2.2,2.4, 2.5,2.7, 10) C (E 1) HI Eurocode 3, ENV 1993-1-1, Design of steel structures Part 1.1 General rules and rules for Buildings (EC 3) 131 Eurocode 8, draft version, Design of structures for earthquake resistance (EC8) 141 EC C S technical publication n°65, Essentials of Eurocode 3 Design Manual for Steel Structures in Building, 1991, First Edition 151 Practical exercises showing applications of design formulas of Eurocode 3 : ECCS technical publication n°71, Examples to Eurocode 3,1993, First Edition 161 "Design handbook for sway buildings", from Sidercad (Italy) ΠI Software for the check of main formulas in Eurocode 3:"EC 3 tools" (available for PC computer, Windows 3.1), from CT1CM (France) /8/ Eurocode 3 Background Document 5.03 : "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 factors", April 1989. 191 Paper "Application de l'Eurocode 3 : classement des sections transversales en I", by Bureau A. and Galea Y., (CTICM), Construction métallique, n° 1-1991.

43

[1.6]

O.c

Symbols and notations

O.e.!

Symbols

(1) See Appendix A for a list of symbols used in this design handbook. Those symbols are conform to Eurocode 3. Q.C.2

[1.6.7]

Convention for member axes

(1) For steel members, the conventions used for cross-section axes are: xx along the member . generally: yy cross-section axis parallel to the flanges zz cross-section axis perpendicular to the flanges or parallel to the web . for angle sections: yy axis parallel to the smaller leg zz axis perpendicular to the smaller leg . where necessary: uu major axis (where this does not coincide with the yy axis) vv minor axis (where this does not coincide with the zz axis) (2) The convention used for subscripts which indicate axes for moments is: "Use the axis about which the moment acts." (3) For example, for an I-section a moment acting in the plane of the web is denoted M y because it acts about the cross-section axis parallel to the flanges. 0.C.3

Dimensions and axes of rolled steel sections

(1) "asymmetrical" (I and D ) and "monosymmetrical" ( [, Τ and L) rolled steel sections are shown in table 0.1.

44

0-C.4

Notations in flow-charts

(1) AU the flow­charts appearing in the present design handbook should be read according to the following rules : ­ reading from the top to the bottom, in general ­ the references to Eurocode 3 are given in [...] ­ "n.f" means that the checks are not fulfilled and that stronger sections or joints have to be selected. ­ convention for flow­charts: (FC χ)

Flow­chart number (x)

Title

,___L__, [ Assumption j

—ï—

Action: determination, calculation,

I


— 2 non-dimensional slenderness ratio calculated with a buckling length equal to the system length yield strength area of the cross-section design value of the compressive force elastic critical axial force ( = π2ΕΙ/ L2, with L = system length) factor (= Li I——, with L = system length) EI

ε: [5.2.6.2(4)]

0,5

* row 10: According to the definition of occr introduced in comment on row 8 0 , l < - ^ - < 0,25 .condition which is equivalent to

4 < a c r < 10

* row 11: The actions to be considered in first order elastic global analysis and in second order elastic global analysis are listed in the "generalities about Eurocode 3" (see the first comments on flow-chart 1) in function of the type of frame.

[5.2.4.5]

* rows 12.13.14 : - path @ : Sway moments amplified by factor 1,2 in beams and beam-to-column connections and not in the columns. The definition of "sway moments" is provided in [5.2.6.2 (5)]. - paths (5) and (6) : the introduction of member imperfections eo,d should be considered equivalent to the introduction of distributed loads along the members : eo,d Nsd

Nsd

equivalent to q Nsd

i

,; i

,

Nsd

'

,

wimiq

L

= 8.N Sd .e 0 , d / L 2

|Q = 4.N S d .e 0 < d /L Q 0 Note : the equivalence of eo,d and (q, Q) loading is proposed here for a practical point of view but it is not included in Eurocode 3.

60

comments (6/6) on flow­chart FC 1: * row 13:

Vsd

For the meaning of the ratio ——, refer to comment on row 8. "cr

* row 15:

[Annex E]

L¡,, buckling length of members for sway or non­sway mode

***

Nsd

^ .

»O

Nsd CH

Lb

* row 16:

The classification of cross-sections have to be determined before all the ULS checks of members, cross­sections and webs (rows 17 to 20).

*rows 17,18,19.20,21; The sequence of the Ultimate Limit States checks is not imposed and it is up to the designer to choose the order of the ULS checks which are anyhow all necessary to be fulfilled. On the contrary, the sequence of steps to select the type of analysis is well fixed and defined in rows 5 to 10. * row 19: When the member imperfections eo,d are used in a second order analysis (paths (D and © ) , the resistance of the cross-sections shall be verified as specified in chapter [5.4] but using the partial safety factor γηΙ in place of v mo

[5J. 1.3 (6)]

Lc

Content of the design handbook

LSLl

Scope of the handbook

(1) Actions (loadarrangements) on buildings to be taken into account in the design are presented as described in Eurocode 1 111, (2) The load cases for SLS and for ULS to be considered in the design are defined as prescribed in Eurocode 3 Part 1.1 /2/, (3) The elastic global analysis of steel structures in braced or non-sway buildings according to Eurocode 3 Part 1.1 HI is assumed to be carried out : a) by elastic global analysis of the structure to determine: . the vertical deflections of beams, the horizontal displacements of frames and vibrations of floors and, . the internal forces and moments (N, V, M) in the members and, b) by check of requirements for the Serviceability Limit States and,

61

c) by check of requirements for the Ultimate Limit States : c.l) by check of the resistance of cross-sections and, C.2) by check of the buckling resistance of members and, C.3) by check of local effects (buckling and resistance of webs) and, C.4) by check of joints and connections, for all members characterised by a class of cross-sections at ULS: . classes 1 and 2, which assume a full plastic distribution of stresses over the cross- section at the level of yield strength or, . class 3, which is based on an elastic distribution of stresses across the cross-section with the yield strength reached at the extreme fibres or, . class 4, which makes explicit allowances for the effects of local buckling appearing in the cross-section. (4) The elastic global analysis of steel bracing system according to Eurocode 3 Part 1.1/2/ is assumed to be carried out with the same hypothesis than for steel structures but with specific actions: loads and effects of global imperfections: . from the bracing system itself and, . from all the frames which it braces. (5) This design handbook deals with the analysis of braced or non-sway steel structures subject to static loading. Eurocode 3 (121) and Eurocode 8 (131) should be consulted for the following problems which are not considered here: fatigue, resistance to fire, dynamic analysis or seismic analysis. [9.1.4 (i)]

(6) No fatigue assessment is normally required for building structures except in the following cases: a) members supporting lifting appliances or rolling loads, b) members subject to repeated stress cycles from vibrating machinery, c) members subject to wind-induced oscillations, d) members subject to crowd-induced oscillations. For those fatigue problems the chapter 9 of Eurocode 3 Part 1.1 (¡If) should be consulted.

I.C.2 Definition of the braced frames and non-sway frames [5.2.5.1 (l)] (1) All structures shall have sufficient stiffness to resist to the horizontal forces and to limit lateral sway. This may be supplied by: a) the sway stiffness of the bracing systems, which may be: . triangulated frames . rigid-jointed frames . shear walls, cores and the like b) the sway stiffness of the frames, which may be supplied by one or more of the following: . triangulation . stiffness of the connections . cantilever columns

62

[Annex J]

Semi-rigid connections may be used, provided that they can be demonstrated to provide sufficient reliable rotational stiffness (see [6.9.4]) to satisfy the requirements for sway-mode frame stability (see [5.2.6]). (2) Framing for resistance to the horizontal loads and to sway. Two examples are given in table 1.3: [5.2.5.3 (i)] a) typical example of a frame with "bracing system", which could be sufficiently stiff: . for the frame to be classified as a "bracedframe" . and, to assume that all in-plane horizontal loads are resisted by the bracing system. [5.2.5.3 (2)] [5.2.5.2 (l)]

The criterion of classification as braced or unbraced frames is explained in chapter IV.g. 1.1. b) example of an unbraced frame which could have sufficiently stiff momentresisting joints between the beams and the columns: . for the frame to be classified as a "non-sway frame" . and, to neglect any additional internal forces or moments arising from in-plane horizontal displacements of the nodes of the frame. The criteria of classification as sway or non-sway frames are detailed in chapter IV.g. 1.2.

[5.2.5.2 (3). (4)] [Annex H]

Definition of framing for horizontal loads

Table L3

1) With bracing system : Γ

μ

'

AL w, ir

m

wWT

=

Γ Γ r

y

ν

r

ν

r

Γ ν ι

fl il

Η mw

mw

iiflv

BRACED FRAME

2) Non-sway frames :

*

"

Àf\

FRAME WITH BRACING

Μ

i'

AL

w mm

i'

n

63

wftrr

+

BRACING

SYSTEM

T.c.3

Summarv of the table of contents

- chapter I : . Limit States (SLS, ULS), design requirements; . flow-chart about elastic global analysis of steel frames according to EC 3. . scope, definitions; . tables of SLS and ULS checks; - chapter Π : complete set of data of the structure - chapter III : determination of load arrangements and load cases for . Ultimate Limit States and, . Serviceability Limit States - chapter IV : . frame design and, . SLS checks for frames (see chapter I.c.4). . ULS classifications of frames . braced frame condition and, . non-sway frame condition - chapter V : classification of cross-sections at Ultimate Limit States - chapter VI to LX : . SLS checks for beams (see chapter I.c.4). . ULS checks of members (beams and columns,...) submitted to internal forces and moments (N, V, M) considering the resistance of crosssections, the overall buckling of members (buckling, lateral-torsional buckling) and local effects (shear buckling of webs (V)): see chapter I.c.5 - chapter X : . ULS checks of local effects: resistance of webs to transverse forces F (yield criterion, crushing, crippling, local buckling, flange induced buckling): see chapter I.c.5 - chapter XI : ULS and SLS checks of connections. - chapter ΧΠ: design of steel bracing system I.c.4

Checks at Serviceability Limit States

(1) The table 1.4 presents the different checks which shall be fulfilled by beams and frames at Serviceability Limit States with references to the design handbook: || Table 1.4

Checks at Serviceability Limit States

Type of checks Vertical deflections of beams Beams Frames

Chapter Vm.b.l Chapter Vin.b.l

Horizontal deflections of frames

Vibration of floors

_

Chapter VlII.b.2 Chapter VIII.b.2

Chapter IV.f.l

64

Lía

Checks of members at Ultimate Limit States

(1) The following tables define the different checks which shall be fulfilled at Ultimate Limit States: - by all the members of frames submitted to internal forces and moments (N, V,M), ­ by all webs of cross­sections submitted to transverse forces F. Table 1.5

Member submitted to internal forces, moments and transverse forces

F F v

λ/f*) m

torsion

Ncompression C _r

- ï » 3£„

XX

._ y¡ Π

^

fl

x?* . lvlbendin^\ V intension

"

Λ *U*

Al>

fi..

^.Ncompression Μ , * ^ η 1

±fi «w-r™

U 0 M bending x f -^tension

IF Note:

[5.4] [5.4] [5.4] [5.4] [5.7] [5.7]

[5.3] [5.5] [5.5] [5.6] [5.7] [5.7]

*) the effects of torsion are not considered in the handbook because the Annex G of Eurocode 3 is not officially available yet.

taMe 1,6

Definition of the planes of cross-sections within internal forces, moments (Nsd, Vsd, Msd) and transverses forces Fsd are acting.

table 1.7:

For different types of loading on the members and on the Webs (tension, compression, bending, combined (N,M), transverse forces) the table 1.7 provides the internal forces, moments (N (Ntension» Ncompression). V (Vy,Vz), M(My,Mz)), transverse forces (F) and interactions between them ((V,M),(N,M),(N,V),(N,V,M),...) to be checked at Ultimate Limit States.

table 1.8:

List of references to the design handbook related to all the check formulas at Ultimate Limit States, for different types of loading. The different types of loading on the members and on the webs includes internal forces, moments, transverse forces and interactions between them (see also the more detailed table 1.7). Two types of ULS checks are defined (resistance of cross­sections and stability of members or webs) and refer to the following physical phenomena: . (R) resistance of cross-sections: . tension . compression .shear . bending . resistance on webs to transverse forces . crushing of webs to transverse forces . (5) stability of members or webs (global and local buckling): . local buckling for class 4 cross­sections . Ν buckling and N­M buckling of members . lateral­torsional buckling of members . shear buckling of webs . stability of webs to transverse forces: crippling, buckling . web buckling induced by compression flange

65

The formulas of ULS checks include different parameters depending on the class of the cross-section (see chapter V); they may consider the following cross-section properties: . plastic properties for class 1 or 2 cross-section (Wpf, ...) . elastic properties for class 3 cross-section (We/ ,...) . effective properties for class 4 cross-section (Weff,...) taking into account the occurrence of local buckling. The table 1.8 is related to the classes of cross-section and shows if there are differences between check formulas in function of those classes of crosssection. In Appendix D of the design handbook a similar table (table D.l) is provided (for information) presenting a list of references to Eurocode 3 Part 1.1 (J2f) also related to all check formulas at Ultimate Limit States for different types of loading. (2) In respective following chapters tables present complete lists of the checks to be performed at Ultimate Limit States for members or webs submitted to different loading: in chapter VI, table VI. 1 for members in tension, in chapter VH, table VILI for members in compression, in chapter VIH, table VIILI for members in bending, in chapter LX, table IX. 1 for members with combined axial force and bending moment. Planes within

Table 1.6

H

internal forces, moments (N$d, Vsd, Msd) and transverses forces Fsd are acting

Fsd

Í tP

ers ([5.5]) or we)bs ([5.6Π5.7])

68

II

STRUCTURAL CONCEPT OF THE BUILDING

(1) This chapter intends to list the data of the analysed building concerning the types of structure, members and joints, the geometry and the material properties. The load arrangements applied to the building are defined in chapter m . II.a

Structural model

(1) The type of structure, the type of the bracing system and all the different prescriptions of the project (office building, housing, sport or exhibition hall, parking areas,....) should be defined.

Ill)

Geometric dimensions

(1) The geometry of the building should be defined: - the height, the width and the length of the structure, the number of storeys of the building and the dimensions of the architectural element. - definition of storeys: plane frame with 3 storeys:

II.C

Non structural elements

(1) All the elements of the building which do not bear any loads have to be considered in the evaluation of the self-weight loads: walls, claddings, ceilings, coverings,...

I I.d

Load bearing structure

(1) All the elements which bear the loads should be defined : frames, beams, columns, bracing system, concrete core,....

69

Joints Il.e (1) The design handbook assumes the use of pinned or rigid joints (see chapter XI). Semi-rigid joints are not considered in the design handbook. In the case of semi-rigid joints whose behaviour is between pinned and rigid joints, the designer shall take into account the moment-rotation characteristics of the joints (moment resistance, rotational stiffness and rotation capacity) at each step of the design (predesign, global analysis, SLS and ULS checks). The semi-rigid joints should be designed according to chapter 6.9 and the Annex J of Eurocode 3. Table ILI presents typical types of joints. Typical types of joints

Table 11.1

Pi

r^

0 0 0

o

0 0

0

i S S v - S l * ν î-

PINNED Joint

71

Φ

n.f

Profiles

(1) The selected steel profiles used as beams and columns in the structure and as elements in the bracing system should be listed and precisely referred.

n.g

Floor structure

(1) Composition of the floor system (in situ concrete slab, precast concrete slab, steel sheet deckings, slim floor,...) is needed to determine the self-weight loads. Composite effect between the floor and the beams is not considered in this design handbook.

Il.h

Material properties

[3]

(1) The material properties given in this chapter are nominal values to be adopted as characteristic (unfactored) values in design calculations.

[3.2.2.1]

n.h. 1

Nominal values for hot rolled steel

(1) The nominal values of the yield strength fy and the ultimate strength fu for hot rolled steel are given in table II.4 for steel grades S 235, S 275 and S 355 in accordance with EN 10025 and for steel grades S 275 and S355 in accordance with EN 10113. (2) The european standard EN 10025 specifies the requirements for long and flat products of hot rolled weldable non-alloy structural steels (steel grades: S 235, S 275, S 355). The european standard EN 10113 specifies the requirements for long and flat products of hot rolled weldable fine grain structural steels (steel grades: S 275, S 355, S 420, S 460). (3) Similar values as defined in table Π.4 may be adopted for hot finished structural hollow sections. (4) For a larger range of thicknesses the values specified in EN 10025 and EN 10113 may be used. (5) For high strength steels (S 420 and S 460) specific rules are given in the normative Annex D of Eurocode 3. Their material properties are introduced in table Π.4. (6) The table Π.3 compares the symbolic designations of steel grades according to various standards. The design handbook always uses the single designation of structural steels defined by the european standard EN 10027-1: "S" followed by the value of yield strength expressed in N/mm2 (=MPa). Comparison table of different steel grades designation

Table II.3 EN 10027-1

S 235 \ S275 S 355 S 420 S 460

EN 10113

FeE 275 FeE 355 FeE 420 FeE 460

EN 10025 NF A 35-504/ NF A 35-501 DIN 17102 DIN 17100 BS 4360 ASTM NF A 36-201

Fe 360 Fe 430 Fe 510

E 24 E 28 E 36

E 355 E 420 E 460

72

StE285 StE355 StE420 StE460

St 37-3 St44-3 St 52-3

40 D 43 D 50D 55 C

gr. 50 gr. 60 gr. 65

Table H.4

Nominal values of yield strength fy and ultimate tensile strength fu for structural steels according to EN 10025 and EN 10113 Thickness t (mm)*)

Nominal steel grade EN 10027-1 Designation S 235 S 275 S 355

EN 10025 Standard Fe 360 Fe 430 Fe 510 EN 10113 Standard FeE 275 FeE 355 S 420 M S 460 M

t2b

b < h < 2b | Ze = h

h 2h 22; The sequence of the Ultimate Limit States checks is not imposed and it is up to the designer to choose the order of the ULS checks which are anyhow all necessary to be fulfilled. On the contrary, the sequence of steps to define the assumptions for the global analysis (row IS) is well fixed and defined in rows 8 to 14.

95

[2.3.2.4]

I V.b Static equilibrium (1) For the verification of static equilibrium, destabilizing (unfavourable) actions shall be represented by upper design values and stabilizing (favourable) actions by lower design values. (2) For stabilizing effects, only those actions which can reliably be assumed to be present in the situation considered shall be included in the relevant combination. (3) Variable actions should be applied where they increase the destabilizing effects but omitted where they would increase the stabilizing effects (γς> = 0, in table III.8). (4) Account should be taken of the possibility that non-structural elements might be omitted or removed. (5) For building structures, the normal partial safety factor given in table ΓΠ.8 of chapter ΙΠ apply to permanent actions (YG = 1,0 if favourable actions). (6) Where uncertainty of the value of a geometrical dimension significantly affects the verification of static equilibrium, this dimension shall be represented in this verification by the most unfavourable value that it is reasonably possible for it to reach. I V.c

Load arrangements and load cases

r v . c l Generalities (1) Load arrangements which may be applied to buildings are provided in chapter ULb. (2) Load cases (see chapter ni.c) may be established according to two procedures to study structures submitted to actions: a general procedure presented in flow-chart FC 3.1 (chapter ΠΙ) or, a particular procedure presented in flow-chart FC 3.2 (chapter ΠΓ) which is applicable for braced or non-sway buildings because such structure may be studied by first order elastic global analysis. (3) Two types of load cases shall be considered: load cases for Serviceability Limit States and, load cases for Ultimate Limit States, where differences are related to combination rules: see table ΓΠ.7 for SLS combinations of actions see table ΙΠ.8 for ULS combinations of actions rv.c.2 Frame imperfections [5.2.5.3 (4)] (1) In case of braced frame global imperfections are not necessary for the design of the braced frame itself but they shall be taken into account in the design of the bracing system (see chapter XII). (2) In case of non-sway frame global imperfections are needed for the design of the frame. [5.2.4.1 (l)] (3) Appropriate allowances shall be incorporated to cover the effects of practical imperfections, including residual stresses and geometrical imperfections such as lack of vertically, lack of straightness due to welding or lack of fit and the unavoidable minor eccentricities present in practical connections. [5.2.4.3 (l)] (4) The effects of imperfections shall be allowed for in frame analysis by means of : - an equivalent geometric imperfection in the form of an initial sway imperfection φ or, - equivalent horizontal forces according to table IV.3, either method is permissible. (5) As shown in table IV.3 the initial sway imperfections of a frame are directly proportionate to the relevant applied vertical loads of each load case. Therefore global imperfections of a frame should be calculated for each load case.

96

Global imperfections of the frame

Table IV.3

Initial sway imperfections φ of the frame

equivalent horizontal forces

ECCS ηβ65 table 5 J

F2 1 i i i ·

tel

φΡ2

Fi '

φ Fi

•

l i l i -

■ νy

φ (Fi + F2)

^

' •

φ (Fi + F2)

[5.2/4.3 (4)] (6) The initial sway imperfections φ apply in all horizontal directions but need only be. considered in one direction at a time. The table IV.4 gives the numerical values for φ: φ = k c ks φ 0

[form. (5.2)]

where

Φο=

Ξ55'

k c =Jo,5 + — < 1,0 and V

nr

k g = j 0 , 2 + — .M y

Values of d, tw , c, and tf are defined in table V.2

ε = ^2357Τι

^\MZ

+ : stresses m compression ­ : stresses in tension

fv (N/mm2) ε (if t < 40 mm) ε(ΐί40πιηι_

-■ +

Ν

Φ

b

Aeff

tf

1

t. ε 56,8

Il Il Il

II II II

Aeff

*"

Members in bending (My, Mz)

I

+

I

Φ

p

b 1 t-ε 138,8

i

b

_b£> Φ ^

®-b©

T- ®

6 p

=t°' '

b 1 ί.ε 18,6

kl

φ

b 1 ί.ε 21,4

Φ

b 1 ί.ε 138,8

3D

ε = ^/2357Γ5

118

weff

Weff

T- p ®' b © fb©

ft

Weff

°' 6 -P©+ b © 235

ε (if t < 40 mm) ε (if 40 mm < t < 100 mm)

®4-Γ b©(

-Ζ£ ρ ® : ω

b 1 ι.ε 56,8 fy (N/mrn^)

°'4-Pn

(1) For members in axial tension the design value of the tensile force Nx.sd at each cross-section shall be checked for net section rupture at holes for fasteners : I5A3(1)1

[54.2.2]

N

x.Sd^Nu.Rd =

0*9 A net f „ ΎΜ2

where Nu.Rd is the design ultimate resistance of the net cross-section, A net is the net area of a member or element cross-section with appropriate deductions for all holes and other openings (see table VI.2), f„ is the ultimate tensile strength (see table II.4), 7Ki2 is a partial safety factor (see table 1.2). IF Table VL2 Note:

Gross and net cross-sections -A = gross cross-section - Anet = net area of cross-section

l) Non staggered, holes ; Νx.Sd

Nx.Sd

A = section 1-1 Anet = section 2-2 2Ί Staggered holes :

Ii2 -1— I

Νx.Sd

■*—&"-rit l

Νx.Sd

' i

—φ—(f-f1 • i . rÅ. ­A = section 3­3 ­ Anet = smaller of (section 1­1; section 2­2) 3) Angles with holes in both legs :

C ; spacing of the centres of the same two holes measured perpendicular to the member axis

125

VI.C [5.4.3 (3)]

Particular verifications at ULS for angles connected by one leg

(1) In these particular cases the effects of eccentricities in the connections may be neglected with the following considerations of this chapter. Those considerations should also be given in a similar way to other types of sections connected through outstands such as T-sections ( Τ ) and channels ( [ ). (2) The flow-chart FC 6.2 intends to present the particular cases of this chapter. VI.c.l

Connection with a single row of bolts

[6.5.2.3 (2)] (1) Angles in tension (N x .sd) connected by a single row of bolts in one leg may be treated as concentrically loaded with the following requirements : for a 1 bolt connection

Nx.sd £ N u . R d

for a 2 bolts connection

N

for a 3 bolts connection :

Nx.sd ^ Nu.Rd

where

NujRd &2 do t fu ΎΜ2 ß2, ß3 Anet

ECCS n° 65 table 5.33

2,0(e2-0,5d0)tfu ΎΜ2

A f x.Sd^N u - R d _ ß 2 n e t u

5

YM2

_ ß3 A n e t f u » ΎΜ2

is the design ultimate resistance of the net section, is the edge distance from the center of a fastener hole to the adjacent edge of the angle (see table VI.4), is the hole diameter, is the material thickness, is the ultimate tensile strength (see table Π.4), is a partial safety factor (see table 1.2), are reduction factors dependent on the pitch p i (see table VI.3), is the net area of the angle (see table VI.4) : - if unequal-leg angle connected by its smaller leg, then A n e t = net section area of an equivalent equal-leg angle of leg size equal to that smaller leg, - or, in other cases (equal-leg angle or unequal-leg angle connected by its larger leg) : A n e t = the net section area of the angle.

Table VI.3

Reduction factors & and/k

Pitch

pi

< 2,5 do

3,3 do

3,75 do

4,2 do

>5do

2 bolts

ß2

0,4

0,5

0,55

0,6

0,7

3 bolts and more

ß3

0,5

0,6

0,7

For intermediate values of pi the values of ß 2 and ß3 may be determined by linear interpolation.

126

Table VL4 1)

Connection of angles

Parameters for bolted connections : t

4

Nx.Sd

N.x.Sd

O-O ** m

» m-

Pi Pi 2)

Sf e

i

An»t. net area of the bolted angle : 2.1) if unequal­leg angle connected by its smaller leg

-τι

£ o

-e

^

2.2) if unequal­leg angle connected by its larger leg or if equal­leg angle

-II - j j

L &

"Θ

\ .

3)

A. cross­sectional area of the welded angle : 3.1) if unequal­leg angle connected by its smaller leg : b

c

((((((((((((((((

~lr

I

ΙΓΓΓΓΓΓΓΓΓΓΓΓΓΤΤΠ

3.2) if unequal­leg angle connected by its larger leg of if equal­leg angle b^,

h

l i "Tí {

ί

ffrrrrrrtrrrrrrr.

Τ

{πτΤΤΓΓΓΓΓΓΤΤΤΤΤΓ

127

VI.C.2 [6.6.10(2)]

Connection bv welding

(1) Angles in tension (Nx.sd) welded by one leg may be treated as concentrically loaded with the following assumptions : N x .sd^N u.Rd where

Af, YMO

Nu.Rd

is the design ultimate resistance of the cross-section,

A

is the cross-sectional area of the angle (see table VI.4) : - if unequal-leg angle welded by its smaller leg then A = the gross cross-section area of an equivalent equal-leg angle of leg size equal to that of the smaller leg, - or, in other cases (equal-leg angle or unequal-leg angle welded by its larger leg) : A = the gross cross-section area of the angle,

fy

is the yield strength (see table Π.4),

YMO

is a partial safety factor (see table 1.2).

128

ΥΠ

MEMBERS IN COMPRESSION (Ncompression)

VJl.a

Generalities

(1) For each !oad case (see chapter ΙΠ) the global analysis of the frame (see chapter IV) determines the design value for the following internal force which is applied to members in compression and which shall be checked at ultimate limit states:

i£

3* -

χ -

Ν x.Sd

..-y X

&

(2) The flow-chart FC 7 presents the general procedure to check members in compression at ultimate limit states (see the following page).

(3) The table VILI provides a list of the checks to be performed at Ultimate Limit States for the member submitted to axial compression (Ncompression)· A member shall have sufficient bearing capacity if all the checks (from (J)(l) to (J)(9)) are fulfilled. Several checks (from (T)(3) to φ ( 9 ) ) concern particular cases with specific conditions. All the checks have both references to Eurocode 3 and to the design handbook.

129

Flow-chart (FC 1) : Members in compression (Ncompression)

rows:

ί Determine ULS load cases J

1

Τ

ULS checks C

!T~¡

\

Select beam size (A, 1,1) and steel grade (fy)

,

·

χ.

\

­r .^

\

Γ7Τ

Select stronger section

^

ρ

—

ί Determine the design tensile force from global analysis of the structure: Nsd J i Classify the cross-section in compression J ι

ι

/■

'

\ r

ι Class 1, 2 or 3 cross-section κ·—I Class of cross-section

)

I

'

I

T

V

J

f—

~ι

Calchiate the design compression resistance of the cross-section: NcRd

yes/ \ 1

,

Determine the buckling length Lb of the member for each axis : Lb.y, Lb.z

Bisymmetrical cross-section?

Determine additional bending moment ΔΜ = Ν . e N to be checked with (N,M) interaction

±Z

ί Class of cross-section J

__J"

I

Calculate the shift of centroidal axis: e^

ι

Buckling resistance of the member

ι

J

1 of cross-section Calculate effective area Aeff and ratio β A = Aeff/ A

Nsd < NcRd yes j ι

π Class 4 cross-section ι L

X ι

1

1 r--*

τ

ι Class 1,2 or 3 cross-section ι ι Class 4 cross-section ι _ _ -

s

f

,

1

3

Calculate the non-dimensional slenderness ratio λιοί the member for each buckling axis: λy, λζ

1

Q Multiply λy and λζ by VßÄ )

C

ι Select appropriate buckling curvei

*

t

J

'

1

I Determinere reduction factor χ for each buckling axis: χ , χ J j,

ï

1

Is

r «I

Calculate the design buckling resistance ¡of the member Nb.Rd for each buckling axis: Nby.F(d, Nbz.Rd

t

ί Multiply Nby.Rd and Nbz.Rd by βΑ J -

no 23

yes j

Γ Adopt section J 24

130

Table VILI

List of checks to be performed at ULS for the member in compression IN compression)

(ï) Axia| compressive force N* M : ** General cases: (1) Resistance of cross-section to Nxsd ■' [544(1)J

Nx.Sd — Nc.Rd (design compression resistance of the cross-section J

(2) [Annex G] [Annex G]

[54.8.3 (2)]

Vn.c.l (1)

Stability of member to Nxsd ■' Nx.Sd ^ NbJld (designflexuralbuckling resistance of the member)

[5.5.1.1 (1)J

References :

and, Nx.sd ^ design torsional buckling resistance of member and, Nx.sd ^ design flexural­torsional buckling resistance of member ** Particular cases: (3) Resistance of cross-section to Nxsd, if class 4 monosymmetrical cross-section: interaction (Nx.sd, AMy.sd, AMz.sd) ^ 1 w h e r e A M s d = N X .sd-eN (= additional moment due to the eccentricity of the centroidal axis of the effective cross-section, eN)

Vn.c.2.1 (2) Vn.c.2.2 Vn.c.2.2

Vn.d.l (1) ■

(4) Stability of member to Nxsd if class 4 monosymmetrical crosssection: [5.54(5)]

interaction (Nx.sd , AMy.sd, AMz.sd) ^ 1

Vn.d.2 (1)

where AM$d = N x .Sd-CN (= additional moment due to the eccentricity of the centroidal axis of the effective cross-section, eN)

(5) Stability of member to Nxsd if class 4 monosymmetrical cross-section, i/cN.y

*0and,

if λ w > 0,4 (potential lateral-torsional buckling): Vm.e.2 (3)

[53.2(7)] [5.5.4 (6)]

interaction (Nx.sd » AM y .sd, AMz.sd) ^ 1

Vn.d.2 (2)

where AMsd = N x .sd-6N (= additional moment due to the eccentricity of the centroidal axis of the effective cross-section, e^)

(6) [6523 (2)]

Resistance of net cross-section to Nxsd if angle connected by a single row of bolts in one leg: N x .Sd ¡» Nuüd (design ultimate resistance of the net cross-section, Α,,^)

considering the following cases for determination of Anet: - either, if unequal­leg angle connected by its smaller leg: Anet = the net section area of an equivalent equal­leg angle of leg size equal to that of the smaller leg, ­ or, in other cases (equal­leg angle or unequal­leg angle connected by its larger leg) : Anet = the net section area of the angle (checks nr φ to be continued)

131

Vn.e.l.l(l)

Table VILI

List of checks to be performed at ULS for the member in compression (■N compression)

(T)

References :

Axial compressive force Nr- KA :

** Particular cases: (continuation) (7) Stability of member to Nx_sd if angle connected by a single row of bolts in one leg: N x .Sd— Nb.Rd (design flexural buckling resistance of the member considering the gross cross­sectional area of the angle, A)

[6.5.2.3 (3)]

VILe. 1.2 (1)

w i t h Nbjid ^ N u .Rd (design ultimate resistance of the net cross­section presented in φ(6))

Resistance of cross-section to Nx¿d if angle connected by welding in one leg:

(8) [6.6.10(2)] [6.6.10(3)]

N x .Sd — N u .Rd (design ultimate resistance of the cross­section, A)

Vn.e.2.1 (1)

considering the following cases for determination of A: ­ either, if unequal­leg angle connected by its smaller leg: A= the gross cross­section area of an equivalent equal­leg angle of leg size equal to that of the smaller leg, ­ or, in other cases (equal­leg angle or unequal­leg angle connected by its larger leg) : A= the gross cross­section area of the angle (9)

[6.6.10(3)]

Stability of member to Nxsd if angle connected by welding in one leg: Nx.Sd — Nbj^d (designflexuralbuckling resistance of the member considering the gross cross­sectional area of the angle, A)

VILb

Vn.e.2.2 (1)

Classification of cross­sections

(1) At ultimate limit states the resistance of cross­sections may be limited by its local buckling resistance. In order to take into account that limitation the different elements (flange, web) of the cross­sections shall be classified according to the rules defined in chapter V. (2) For cross­sections submitted to uniform compression (Nx.sd) the classification may specifically be determined according to the procedure defined in chapter V.d.l.

132

VILe

General verifications at ULS

VII.C. 1 Resistance Of CrOSS-SeCtion tO Ncompression

[544 (1)]

(1) For members in axial compression, the design value for the compressive force Nx.sd at each cross-section shall satisfy: N

c.Rd depending on classes of cross-section:

[form. (5.16)]

Nx.Sd ^

N

cRd

where N c R d Νp£Rd A Aeff fy ΎΜ0.ΥΜ1

[5.44 (5)]

Class 1,2 or 3 Af v = Npf.Rd=-^ ΎΜΟ

class 4 _ Aeff f y YMI

is the design compression resistance of the gross cross-section, is the design plastic resistance of the cross-section, is the area of the gross cross-section, is the effective area of the cross-section (see chapter V), is the yield strength (see table Π.4), are partial safety factors (see table 1.2).

(2) Fastener holes need not to be allowed for in compression members, except for oversize and slotted holes. VII.C.2 Stability of member to Nœmpiession (1) The stability of members submitted to concentrical compressive force shall be checked according to the following buckling modes : flexural buckling, torsional buckling and flexural-torsional buckling. VII.c.2.1 Resistance toflexuralbuckling

(1) The compression members shall be checked to flexural buckling mode (buckling by plane bending) according to both principal axes of the section (major axis: yy; minor axis: zz) with the appropriate buckling lengths (Lb.y, LD.z). [53.1.1 (l)] (2) For members in axial compression the design value of the compressive force Nx.sd shall satisfy: Nb Rd depending on classes of cross-section: [form. (5.45)1

N

X.Sd ^ Nby.Rd

Nx.Sd ^ Nbz.Rd

Class 1, 2 or 3 _ Xy A f y

Class 4 _ Xy Aeff fy

ΎΜΙ _ XZ A f y

ΎΜΙ _ XZ Aeff f y

ΎΜΙ

ΎΜΙ

where N ^ j ^ , N b ^ R d , Nbjid are the design buckling resistances of compression member about y and ζ axes, and in general, Xy, Xz are the reduction factors for the buckling mode about y and ζ axes, A is the area of the gross cross-section, Aeff is the effective area of the cross-section (see chapter V), is the yield strength (see table Π.4), ΎΜ1 is a partial safety factor (see table 1.2).

133

[5.5.1.2 (i)] (3) For constant axial compression in members of constant cross-section, the value of χ (Xy> Xz ) is related to the appropriate non-dimensional slenderness λ ( λ γ , λ ζ ) : [form. (5.46)]

x = f(A) =

ι2 Φ+νψ -λ?

, buttø 69ε :

table Vm.7

Vz.Sd — VbaUd (design shear buckling resistance)

Vm.d.2 (5)

Resistance of cross-section to MsdM s d ^ McRd (design uniaxial bending moment resistance of the cross­section)

VDI.e.1 (1)

Stability of member to Mysd >if ^LT > 0,40 :

Vm.e.2 (3)

My.Sd — Mb.Rd (design lateral­torsional buckling resistance moment of the member)

VDI.e.2 (4)

Biaxial bending moments (My sd. Mz