Eurocode 3 Simplified

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

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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

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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.

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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)

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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.

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1. conceptional rype of structure different braced non sway structures <, 20 storeys

: Classification non­sway: Vsd / VCT <, 0.1 braced: φ h £ 0.2 φ ^

I

2. occupancies types of occupancy

­ ware house ­ office building ­ industrial hall

*

3.shape shape of the building

(

Basis of design. Imposed loads on floor and roofs

^

■cEC 1: Wind loads, Snow loads

Τ

4. structural concept structural model Geometric dimensions Non­structural elements Load bearing structure Joints Profiles

3 }

EC 3: Non­sway

Product standards: EN 10025, EN 10113 EC 3 ­> b /1 classification

Floor structure Material properties 5. action effects determination of the action effects (global and local)

EC 1: Load cases EC 3: Load combinations

elastic or plastic model SLS

ULS

I

6. dimensioning and verification SLS limits ULS limits Frame stability deformations vibrations Static equilibrium Resistance of cross section

EC 3: Imperfections EC 3: Modelling depending on b /1 classification 1 s t order analysis

V_

• tension • comprei»ion • bending moment

- bending montent vid »hear · bending momtia and axial force - bending moment, sbear and axial force

- abear

· transverse farces c a webs

- ine ar boe kl mg

Resistance of members (stability) • compression members : bocfcling - lateral torsional buckling of beams - bending and axial ami ion • bending and axial compresaseli

Legend Keywords Γ I Requirement & References

)

C Object

Connection

I

- joints • base of colorons

Exercise 1. Verification of an existing braced non­sway structure Figure 1

15

I

1. conceptiqnal type of structure non­sway wind bracing in a building (latticed structure )

EC 3: Classification non­sway :VSd / VCT <, 0.1 1 s t order theory

. Τ .„ 2. occupancies part of an office building

EC 1: Basis of design, vertical loading m Horizontal loading

3. shape ­ position in the building ­ locations from load introduction and con­ nections from floors, roofs, claddings etc.

J

4. structural concept structural model Geometric dimensions Non­structural elements Joints Profiles

Vertical f orces from gravity loads, imposed loads, snow and wind loads Horizontal forces from wind, imperfections

EC 3: Non­sway Product standards: EN 10025, EN 10113 EC 3 ­> b / 1 classification

Material properties

J 5. action effects

EC 1: Load cases EC 3: Load combinations

determination of the action effects (global and local)

EC 3: Imperfections EC 3: Modelling depending on b / 1 classification

elastic or plastic model SLS

ULS

1 s t order analysis

6. dirnehsioning and verification SLS limits ULS limits deformations Frame stability vibrations Static equilibrium Resistance of cross section - tension - compression • bending moment - shear

- bending moment and shear - bending moment and axial force - bending moment, shear and axial force - transverse forces on webs ■ shear buckling

Resistance of members (stability) - compression members : buckling - lateral torsional budding of beams - bending and axial tension - bending and axial compress ion

Legend Keywords WÊÉBÊÊ Requirement & References

C Object

Connection -joints • baae of columns

Exercise 2.Verification of a non­sway wind bracing in a building Figure 2

16

1. conceptional type of structure Braced non sway structure (defined)

I

2. occupancies types of occupancy (defined) - office building 3. shape shape of the building (defined)

1

J

4. structural concept structural model Geometric dimensions (defined) Non-structural elements (not defined) Load bearing structure (not defined) Type of joints (defined) Profiles ( not defined) 7. optimisation of the weight Floor structure (not defined) Material properties (not defined)

Profiles: - max 3 different profiles for the columns Type of joints: - hinged or rigid connections Steel: FeE 235 or FeE 355 or FeE 460 grades

I

5. action effects determination of the action effects (global and local) elastic or plastic model SLS

t

ULS

6. dimensioning and SLS limits deformations vibrations

t

verification ULS limits Frame stability Static equilibrium Resistance of cross section and axial force abear and axial force

■ compression

- sbear bedding

Resistance of members (stability) - cflfupyraHin membera ι bockung - lateral torsional bedding of beams • ^"Hiraj and axial tension * bending and axial compresiion

Connection •joints

- base of columns

Exercise 3.Design of a braced non-sway structure Figure 3

17

plane view

lift

Χ

front view Ν ζ

!

II

ce

I CA

C

Reference number 2 6 7 9 10 13

Engineering office

n°

X Y storeys Joints n= (m) (m) Adem 1 30 10 5 Rigid Rambøll, Hannemann & Højlund 2 30 10 15 Rigid Veritas 3 50 14 10 Hinged Socotec 4 50 14 15 Hinged Sofresid 5 50 18 20 Rigid Danieli 6 50 18 15 Hinged Exercise 3 : Type of building to be designed Figure 4

18

Eurocode 3 Formulae References

···· · i

Λ. C« · ■ ·

1. Conceptional type of structure. 1.1. non-sway ­> Chapter 5.2.5.2 1.2. braced ­> Chapter 5.2.5.3 1.3 storeys 2. Occupancies. 2.1. Type of building, (category,...) 2.2. Imposed loads on floors and roof (p and P) ­> Chapter EC 1, part 2.4: Imposed load 3, Shape, 3.1. Wind loads fw) ­> Chapter EC1 Part 2.7: Wind loads. 3.2. Snow loads (s) ­> Chapter EC1 Part 2.5: Snow loads. 4. Structural concept. 4.1. Structural model. 4.2. Geometric dimensions. 4.3. Non structural elements. 4.4. Load bearing structure. 4.5. Joints. 4.6. Profiles. 4.7. Floor structure. 4.8. Material properties. 5. Action effects. 5.1. Load cases. ­> EC1. ­ permanent loads: g and G ­ variable loads: q and Q: ­ imposed loads: ρ and Ρ (presentparagraph 2.2.) - wind loads: w (presentparagraph 3.1.) - snow loads: s (presentparagraph 32.) 5.2. Load combinations. ­> EC3. SLS: -> Chapter 2.3.4 clause (5), formulae (2.17) and (2.18) ULS: ­> Chapter 2.3.3.1 clause (5), formulae (2.11) and (2.12) 5.3. Imperfections. -> EC3. Frame : ­> Chapter 5.2.4.3 clause (1) formula (5.2) Bracing system: ­> Chapter 5.2.4.4 clause (1) formulae (5.3) and (5.4) [Members : ­> Chapter 5.2.4.2. clause (4) formula (5.1)7 5.4. Elastic or plastic model -> EC3: Chapter 5.3: classification of cross­sections (b/t ratios). Flange: ­> table 5.3.1 (sheet 3) Web: ­> table 5.3.1 (sheet 1) ­> Chapter 5.4.6 clause (7) shear buckling => (presentparagraph 72.9 ) Section: ­> Chapter 5.3.4 for elastic global analysis ­> Chapter 5.3.3 for plastic global analysis Figure 5

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Eurocode 3 Formulae References 6. Verification SLS. -> Chapter 4 6.1. Global analysis. -> beams, portal f rames,structural frames Calculation for - > bracing system δ vertical and δ horizontal 6.2. Deformations. 6.3. Vibrations.

-> Chapter 4.2.2 clause (1) δ vertical table 4.1, figure 4.1 clause (4) δ horizontal -> Chapter 4.3. (ECCSpublication n°65: table4.4;... ;

7. Verification ULS. 7.1. Global analysis.

= > internal forces: Μ, Ν and V - Elastic analysis -> Chapter 5.2.1.3 - Plastic analysis -> Chapter 5.2.1.4 - 1st or 2nd order analysis (present paragraph 1.1 ) 7.2. Resistance of cross-sections. -> Chapter 5.4 7.2.1. tension. -> Chapter 5.4.3 clause (1) formula (5.13) 7.2.2. compression.^ Chapter 5.4.4 clause (1) formula (5.16) 7.2.3. bending moment.-> Chapter 5.4.5 -> Chapter 5.4.5.1 clause (1) formula (5.17) clause (2) formula (5.18) f Ύ -> Chapter 5.4.5.3 clause(l) formula(5.19) => A v n e t > -2- ,­iÖ­ U

' Mo

0.9

(remark: y m factors should be ignored) 7.2.4. shear. ­> Chapter 5.4.6 clause (1) formula (5.20) clause (2): Ayz Avy: ECCS publication n°65: table 5.14 clause (8) formula (5.21) clause (9) 7.2.5. bending and shear. -> Chapter 5.4.7 clause (2) clause (3) a), b) formula (5.22) for cross­sections with unequal flanges: M S d Rd + (Mp 1>Rd ­ Mf >Rd )1 ­

VSd ­ 1 'pl,Rd

^Mc,Rd

7.2.6. bending and axial force. Class 1 and 2 cross-sections: -> Chapter 5.4.8.1 clause (3) clause (4) formulae (5.25) and (5.26) clause (11) formula (5.35) Class 3 cross-sections: -> Chapter 5.4.8.2 clause (1) formula (5.37) 7.2.7. bending, shear and axial force. -> Chapter 5.4,9 clause (2) clause (3) ­> biaxial bending: (ECCS publication η °65: tables 5.15 and 5.16) Figure 6

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Eurocode 3 Formulae References 7.2.8. transverse forces on webs. -> Chapter 5.4.10 clause (3) -> clause (1) formula (5.41) clause (2) formula (5.42) figure 5.4.3 or -> clause (4) formula (5.43) clause (5) formula (5.44) -> Chapter 5.7.1 clause (3) figure 5.7.1 (a) clause (4) figure 5.7.1 (b) clause (5) -> Chapter 5.7.2 clause (3) figure 5.7.2 -> Chapter 5.7.3 Crushing clause (1) formulae (5.71) and (5.72) ƒ clause (4) formula (5.74) J -> Chapter 5.7.4 Crippling clause (1) formula (5.77) clause (2) formula (5.78) -> Chapter 5.7.5 Buckling clause (1) formula (5.79) clause (3) figure 5.7.3 7.2.9. shear buckling. -> Chapter 5.6.1 clause (1) limit condition (present paragraph 5.4 ) 7.2.10 flange-induced buckling. -> Chapter 5.7.7 ECCS publication n °65: table 520 7.3. Resistance of members. (->for 1 st order analysis) 7.3.1. compression members: buckling. -for 1 st order elastic analysis: -> Chapter 5.5.1.1 clause (1) formula (5.45) -> Chapter 5.5.1.2 clause (1) formula (5.46) with table 5.5.1, or table 5.5.2 -> Chapter 5.5.1.4 clause (1) table 5.5.3 clause (3) formula (5.47) -> Chapter 5.5.1.5 clause (2) Annex E - for 2 "d order elastic analysis: -> 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 a
ci ) eo,d

designation of a buckling curve throat thickness of filllet weld geometrical data of the effects of actions geometrical data for the resistance design throat thickness for submerged arc welding designation of a buckling curve distance between fastener holes and edge accidental action; area of building loaded by external pressure of wind; area of gross cross-section effective area of class 4 cross-section effective area of class 4 cross-section subject to uniform compression (single N x .sd) effective area of class 4 cross-section subject to uniaxial bending (single My.sd or single M z .sd) net area of cross-section reference area for C f (wind force) tensile stress area of bolt shear area of cross-section effective shear area for resistance to block shear shear area of cross-section according to yy axis shear area óf cross-section according to zz axis designation of a buckling curve; flange width; building width effective breadth design punching shear resistance of the bolt head and the nut designation of a buckling curve; out stand distance altitude factor for reference wind velocity dynamic factor for wind force direction factor for reference wind velocity exposure coefficient for wind pressure and wind force wind force coefficient external pressure coefficient for wind pressure roughness coefficient for determination of c e topography coefficient for determination of c e temporary (seasonal) factor for reference wind velocity nominal value related to the design effect of actions factors for determination of F v jyc factors for determination of MC T designation of a buckling curve; web depth bolt diameter mean diameter of inscribed and circumscribed circles of bolt head or nut hole diameter shift of relevant centroidal axis of the class 4 effective cross-section subject to uniform compression (single N x .sd) shift of the y centroidal axis of the class 4 effective cross-section subject to uniform compression shift of the ζ centroidal axis of the class 4 effective cross-section subject to uniform compression shift of relevant centroidal axis of the class 4 effective cross-section subject to uniaxial bending (single My.Sd or single Mz.Sd) equivalent initial bow imperfection design value of equivalent initial bow imperfection

ei, e2 E ECCS ECSC

distance between hole fastener and edge modulus of elasticity or Young Modulus; effect of actions at SLS European Convention for Constructional Steelwork European Community of Steel and Coal

Aeff Atff.N Aeff.M Anet A re f Ag Av Av.net A v .y A v .z b beff Bp.Rd c CALT

ca DIR ce Cf Cpe cr ct C

CTEM

Cd C i , C2 C1.C2.C3 d d d,,, do βΝ eNy βΝζ eM

23

EC 1 EC 3 EC 8 Ed Ek fd fe fmin fu fub f, ¿b fyb fyw F, Fi, F2 FC FbUd FbJUc Fd Ffr Fh.sd Fk Fp.Rd Fsd Fsk FsHd Fs.Rd.ser Fs.Rk Ft.Rd Ft .Rk Ft.sd FvRd FvRk Fv.sd Fv.sd.ser Fw Fw.Rk Fw.sd g G Gd Gk h ho H i I Ieff It Iw Iz k k kur k
List of symbols (2/6) Eurocode 1 (/l/) Eurocode 3 (/2/) Eurocode 8 (/3/) design value of the effect of action characteristic value of effects of actions at SLS design natural frequency natural frequency recommended limit of natural frequency ultimate tensile strength nominal value of ultimate tensile strength for bolt yield strength basic yield strength of the flat steel material before cold forming nominal value of yield strength for bolt yield strength of the web action (load, transverse force, imposed deformations,...) flow-chart design bearing resistance per bolt characteristic value of bearing resistance per bolt design value of action friction force force on bolt calculted from Msd and/or Fbjtd characteristic value of action design punching shear resistance per bolt design transverse force applied on web through the flange characteristic value of transverse force design slip resistance per bolt at the ultimate limit state design slip resistance per bolt at the serviceability limit state caracteristic slip-resistance per bolt and per friction interface design tension resistance per bolt characteristic value of tension resistance per bolt design tensile force per bolt for the ultimate limit state design shear resistance per bolt characteristic value of shear resistance per bolt and per shear plane design shear force per bolt for the ultimate limit state design shear force per bolt for the serviceability limit state resultant wind force characteristic value of resistance force of fillet weld design force of fillet weld distributed permanent action; dead load permanent action design permanent action characteristic value of permanent action overall depth of cross-section; storey height; building height overall height of structure total horizontal load radius of gyration about relevant axis using the properties of gross cross-section second moment of area A second moment of effective area Aeff (class 4 cross-section) torsional constant warping constant second moment of area about zz axis subscript meaning characteristic (unfactored) value effective length factor factor for lateral-torsional buckling with N-M interaction buckling factor for outstand flanges effective length factor for warping end condition factors for N-M interaction

24

ί L Lb

LTB Ly

m max min M M b .Rd MCT M cRd M€ Mf.Rd MN.Rd MN.VJld

MN.V.yJRd MN.V.z.Rd MN.y.Rd MN.z.Rd Mpf Mp£Rd Mp/iw.Rd Mp£y.Rd MptzJRd

MRd Msd Mv.Rd Mw.sd My My.Sd Mz Mz.sd η

rie nr n8 Ν NAD NbÄd Nb.yJld NbiJld Ν compression Ner NcRd

Nxsd NpCRd

List of symbols (3/6) roughness factor of the terrain portion of a member effective length for out­of­plane bending system length; span length; weld length buckling length of member lateral­torsional buckling distance between extreme fastener holes mass per unit length maximum minimum bending moment design resistance moment for lateral­torsional buckling elastic critical moment for lateral­torsional buckling design resistance moment of the cross­section torsional moment elastic moment capacity design plastic resistance moment of the cross­section consisting of the flanges only reduced design plastic resistance moment allowing for axial force Ν reduced design plastic resistance moment allowing for axial force Ν and by shear force V reduced design plastic resistance moment about yy axis allowing for axial force Ν and shear force V reduced design plastic resistance moment about zz axis allowing for axial force Ν and shear force V reduced design plastic resistance moment about yy axis allowing for axial force Ν reduced design plastic resistance moment about zz axis axial force Ν plastic moment capacity design plastic resistance moment of the cross­section design plastic resistance moment of the web design plastic resistance moment of the cross­section about yy axis design plastic resistance moment of the cross­section about zz axis design bending moment resistance of the member design bending moment applied to the member design plastic resistance moment reduced by shear force design value of moment applied to the web bending moment about yy axis design bending moment about yy axis applied to the member bending moment about zz axis design bending moment about zz axis applied to the member number of fastener holes on the block shear failure path number of columns in plane number of members to be restrained by the bracing system number of storeys normal force; axial load National Application Document design buckling resistance of the member design buckling resistance of the member according to yy axis design buckling resistance of the member according to zz axis normal force in compression elastic critical axial force design compression resistance of the cross­section design value of tensile force applied perpendicular to the fillet weld design plastic resistance of the gross cross­section

25

NRd Nsd NLRd rN tension

Nu.Rd N x .sd Pl»P2 Ρ q qk qref

Q

Qd Qk Vkmax

r R

Ra,Rd Rb,Rd Rd Rk Ry,Rd S S Sd Sk Ss

S Sd Sk

SLS

t tf tp tp tw U

ULS v Vref Vref.O

V

VbaJld Ver V//Sd Vj.sd Vp£Rd VpiyJld Vp£ z Jld vRd Vsd Vy Vy.Sd

vz

VZ.Sd w

List of symbols (4/6) design resistance for tension or compression member design value of tensile force or compressive force design tension resistance of the cross-section normal force in tension design ultimate resistance of the net cross-section at holes for fasteners design internal axial force applied to member according to xx axis distances between bolt holes Point load imposed variable distributed load characteristic value of imposed variable distributed load reference mean wind pressure imposed variable point load design variable action characteristic value of imposed variable point load variable action which causes the largest effect radius of root fillet rolled sections design crippling resistance of the web design buckling resistance of the web design resistance of the member subject to internal forces or moment characteristic value of Rd design crushing resistance of the web snow load thickness of fillet weld design snow load characteristic value of the snow load on the ground length of stiff bearing effects of actions at ULS design value of an internal force or moment applied to the member characteristic value of effects of actions at ULS Serviceability Limit states design thickness, nominal thickness of element, material thickness flange thickness thickness of the plate under the bolt head or the nut thickness of a plate welded to an unstiffened flange web thickness major axis Ultimate Limit States minor axis reference wind velocity basic value of the reference wind velocity shear force; total vertical load design shear buckling resistance elastic critical value of the total vertical load design value of shear force applied parallel to the fillet weld design value of shear force applied perpendicular to the fillet weld design shear plastic resistance of cross-section design shear plastic resistance of cross-section according to yy axis (// to web) design shear plastic resistance of cross-section according to zz axis (_L to flange) design shear resistance of the member design shear force applied to the member; design value of the total vertical load shear forces applied parallel to yy axis design shear force applied to the member parallel to yy axis shear force parallel to zz axis design internal shear forces applied to the member parallel to zz axis wind pressure on a surface

26

List of symbols (5/6) design wind load wind pressure on external surface welded sections elastic section modulus of effective class 4 cross­section elastic section modulus of effective class 4 cross­section according to yy axis elastic section modulus of effective class 4 cross­section according to zz axis elastic section modulus of class 3 cross­section elastic section modulus of class 3 cross­section according to yy axis elastic section modulus of class 3 cross­section according to zz axis plastic section modulus of class 1 or 2 cross­section plastic section modulus of class 1 or 2 cross­section according to yy axis plastic section modulus of class 1 or 2 cross­section according to zz axis axis along the member characteristic value of the material properties principal axis of cross section (parallel to flanges, in general) principal axis of cross section (parallel to the web, in general) reference height for evaluation of c e

Wd we W Weff Weff.y Weff.z Wef We£y We£z Wpi WpÉy Wp£Z x, xx Xk y, yy z, zz Ze 2u

Oreek symbols

α α α aa PA βM ßMl/r ßMy βκίζ βw ßw YF YG YM YMb 7Ms.ser TMW YMO

coefficient of frequency of the basis mode vibration coefficient of linear thermal expansion factor to determine the position of the neutral axis coefficient of critical amplification or coefficient of remoteness of critical state of the frame non­dimensional coefficient for buckling equivalent uniform moment factor for flexural buckling equivalent uniform moment factor for lateral­torsional buckling equivalent uniform moment factor for flexural buckling about yy axis equivalent uniform moment factor for flexural buckling about zz axis non-dimensional coefficient for lateral-torsional buckling correlation factor (for a fillet weld) partial safety factor for force or for action partial safety factor for permanent action partial safety factor for the resistance at ULS

ΎΜΙ YM2 YQ δ Ob 5d 6dv

partial safety factor for the resistance of bolted connections partial safety factor for the slip resistance of preloaded bolts partial safety factor for the resistance of welded connections partial safety factor for resistance at ULS of class 1,2 or 3 cross-sections (plasticity or yielding) partial safety factor for resistance of class 4 cross-sections (local buckling resistance) partial safety factor for the resistance of member to buckling partial safety factor for the resistance of net section at bolt holes partial safety factor for variable action relative horizontal displacement of top and bottom of a storey horizontal displacement of the braced frame design deflection design vertical deflection of floors, b e a m s , . . .

¿¿d OHmax δς

design horizontal deflection of frames recommended limit of horizontal deflection in plane deflection of the bracing system due to q plus any external loads

YMI

27

δς δ\, Ôvd °Vmax δο δι θ2 Δ

θ λ λι λ λβο.ν λβΚ.y λβιϊ.ζ XLT λρ λν λy λζ μ Hi μι,τ μγ μζ ρ ρ py pz σ

List of symbols (6/6) deflection due to variable load (q) horizontal displacement of the unbraced frame design vertical deflection of floors, beams,... recommended limit of vertical deflection pre­camber (hogging) of the beam in the unloaded state (state 0) svariation of the deflection of the beam due to permanent loads (G) immediatly after loading (state 1) variation of the deflection of the beam due to the variable loading (Q) (state 2) displacement 235 (with fy in N/mm2)

J

rotation slenderness of the member for the relevant buckling mode Euler slenderness for buckling non­dimensional slenderness ratio of the member for buckling effective non­dimensional slenderness of the member for buckling about w axis effective non­dimensional slenderness of the member for buckling about yy axis effective non-dimensional slenderness of the member for buckling about zz axis non-dimensional slenderness ratio of the member for lateral-torsional buckling plate slenderness ratio for class 4 effective cross-sections non-dimensional slenderness of the member for buckling about vv axis non dimensional slenderness ratio of the member for buckling about yy axis non dimensional slenderness ratio of the member for buckling about zz axis factor for FsjRk depending on surface class snow load shape coefficient factor for N-M interaction with lateral-torsional buckling factor for N-M interaction factor for N-M interaction density reduction factor due to shear force Vsa reduction factor due to shear force Vy.sd reduction factor due to shear force Vz.sd normal stress

Gq numerical values for the stabilizing forces of a bracing system GxEd, <*xm.Ed» design values of normal stresses for web check with Von Mises criteria ^z£d

τ υ φ χ %Ul Xmin Xy Xz

shear stresss Poisson's ratio initial sway imperfection of the frame reduction factor for the relevant buckling mode reduction factor for lateral-torsional buckling minimum of %y and χ ζ reduction factor for the relevant buckling mode about yy axis reduction factor for the relevant buckling mode about zz axis

28

2. List of tables in the "Design Handbook" O.c Table 0.1 I Table 1.1 Table 1.2 Table 1.3 Table 1.4 Table 1.5 Table 1.6 Table 1.7 Table 1.8 Π Table Π.1 Table Π.2 Table Π.3 Table Π.4 Table Π.5 Table Π.6 Table Π.7 Table Π.8 ΙΠ Table ΠΙ.1 Table ΠΙ.2 Table ΠΙ.3 Table ΠΙ.4 Table ΠΙ.5 Table ΠΙ.6 Table ΠΙ.7 Table ΙΠ.8 Table ΙΠ.9 IV Table IV. 1 Table IV.2 Table IV.3 Table IV.4 Table IV.5 Table IV.6 Table V.l Table V.2 Table V.3

List of tables (1/3) Pages of the Handbook

SYMBOLS AND NOTATIONS Dimensions and axes of rolled steel sections INTRODUCTION Summary of design requirements Partial safety factor γΜ for the resistance Definition of framing for horizontal loads Checks at Serviceability Limit States Member submitted to internal forces, moments and transverse forces Planes within internal forces, moments (Nsd> V$d, Msd) and transverses forces Fsd are acting Internal forces, moments and transverse forces to be checked at ULS for different types of loading List of references to chapters of the design handbook related to all check formulas at ULS STRUCTURAL CONCEPT OF THE BUILDING Typical types of joints Modelling of joints Comparison table of different steel grades designation Nominal values of yield strength f« and ultimate tensile strength fu for structural steels to EN 10025 and EN 10113 Maximum thickness for statically loaded structural elements Maximum thickness for statically loaded structural elements Nominal values of yield strength fyb and ultimate tensile strength fub for bolts Material coefficient LOAD ARRANGEMENTS AND LOAD CASES Load arrangements (Ffc) for building design according to EC1 Imposed load (qk, Qk) on floors in buildings Pressures on surfaces Exposure coefficient c e as a function of height ζ above ground External pressure Cpe for buildings depending on the size of the effected area A Reference height ZQ depending on h and b Combinations of actions for serviceability limit states Combinations of actions for ultimate limit states Examples for the application of the combinations rules in Table III.8. All actions (g, q, P, s, w) are considered to originate from different sources DESIGN OF BRACED OR NON-SWAY FRAME Modelling of frame for analysis Modelling of connections Global imperfections of the frame Values for the initial sway imperfections φ Specific actions for braced or non-sway frames Recommended limits for horizontal deflections CLASSIFICATION OF CROSS-SECTIONS Definition of the classification of cross-section Determinant dimensions of cross-sections for classification Classification of cross-section : limiting width-to thickness ratios for class 1 & class 2 I cross-sections submitted to different types of loading

29

46 51 52 63 64 65 66 67 68 70 71 72 73 74 75 75 76 80 81 82 83 83 84 85 86 86 88 87 97 98 99 100

105 112 113

Table V.4 Table V.5 Table V.6 Table V.7 Table V.8 Table V.9 Table V.10 VI Table VI. 1 Table VI.2 Table VI.3 Table VI.4

vn Table Vn.l Table Vfl.2 Table Vfl.3 Table VH.4 Table Vfl.5 Table VH.6

vm Table Vm.l Table vm.2 Table Vni.3 Table Vm.4 Table vm.5 Table vm.6 Table vm.7 Table Vffl.8 Table Vin.9 Table Vm. 10 Table Vm. 11 Table Vm. 12 Table VIfl.13 Table Vm. 14 EX Table DC. 1 Table DC.2 Table K . 3

List of tables (2/3) Pages of the Handbook Classification of cross­section : limiting width­to thickness ratios for 114 class 3 I cross­sections submitted to different types of loading Buckling factor k
30

131 134 134 135 136 137

143 147 147 148 150 151 151 152 152 156 156 157 159 160

164 170 171

Table K.4 Table DÍ.5 Table DC.6 Table DC.7 Table Di. 8 Table DÍ.9

Table X.l Table X.2 Table X.3 Table X.4 Table X.5 Table X.6 Table X.7 Table X.8 Table X.9 XI Table XI. 1 Table XI.2 Table XI.3 Table XI.4 Table XI.5 Table XI.6 Table XI.7 Table XI.8 Table XI.9 Table XI. 10 Table XI. 11 Table XI. 12 Table XL 13 Table XL 14 Table XL 15 Table XL 16 XII Table ΧΠ.1 Table ΧΠ.2 Table ΧΠ.3 Table ΧΠ.4 Table D.l

List of tables (3/3) Pages of the Handb ' Interaction formulas for the (N,M) stability check of members of Class 1 or 2 175 Interaction formulas for the (NM) stability check of members of Class 3 176 General interaction formulas for the (N,M) stability check of members of Class 4 177 Supplementary interaction formulas for the (N,M) stability check of members of Class 4 178 Reduced design resistance Ny.Rd allowing for shear force 179 Reduced design plastic resistance moment MN.VJM allowing for axial load and shear force for Class 1 or 2 cross­sections 181 TRANSVERSE FORCES ON WEBS (F ; (F,N,V,M)) Failure modes due to load introduction 187 Stresses in web panel due to bending moment, axial force and transverse force 188 Yield criteria to be satisfied by the web 189 Load introduction 190 Length of stiff bearing, s s 190 Interaction formula of crippling resistance and moment resistance 191 Effective breadth beff for web buckling resistance 192 Compression flange buckling in plane of the web 1*93 Maximum width­to­thickness ratio d/tw 193 CONNECTIONS Designation of distances between bolts 196 Linear distribution of loads between fasteners 196 Possible plastic distribution of loads between fasteners. Any realistic combination could be used, e.g. 197 Prying forces 197 Categories of bolted connections 198 Bearing resistance per bolt for recommended detailing for t = 10 mm in [kN] 199 Shear resistance per bolt and shear plane in [kN] 200 200 Long joints 201 Tension resistance per bolt in [kN] 201 Interaction formula of shear resistance and tension resistance of bolts Characteristic sup resistance per bolt and friction interface for 8.8 and 10. bolts, where the holes in all the plies have standard nominal clearances 202 Common types of welded joints 203 204 Throat thickness 204 Action effects in fillet welds 205 Resistance of a fillet weld 206 Effective breadth of an unstiffened tee joint DESIGN OF BRACING SYSTEM Load arrangements of the bracing system 216 Bracing system imperfections 218 Values for the equivalent stabilizing force Zq 218 Bracing system imperfections (examples) 219 APPENDK D List of references to Eurocode 3 Part 1.1 related to all check formulas at ULS 221

31

3. List offlow-chartsin the "Design Handbook"

©

Chapter Pages Elastic global analysis of steel frames according to Eurocode 3 General Details Comments (6 pages)

I I

14 15 16 to 21

[FC 3.1] Load arrangements & load cases for general global analysis of

m

38

ni

39

(FCM)Elastic global analysis of braced or non­sway steel frames according to EC 3 General Details Comments (4 pages)

IV IV IV

50 51 52 to 55

ÍFC 5. lì Classification of I cross­section

V

62

(FC 5.2J Calculation of effective cross­section properties of Class 4

rv

63

VI

82

VI

83

vn

90

vm

102

ΧΠ ΧΠ ΧΠ

168 169 170 to 175

the structure [FC 3.2J Load arrangements & load cases for first order elastic global analysis of the structure

cross­section (FC6.Ì) (FC 6.11 Members in tension (Ntension) (FC6.2)

(FC7)

Angles connected by one leg and submitted to tension

Members in compression (Ncompression)

(FC 8Î Design of I members in uniaxial bending (Vz;My;(Vz,My)) or (Vy;Mz;(VyJvIz); ÍFC 12ÌElastic global analysis of bracing system according to Eurocode 3 General Details Comments (6 pages)

32

Design handbook according to Eurocode 3 for braced or non-sway steel buildings

Short title: EC 3 for non-sway buildings

Profil ARBED-Recherches Chantrain Ph. Conan Y. Mauer Th.

TABLE OF CONTENTS 0

PRELIMINARIES

0.a

O.u.l

0.a.2 0.a.3 O.a.4 0.a.5 O.b

Foreword Generalities Objective of this design handbook Warning How to read this design handbook Acknowledgements References

41 41 41 41 41 42 42 43

O.c Symbols and notations O.c.l Symbols O.c.2 Convention for member axes 0.C.3 Dimensions and axes of rolled steel sections 0.C.4 Notations in flow-charts O.d Definitions and units O.d.1 Definition of special terms 0.d.2 Units

44 44 44 44 45 47 47 ' 47

INTRODUCTION

La Basis of design I.a.1 Fundamental requirements I.a.2 Definitions I.a.2.1 Limit states I.a.2.2 Actions I.a.2.3 Material properties I.a.3 Design requirements I.a.3.1 General I.a.3.2 Serviceability Limit States I.a.3.3 Ultimate Limit States Lb General flow-charts about elastic global analysis I.b.l Flow-chart FC LElastic global analysis of steel frames according to EC 3 Lb. 1.1 Flow-chart FC 1: general I.b.1.2 Flow-chart FC 1: details I. b. 1.3 Comments on flow-chart FC 1 Le Content of the design handbook I.c.1 Scope of the handbook I.C.2 Definition of the braced frames and non-sway frames I.C.3 Summary of the table of contents I.C.4 Checks at Serviceability Limit States I.C.5 Checks of members at Ultimate Limit States

35

f

._ .R 7° ~™ 49 49

50 50 50 50 53 53 53 53 56 61 61 62 64 64 65

TABLE OF CONTENTS Π

STRUCTURAL CONCEPT OF THE BUILDING

69

n.a Structural model 69 n.b Geometric dimensions 69 n.c Non structural elements 69 n.d Load bearing structure 69 n.e Joints ? 0 n.f Profiles 'Jl U.g Floor structure 7­ U.h Material properties 72 n.h. 1 Nominal values for hot rolled steel 7~ n.h.2 Fracture toughness n.h.3 Connecting devices \? 75 n.h.3.1 Bolts U.h.3.2 Welding consumables 76 n.h.4 Design values of material coefficients 76

m

IV

LOAD ARRANGEMENTS AND LOAD CASES

77

ULa Generalities ni.b Load arrangements m.b.l Permanent loads (g and G) m.b.2 Variable loads (q, Q, w and s) III.b.2.1 Imposed loads on floors and roof (q and Q) m.b.2.2 Wind loads (we,i, F w ) m.b.2.2.1 Wind pressure (we¿) m.b.2.2.2 Wind force (Fw) m.b.2.3 Snow loads (s) ULc Load cases m.c.l Load cases for serviceability limit states m.c.2 Load cases for ultimate limit states

77 80 80 80 80 81 81 84 84 85 85 86

DESIGN OF BRACED OR NON­SWAY FRAME

87

rV.a Generalities IV.a.l Analysis models for frames IV.a.2 Flow­chart FC 4:Elastic global analysis of braced or non­sway steel frames according to Eurocode 3 IV.a.2.1 Flow­chart FC 4 general rV.a.2.2 How­chart FC 4 details rv.a.2.3 Comments on flow­chart FC 4 rv.b Static equilibrium rv.c Load arrangements and load cases IV.c.l Generalities IV.C.2 Frame imperfections rV.d Frame stability rv.e First order elastic global analysis rV.e.l Methods of analysis IV.e.2 Effects of deformations IV.e.3 Elastic global analysis rv.f Verifications at SLS rv.f.l Deflections of frames rv.g Verifications at ULS rv.g.l Classification of the frame rv.g. 1.1 Hypothesis for braced frame rv.g. 1.2 Hypothesis for non­sway frame rv.g.2 ULS checks

87 87

36

89 89 89 92 96 96 96 96 97 98 98 98 99 99 100 10 ° *00 *00 100 100

TABLE OF CONTENTS V

VI

VII

CLASSIFICATION OF CROSS-SECTIONS

ΙΟΙ

V.a Generalities V.b Definition of the cross-sections classification V.c Criteria of the cross-sections classification V.c. 1 Classification of compression elements of cross-sections V.C.2 Classification of cross-sections V.c.3 Properties of class 4 effective cross-sections V.d Procedures of cross-sections classification for different loadings V.d. 1 Classification of cross-sections in compression V.d.2 Classification of cross-section in bending V.d. 3 Classification of cross-sections in combined (N,M)

101 104 106 106 106 106 109 109 109 110

M E M B E R S IN TENSION (Ntension) Vl.a Generalities VLb General verifications at ULS Vl.b. 1 Resistance of gross cross-section to Ntension VI.b.2 Resistance of net cross-section to Ntension VLc Particular verifications at ULS for angles connected by one leg VI.c. 1 Connection with a single row of bolts VI.C.2 Connection by welding M E M B E R S IN COMPRESSION (NCOnipression) Vn.a Generalities VILb Classification of cross-sections VII.c General verifications at ULS Vn.c.l Resistance of cross-section to Ncompression VII.C.2 Stability of member to Ncompression Vn.c.2.1 Resistance to flexural buckling Vn.c.2.2 Resistance to torsionnal buckting and to flexural-torsional buckling VILd Particular verifications at ULS for class 4 monosymmetrical cross-section VILd. 1 Resistance of cross-section to Ncompression VII.d.2 Stability of member to Ncompression VILe Particular verifications at ULS for angle connected by one leg VILe. 1 Connection with a single row of bolts Vn.e. 1.1 Resistance of cross-section to NCOmpression Vn.e. 1.2 Stability of member to Ncompression VII.e.2 Connection by welding Vn.e.2.1 Resistance of cross-section to Ncompression Vn.e.2.2 Stability of member to NCOmpression

VIII MEMBERS IN BENDING (V ; M ; (V, M))

VHLa Generalities VHLb Verifications at SLS Vm.b.l Deflections Vin.b.2 Dynamic effects - vibrations VIII.c Classification of cross-section VIILd Verifications at ULS to shear force Vsd Vin.d. 1 Resistance of cross-section to Vsd VIII.d.2 Stability of web to Vz.sd Vin.e Verifications at ULS to bending moment Msd Vin.e. 1 Resistance of cross-section to Msd Vm.e.2 Stability of member to My.sd Vin.f Verifications at ULS to biaxial bending moment (My.sd> Mz.sd) Vin.f. 1 Resistance of cross-section to (My.sd, Mz.sd) Vm.f.2 Stability of member to (My.sd, Mz.sd)

37

121 121 124 124 125 126 126 · 128 129 129 132 J 33 ^ 133 137 J38 ^ ° ^8 139 139 ^9 139 139 139 139

140 140 145 145 147 147 148 148 150 152 152 I53 156 156 157

TABLE OF CONTENTS

LX

X

XI

Vm.g Verifications at ULS to combined (Vsd, Msd) Vrn.g.1 Resistance of cross-section to (Vsd. Msd) Vin.g. 1.1 Shear force Vsd and uniaxial bending Msd Vin.g. 1.2 Shear force Vsd and biaxial bending moment Msd Vm.g.2 Stability of web to (Vz.Sd,My.Sd)

MEMBERS WITH COMBINED AXIAL FORCE AND BENDING MOMENT ((N, M) ; (N, V; M))

157 157 157 158 159 161

Di.a Generalities K.b Verifications at SLS LX.b.l Deflections LX.b.2 Vibrations DC.c Classification of cross-section DCd Verifications at ULS to (N,M) LX.d. 1 Resistance of cross-section to (Nsd, Msd) LX.d. 1.1 Uniaxial bending of class 1 or 2 cross-sections LX.d. 1.2 Biaxial bending of class 1 or 2 cross-sections LX.d. 1.3 Bending of class 3 cross-sections LX.d. 1.4 Bending of class 4 cross-sections LX.d.2 Stability of member to (Nsd,Msd) K.d.2.1 Stability of member to (Ntension» My.sd) LX.d.2.2 Stability of member to (Ncompression* Msd) DC.e Verifications at ULS for (N$d ,Vsd) LX.e.l Resistance of cross-section to (Nsd.Vsd) JX.f Verifications at ULS to (Nsd ,Vsd,Msd) LX.f.l Resistance of cross-section to (Nsd>Vsd>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

<

^ Z 7 o ^ o , y ^ ì otherflow­chax,number(y) yes 1 ι τ » the dotted line ( ) means that path has to be followed through the box (^

Results

J

45

Table 0.1

Dimensions and axes of rolled steel sections

"?'

ΓΪ7

y —

1 =£tf

+

*·

I

ζ

ttf y Htw

46

■7e

— y

[14.2 (i)]

O.d

Definitions and units

iLdJ

Definition of special terms

(1) The following terms are used in Part 1.1 of Eurocode 3 with the following meanings: Frame: Portion of a structure, comprising an assembly of directly connected structural elements, designed to act together to resist load. This term refers to both rigid-jointed frames and triangulated frames. It covers both plane frames and threedimensional frames. Sub-frame: A frame which forms part of a larger frame, but is treated as an isolated frame in a structural analysis. Type of framing: Terms used to distinguish between frames which are either: Semi-continuous, in which the structural properties of the connections need explicit consideration in the global analysis. Continuous, in which only the structural properties of the members need explicit consideration in the global analysis. Simple, in which the joints are not required to resist moments. Global analysis: The determination of a consistent set of internal forces and moments (N, V, M) in a structure, which are in equilibrium with a particular set of actions on the structure. First order global analysis: Global analysis using the initial geometry of the structure and neglecting the deformation of the structure which influences the effects of actions (no Ρ-Δ effects). Second order global analysis: Global analysis taking into account the deformation of the structure which influences the effects of actions (Ρ-Δ effects). Elastic global analysis: First-order or second-order global analysis based on the assumption that the stress-strain behaviour of the material is linear, whatever the stress level; this assumption may be maintained even where the resistance of a crosssection is based on its plastic resistance (see chapter V about classification of crosssections). System length: Distance between two adjacent points at which a member is braced against lateral displacement in a given plane, or between one such point and the end of the member. Buckling length: System length of an otherwise similar member with pinned ends, which has the same buckling resistance as a given member. Designer: Appropriately qualified and experienced person responsible for the structural design. Q&2

[1.5 (2)]

ilniiS

(1) For calculations the following units are recommended in accordance with ISO 1000: Forces and loads Unit mass Unit weight Stresses and strengths Moments (bending....)

kN, kN/ m , kN/ m 2 : kg/m3 : kN/ m 3 : N/mm2 (=MN/ m 2 or MPa) kNm.

47

I INTRODUCTION La

Basis of design

(1) The table 1.1 summarizes this chapter La providing the practical principles of design requirements. Details and explanations are given in the following sub-chapters I.a.l to I.a.3. I.a.l

Fundamental requirements

[2.1 (l)]

(1) A structure shall be designed and constructed in such a way that: . with acceptable probability, it will remain fit for the use for which it is required, having due to regard to its intended live and its cost, and . with appropriate degrees of reliability, it will sustain all actions and influences likely to occur during execution (i.e. the construction period) and use (i.e. the service period) and have adequate durability in relation to maintenance costs.

[2.1 (2)]

(2) A structure shall also be designed in such a way that it will not be damaged by events like explosions, impact or consequences of human errors, to an extent disproportionate to the original cause.

[2.1 (4)]

(3) The above requirements shall be met by the choice of suitable materials, by appropriate design and detailing and by specifying control procedures for production, construction and use as relevant for the particular project. I.a.2

Definitions

I.a.2.1

Limit states

(1) Eurocode 3 is a limit state design code in which principles and rules are given for the verification of: . Serviceability Limit States (SLS) and, . Ultimate Limit States (ULS). [2.2.1.1 (l)] (2) The limit states are states beyond which the structure no longer satisfies the design performance requirements. (3) These limit states are referred to physical phenomena as for instance: [2.2.1.1 (6)] a) for SLS, problems which may limit the serviceability because of: . deformations or deflections which adversely affect the appearance of effective use of the structure (including the proper functioning of machines or services) or cause damage to finishes or non-structural elements, . vibration which causes discomfort to people, damage to the building or its contents, or which limits its functional effectiveness. [2.2.1.1 (4)] b) for ULS, problems which may endanger the safety of people and thus be regarded as ultimate limit because of: . loss of equilibrium of structure or any part of it, considered as a rigid body, . failure by excessive deformation, rupture, or loss of stability of the structure or any part of it, including supports and foundations.

48

ΙΛ.22

Actions

(1) Details about actions are provided in Eurocode 1 [2.2.2.1 (i)] (2) An action (F) is: . a force (load) applied to the structure (direct action), or . an imposed deformation (indirect action); for example, temperatures effects or differential settlement. [2.2.2.1 (2)] (3) Actions (F) are classified as: . permanent actions (G), e.g. self-weight of structures, fittings, ancillaries and fixed equipment . variable actions (Q), e.g. imposed loads (q), wind loads (w) or snow loads (s) . accidental actions (A), e.g. explosions or impact from vehicles. [2.2.2.2 (l)] (4) Characteristic values F^ of actions are specified: . in Eurocode 1 or other relevant loading codes, or . by client, or the designer in consultation with the client, provided that the minimum provisions specified in the relevant loading codes or by the competent authority are observed. [2.2.2.4(1)] (5) The design (factored) values Fd of an action (for instance Gd, Q
[form. (2.2)]

[2.2.3.1 (3)] [2.2.3.2 (2)]

[form. (2.3)]

(6) The combinations of actions respectively for ULS and for SLS are given in chapter ΙΠ. (7) Design values of the effects of actions: The effects of actions (E) are responses (for example, internal forces and moments (Nsd. Vsd» Msd), stresses, strains, deflections, rotations) of the structure to the actions. Design values of the effects of actions (Ed) are determined from the design values of the actions, geometrical data (ad) and material properties when relevant: Ed = E(Fd>ad,...) I.a.2 3 Material properties (1) characteristic values of material properties: Material properties for steel structures are generally represented by nominal values used as characteristic values (unfactored) (Xk)· (2) design values of material properties: For steel structures, the design (factored) resistance Rd (for example, design resistance for tension (NRd), buckling (NRd), shear (VRd) , bending (MRd)) is generally determined directly from the characteristic (unfactored) values of the material properties (Xk) and geometrical data (a^): R d =R(X k a k ,. ) / γ Μ where YM is the partial safety factor for the resistance(the different YM factors are explicitly introduced in the design formulas and their values are given in table 1.2)

49

I.a.3 [2.3.1 (l)] [2.3.1 (2)] [2.3.1 (3)] [2.3.1 (4)]

Design requirements

r.a.3.1 General (1) It shall be verified that no relevant limit state is exceeded (2) All relevant design situations and load cases shall be considered. (3) Possible deviations from the assumed directions or positions of actions shall be considered. (4) Calculations shall be performed using appropriate design models (supplemented, if necessary, by tests) involving all relevant variables. The models shall be sufficiently precise to predict the structural behaviour, commensurate with the standard of workmanship likely to be achieved, and with the reliability of the information on which the design is based.

I.a.3 2 Serviceability Limit States [2.3.4 (l )] (1 ) It shall be verified that: [form. (2.13)] Ed^Cd or E d < R d where

Ed

is the design effect of actions, determined on the basis of one of the combinations defined below, Cd is a nominal value or a function of certain properties of materials related to the design effect of actions considered. (2) Practical checks of SLS (see chapter I.b.3) in floors and frames for instance: ( g Vd> S Hd) ^ (5vma*> S Hmax) f d ^ f min

is the design vertical deflection of floors (recommended limits oVmax = L/250» —) is the design horizontal deflection of frames ÖHd (recommended limits δππ,^ = h/300» —) is the design natural frequency of floors fd (recommended limits fmin = 3 Hz,...) I,a,3,3 Ultimate Limit States [2.3.2.1 (2)] (1) When considering a limit state of rupture or excessive deformation of a section, member or connection (fatigue excluded) it shall be verified that: where

[form. (2.7)]

övd

Sd^Rd Sd is the design value of an internal force or moment (or of a respective vector of several internal forces or moments) Rd is the corresponding design resistance, associating all structural properties with the respective design values. (2) Practical checks of ULS (see chapter I.b.4) in members for instance: where

where

(N S d ,V S d ,M S d )<(N R d ,V R d ,M R d ) condition concerning separate internal forces or moments or, interaction between them ((V,M), (Ν, M),...) (Nsd. Vsd, Msd) are design internal forces and moments applied to the members, (NRd, VRd, MRd) are design resistance of the members.

50

Table LI

Summary of design requirements

11 frame submitted to SLS and ULS combinations of design actions Fd (G d , Qd, w d , s d ,...): [form. (2.1)]

|Fd=Y F Fk where

F^ YF

is the characteristic value of actions is the partial safety factor for the considered action (see chapter ΠΓ)

2) after global analysis of the frame: ­ design effects of actions (e.g. deflections, frequencies) (for SLS): Ed H 5 d , fd) ) ­ design values of internal forces and moments (for ULS): S d (=(Nsd, Vsd, M S d ) ) 3) verification conditions at limit states: ­ for SLS checks (see chapter I.b.4): [2.3.4(1)]

. in general: where

EH
is the nominal value related to the design effect of considered actions (design capacity). (ô V d>5 Hd ) < (ôvmax'a H m a x

for instance:

f d ^ f min

where

is the design vertical deflection of floors OVd is the design horizontal deflection of frames ÖHd is the design natural frequency of floors fd °Vmax .8Hmax»fmin are recommended limits (for instance: L/250, h/300, 3

Hz

>

for ULS checks (see chapter I.b.5): [2.3.2.1 (2)]

. in general: where

Sd < R Rd

is the design resistance (=(NRd, V R d , M R d )):

Rd = Rk/YM

[form. (2.3)]

where

for instance:

Rk YM

is the characteristic value of the used material is the partial safety factor for the resistance (see table 1.2)

(NSd,VSd>Msd)<;(NRd,VRd,MRd) condition concerning separate internal forces or moments or, interaction between them ((V,M), (N,M),..)

51

Table 1.2

Partial safety factor YM for the resistance

The design values of

- the resistances of cross-sections - the buckling resistance of members - and, the resistances of connections shall be determined with the following partial safety factors YM: - at Ultimate Limit States; =

M

=

W

- resistance of class 1,2 or 3 cross-section*) : (plasticity or yielding)

ΎΜΟ

- resistance of class 4 cross-section*) (local buckling)

:

YMI

- resistance of members to buckling (global and local buckling)

:

ΎΜΙ = Μ

- resistance of net section at bolt holes

:

YM2 = 1 . 2 5

- resistance of bolted connections

:

ÏMb=1.25

- resistance of welded connections

:

YMW = 1'25

:

ÏMs.ser ~~*>*

- at Serviceability Limit States: - slip resistance of preloaded bolts Note 1 :

The different JM factors are explicitly introduced in 1he design formulas.

Note 2:

The yui factors are provided according to the official version of Eurocode 3. Those "boxed" values are only indicative. The value s of YM to be used in practice are fixed by the national authorities in each country and published in the relevant National Application Document (NAD)

*) The classification of cross-sections is defined in chapter V

52

Lb

General flow-charts about elastic global analysis

(1) Chapter Lb. 1 presents flow-chart FC 1 about elastic global analysis of steel frames (in general) according to Eurocode 3. (2) Chapter IV.a.2 presents flow-chart FC 4 about elastic global analysis of braced or nonsway steel frames according to Eurocode 3. (3) Chapter XILa. 1 presents flow-chart FC 12 about elastic global analysis of bracing system according to Eurocode 3. Lb. 1

Flow-chart FC 1 : Elastic global analysis of steel frames according to Eurocode 3

(1) The flow-chart FC 1 aims to provide a general presentation of elastic global analysis of steel frames according to Eurocode 3. (2) The present design handbook only deals with the path φ of FC 1 elastic global analysis of braced or non-sway frames (presented in FC 4 in chapter IV). All the details are given in chapters Π to XI of the handbook. (3) The elastic global analysis of sway frames is out of the scope of the present design handbook; the assumptions of the elastic global analysis of sway frames are briefly presented - just for information - in the paths (D to (D of FC 1. (4) The flow-chart FC 1 refers to flow-chart FC 12 about elastic global analysis of bracing system according to Eurocode 3. The flow-chart FC 12 and all the details about bracing system design are given in chapter ΧΠ. (5) The flow-chart FC 1 is divided in 3 parts: Lb. 1.1 general part (1 page) Lb. 1.2 details (1 page) Lb. 1.3 comments (6 pages) Ib.1.1

Flow-chart FC 1: cenerai see the following page

LJLLZ

Flow-chart FC 1: details see the second following page

53

Flow-chart ΓFC 1) : Elastic global analysis of steel frames according to Eurocode 3 (General) row:

Actions Predesign SLS checks

Choice of the type of global analysis for ULS 10

ULS global analysis of the frame to determine the internal forces and moments (N, V, M)

13

14

ULS checks of members

16

submitted to internal forces and moments (N, V, M) II

19

ULS checks of local effects ULS checks of connections 54

20

Flow­chart

( FC l) : Elastic global analysis oí Steel frames according to Eurocode 3

(Details) row:

Determination of load arrangements (EC1 and EC 8)

1

Load cases for SLS [2.3.4.]

Load cases for ULS [2.3.3.] C~ ^

Predesign of members^beams & columns => Sections^ with pinned and/or rigid connections ι

Frame with bracing system /

~^l JT

not fulfilled

notfulfilled

SLS checks [Chap. 4]

ULS checks [Chap. 5]

Design of the bracing system

ι

Frame without bracing system

Classification of the frame

, Braced framed yes

S.

\no

Global imperfections of the frame [5.2.4.3.]

6 b £ 0 , 2 5u [5.2.5.3. (2)]

1

Non-swayframeyes /Non­sway frame [5.2.5.2.Λ Vsd £ 0 , 1

£. «δ, ε:

Sway frame

m

1 λ > 0,5 [A.fy / NSd] 0 · 5 V T

no

[5.2.4.2.(4)]

v

yes / 0,1 < ^ . < 0,25 \nov Ver [5.2.6.2. (4)]

FIRST

'ORDER ANALYSIS

±

Non­sway mode buckling length approach

Sway mode buckling length approach

[5.2.6.2(1) a)][5.2.6.2. (7)]:

[5.2.6.2(1) b)][5.2.6.2. (8)1:

with sway moments amplified by factor l/(l-VSd/Vcr) [5.2.6.2.(3)]

Ό

ι SECOND

©-

Mjembers imperfectiojis l eo,d

with sway moments amplified by factor 1,2 in beams & connections

©

i

eo,d where necessary

152.62.(2)]

[5.2.4.5.(3)]

--0

I Sway mode L b )

ÍNon­sway mode

ï ' Classification of cross­section [Chap. 5.3] ' 1

±

±

Checks of the in­plane stability: members buckling [Chap. 5 J ]

φ-: yes

<5

16

not fulfilled (n.f.)

I

Checks of local effects (buckling and resistance of webs) [Chap. 5.6 and 5.7]

55

[5.2.4.5.(2)]

«a,

Checks of resistance of cross­sections [Chap. 5.4]

Checks of connections [Chap. 6 and Annex J]

ï

eo,d in all members

Lb

Checks of the out­of­plane stability: members and/or frame buckling [Chap. 5.5] f

[5.2.4.5.]

—fá—/members \_ \ with eo.d /

Non­sway mode iL b

r-

ORDER ANALYSIS'

nf.

yi yi ->n£

I.b.l .3

Comments on flow-chart FC 1

comments (1/6) on flow-chart FC 1: * Generalities about Eurocode 3: - AU checks of (ULS) Ultimate Limit States and all checks of (SLS) Serviceability Limit States are necessary to be fulfilled. - According to the classification of cross-sections at ULS (row 14; chapter V of the design handbook) Eurocode 3 allows to perform:

[5.2.1.2(1)]

. plastic global analysis of a structure only composed of class 1 cross-sections when required rotations are not calculated [5.3.3 (4)] or, . elastic global analysis of a structure composed of class 1. 2. 3 or 4 cross-sections assuming for ULS checks, either a plastic resistance of cross-sections (class 1 and 2) or, an elastic resistance of the cross-sections, without local buckling (class 3) or, with local buckling (class 4 with effective cross-section). - In order to determine the internal forces and moments (N. V. M) in a structure Eurocode 3 allows the use of different types of elastic global analysis either: a) first order analysis using the initial geometry of the structure or,

[5.2.1.2 (2)]

b) second order analysis taking into account the influence of the deformation of the structure - First order analysis (row 11) may be used for the elastic global analysis in the following cases (types of frames): The first order elastic global analysis of the frame should take into account actions types of frames 1) braced frames &)

the vertical loads

the horizontal loads

[5.2.5.3 (5)]

the member imperfections (row 12)

X(b)

(path®)

[5.2.5.3 (3)]

the global imperfections of the frame (row 7)

2) non-sway frames (path φ )

X

X

3) sway frames (c) (paths © and © )

X

X

Notes : (a) braced frames are frames which may be treated as fully supported laterally by a bracing system. (b) only the part of horizontal loads which are applied to the frame but not assumed to be transmitteii to the bracing system through the floors. (c) use of design methods which make indirect allowance for second-order effects.

56

comments (2/6) onflow-chartFC 1: [5.2.1.2(3)]

- Second order analysis (row 11) may be used in all cases (types of frames) :

^v.

actions

types of ^«x. frames ^ \ 1) for sway frames

The second order elastic global analysis of the frame should take into account the member the horizontal the global the vertical loads imperfections of the imperfections loads frame (row 7) (row 12)

(path ® ) (path <§» 2) for frames in general (path ©)(*>) [5.24.5(3)]

X

X

X

X

X

X

X(a)

X

X

X

X

Notes : fa) members imperfections are introduced where necessarv. (b) the more complex possibility of second order global analysis of the frame (path © ) could be conservative because it allows the bypass of the "sway or non-sway frame" classification and consequently : - either the first order analysis might be sufficient, - or, the introduction of member imperfections would not be necessary in all members. On the other hand, particular care shall be brought to the introduction of member imperfections ( eo,d) which would be imposed for the global analysis in the realistic directions corresponding to the deformations of the members for the failure mode of the frame; that failure mode of the frame is related to the combination of applied external loads; otherwise, with more favourable direction of member imperfections, the second order global analysis might overestimate the bearing capacity of the frame. - in the flow-chart FC 1 from path φ to path (D (from left to right) the proposed methods for global analysis become more and more sophisticated.

* row 1: EC 1: Draft EC 3: ENV 1993-1-1 EC 8: Draft

Eurocode 1 Basis of design and actions on structures Eurocode 3 Design of steel structures, Part 1.1: general rules and rules for buildings. Eurocode 8 Design of structures for earthquake resistance

57

comments (3/6) on flow-chart FC 1: [Chap. 5] [Chap. 4]

* rows 2.4: -ULS -SLS

means Ultimate Limit States means Serviceability Limit States

* row 3: This flow­chart concerns structures using pinned and/or rigid joints. In the case of semi-rigid joints whose behaviour is between pinned and rigid joints, the designer shall take into account the moment­rotation 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 semi­rigid joints should be designed according to chapter 6.9 and the Annex J of Eurocode 3. [4.2.1 (5)]

[5.2.5.3 (2)]

row 4: For SLS checks, the deflections should be calculated making due allowance for any second order effects, the rotational stiffness of any semi­rigid joints and the possible occurrence of any plastic deformations. * row 6: braced frame

unbraced frame

5 b <0,2ô u The frame is braced if: where δι>: horizontal displacement of the frame with the bracing system ôu: horizontal displacement of the unbraced frame, according to first order elastic global analysis of the frame either with hypothetic horizontal loads or with each ULS load case. Note : in the case of simple frames with all beam­column nodes nominally pinned, the frame without bracing would be hypostatic, hence c\j is infinite and thus the condition 6b ^ 0,2 δ\ι is always fulfilled. [5.2.4.3]

* row 7: global imperfections of the frame initial sway imperfections of the frame F2

equivalent horizontal forces F2

JMii

Σ could be applied in the form of φ Fi

»

φ (Fi + F2) 2

58

φ (Fi + F2) 2

comments (4/6) on flow-chart FC 1: * row 8:

[5.2.5.2]

classification of swav or non­swav frame:

A frame may be classified as non-sway if according to first order elastic global analysis of the frame for each ULS load case, one of the following criteria (see row 9) is satisfied: either, ai in general [5.2.5.2 (3)] Sd _ cr

where Vsd: VCT:

α cr

, condition which is equivalent to

aCT > 10

design value of the total vertical load elastic critical value of the total vertical load for failure in a sway mode ( = π2ΕΙ / L2 with L, buckling length for a column in a sway mode; V cr of a column does not correspond necessarily to V cr of the frame including that column) coefficient of critical amplification or coefficient of remoteness of critical state of the frame

aCT : or,

< 0,1

b) in case of building structures with beams connecting each columns at each storey level:

[5.2.5.2(4)]

δ.χν_δ.(ν 1 -Γ·ν 2 ) h.^H

where H, V: δ: h: H, V, δ

h.(H 1 + H 2 )

< 0,1

total horizontal and vertical reactions at the bottom of the storey. relative horizontal displacement of top and bottom of the storey, height of the storey. are deduced from a first order analysis of the frame submitted to both horizontal and vertical design loads and to the global imperfections of the frame applied in the form of equivalent horizontal forces (see comments on row 7).

Notes: ­ A same frame could be classified as sway according to a load case (V$dl for instance) and as non­sway according to another load case ( Vsd2 for instance). For multi­storeys buildings the relevant condition is condition which is equivalent to

' ν * Λ or åen are related to the storey i. where v V cny

59

Sd cr

= maximum

'2*i

a w = minimum (Ocri)»

comments (5/6) on flow-chart FC 1: [5.2.4.2 (4)]

* row 9:

Members imperfections may be neglected except in sway frames in the cases of members which are subject to axial compression and which have moment resisting connections, if :

λ>0,5

"Afyl

.condition which is equivalent to

.NSd.

where λ : fv,: A: Nsd·' Ncr:

N

Ν « >

4"

π or equivalent to ε > — 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

<£

-rl

&

Vz.sd My.sd

FsdT Nsd

{

xy (xaxis) xz

Mx.sd

·

y.Sd

'z.Sd

xy

xz

My.Sd

Mz.Sd

Fsd

xz

xy

xz

moment of torsion (is not considered in the handbook because the Annex G of Eurocode 3 is not officially available yet).

66

Table L7

Internal forces, moments and transverse forces to be checked at ULS for different types of loading Internal forces, moments and transverse forces and, interactions between them

Type of loading on the members and on the webs

* x—

N x.Sd

.y ·— X

y"

Members in tension (braces,...) : chapter VI

e£ I I

ζ

Ν tension

Nx.sd x —

Λ—X

Members in c ompression (columns,...) : chapter Vu

I I

ζ

Ν,compression ζ I

e. X

M z.Sd

-'■' 1,3 .Xp

—

Vz;sdMy.Sd

Members in bending (beams,...) : chapter VIH Μ

(Μν,Μ,)

(V,M)

(V,My,Mz)

Μ z.Sd y.Sd .

Nx.sd

Κ lo XP

χ -

Members with c ombined (Ν, M) (beams-columns,...) : chapter LX

Vz:sdMy.sd

ι ι ζ

(N,M)

(N,MV,MZ)

u

(N,V)

(N,V,M)

(N,V,MV,MZ)

Fsd I |Fsd ? V

τ—Γ

r

ι

Nx.sd

'

N

x.sd

My.Sd

ι ζ

Fsd

(F,N) (F,VZ)

z.Sd ι

.-y

x—

Transverse forc es on webs : chapter X

N x . Sd

(F,N,VZ)

67

(F,MV)

(F,N,MV)

(F,V z ,My)(F,N,V z ,M v )

Table 1.8 List of references to chapters of the design handbook related to all check formulas at ULS Typ«; References to the design handbook for ULS checks Internal forces moments, and Physical phenomena of in function of classes of cross­sections (chapter V) : class 3 class 4 transverse forces check s classes 1 or 2 | tension resistance (gross & net section) VI.b.1 (1) + VI.b.2 (1) + VI.c.1 (l) + VI.c.2 (1) R 1. Ntension compression resistance vn.c.l (1) vn.c.i (1) 2. Ncompression R Ν buckling of members VII.c.2.1(2) + VII.c.2.2 VHc.2.1 (2) S shear and block shear resistances Vin.d.l (1) R 3. V shear buckling VIII.d.2 (5) S uniaxial bending resistance VIII.e.l (1) VHI.e.1 (1) R VIII.e.1 Í1) 4. M lateral­torsional buckling (My) (LTB) Vin.e.2 (4) Vm.e.2 (4) Vin.e.2 (4) S 5. (My,Mz) biaxial bending resistance Vm.f.l (1) vm.f.i (1) R Vffl.f.1 (1) 6. (V,M) (V z ,M y )

S vm.f.2 (1) + (2) Vm.f.2 (1) + (2) VIII.f.2 (1) + (2) biaxial flexural buckling uniaxial bending & shear resistance vm.g.i.i(i) R uniaxial bending & shear buckling VIH.g.2(3) S

7. ( ν , Μ ^ Μ ζ )

R

(V z ,M y ,M z ) 8. (N,M) (Ntension,My) (NComp..My) (Ncomp^Mz) 9. (N,M y ,Mz)

S R S S

s R

11. (N,V,M)

S R S R

(N,VZ,My) 12. (N,VJvlyJVlz)

S R

10. (N, V)

(N,V z ,M y ,M z ) S 13. F,(F,N),(F,My), R

biaxial bending & shear resistance uniaxial bending & shear buckling vm.g.2 (3) uniaxial bending & axial force resistance IX.d.1.4 (2) DCd.l.l(l) DC.d.l.3(2) lateral­torsional buckling (LTB) IX.d.2.1 (1) K.d.2.1 (1) IX.d.2.2 (2), (3) IX.d.2.2 (2), (3) IX.d.2.2 (2), (3) N­M buckling + LTB IX.d.2.2 (3), (4) IX.d.2.2 (3), (4) IX.d.2.2 (3), (4) N­M buckling IX.d.1.4 (1) biaxial bending & axial force resistance IX.d.1.2 (1) IX.d. 1.3(1) IX.d.2.2 (1), (2) IX.d.2.2 (1), (2) rX.d.2.2(l),(2) (N­biaxial M) buckling + LTB rx.e.l (1) rx.e.l (1) shear and axial load resistance shear buckling Vm.d.2 (5) uniaxial bending & IX.f.1.4 (2) IX.f.1.1 (1) IXI.1.3 (2) shear and axial force resistance IX.f.2 (3) (N­uniaxial M) resistance & shear buckling Vin.g.l.2(2)

Vm.g.l.2(3)

Vm.g.l.2(3)

rx.f.i.2(i)

IX.f.1.3 (1)

rX.f.1.4 (1)

X.c.1 (1)

IX.f.2 (3) X.c.1 (1)

X.c.1 (1)

biaxial bending & shear and axial force resistance (N­uniaxial M) resistance & shear buckling transverse force (+N, +M y ) resistance j

(FFMy) F

R S

X.c.2 (1) X.d.1.1 ((1), (2)) + X.d.2 ((1), (2), (3))

(F%)

S

X.d. 1.2(1)

S 14. (F.V^.CF^.Vz), R (F,V z ,M y ), (F,N,Vz,My) S

tvpe of loading

tvpe of checks:

crushing crippling + buckling crippling

X.e(l)

X.e(l)

X.e(l)

X.c.1 (1)

X.c.1 (1)

X.c.1 (1)

IX.f.2 (3)

compression flange induced buckling transverse forces + shear V z (+N, +M y ) resistance (N­uniaxial M) resistance & shear buckling

1. = tension members 2. = compression memb•ers 3. to 7. = members in bendin g 8. to 12. = members with combined N­M 13. to 14. » transverse forces oi ι webs R = resistance of cross­sections ([5.4] 5 = Stability of memt>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

<"

0

o

0 t^^^^m

0

3^"

-vRigid joints

■■u

■r

Hr Φ*

£=

* \ -

Semi-rigid joints

Pinned joints

70

(2) The table II.2 presents the modelling of joints. The joints may be modelled by nodes offset from the member centrelines to reflect the actual locations of the connections.

ΓTable IL2 Type of joint

Modelling of joints Modelling

Behaviour

M 11

Mu

Φ

RIGID Joint

SEMI­RIGID Joint

M

K> 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

t<40mm fy (N/mm2) fu (N/mm2) 235 275 355

360 430 510

40 mm < t < 100 mm**) fy (N/mm2) fu (N/mm2) 215 255 335

340 410 490

255 390 S 275 275 370 335 355 490 S 355 470 420 390 500 S 420 500 460 430 530 S 460 530 Notes: i J— ") t is the nominal thickness of the element (Γ ir ■-t - of the flange of rolled sections (t = tf) - of the particular elements of the welded sections **) the condition 40 mm < t < 63 mm should be taken for plates and other flat products in steels of delivery condition TM to EN 10113-3. II.h.2

Fracture toughness

[3.2.2.3]

(1) The material shall have sufficient fracture toughness to avoid brittle fracture at the lowest service temperature expected to occur within the intended life of the structure. (2) In normal cases of welded or non-welded members in building structures subject to static loading or fatigue loading (but not impact loading), no further check against brittle fracture is necessary if the conditions given in tables Π.5 and Π.6 are satisfied. Tables Π.5 and Π.6 provide the maximum thicknesses of the structural elements which are allowable for certain lowest service temperatures and for different steel grades in accordance to the EN 10025 and EN 10113 standards. (3) For all other cases reference should be made to informative Annex C.

73

[table 3.2]

Table Π.5

Maximum thickness for statically loaded structural elements

Steel grade and quality

Maximum thickness (mm) for lowest service temperature of -10°C

0°C Service condition 5)

-20°C

SI

S2

SI

S2

SI

S2

108 250 250

30 75 212

74 187 250

22 53 150

63 150 250

19 45 127

45 123 250

14 33 84

EN 10027

EN 10025 D

S235JR S 235 JO S 235 J2

Fe 360 Β Fe 360 C Fe 360 D

150 250 250

S 275 JR S 275 JO S 275 J2

Fe 430 Β Fe 430 C Fe 430 D

90 250 250

41 110 250 26 63 150

S 355 JR S 355 JO S 355 J2 S355K2

Fe 510 Β Fe 510 C Fe 510 D Fe 510 DD 2)

40 106 250 250

12 29 73 128

29 73 177 250

9 21 52 85

21 52 150 250

6 16 38 59

EN 10113 3) S 275 M S 275 ML

Fe E 275 KG 4 ) Fe E 275 KT

250 250

250 250

250 250

192 250

250 250

150 250

S 355 M S 355 ML

Fe E 355 KG 4 ) Fe E 355 KT

250 250

128 250

250 250

85 250

250 250

59 150

Service conditions 5 ):

SI

either:

. non-welded, or . in compression S2 as welded, in tension In both cases of service conditions this table assumes loading rate RI (normal static or slow loading; no impact loading) and consequences of failure condition C2 (fracture critical members or joints with potential complete structural collapse).5) Notes: 1) For rolled sections over 100 mm thick, the minimum Charpy V-notch energy specified in EN 10025 is subject to agreement. For thicknesses up to 150 mm, a minimum value of 27 J at the relevant specified tests temperature is required and 23 J for thicknesses over 150 mm up to 250 mm. 2) For steel grade Fe 510 DD to EN 10025, the specified minimum Charpy V-notch energy value is 40 J at -20°C. The entries in this row assume an equivalent value of 27 J at -30°C. 3)

For steels of delivery condition N to EN 10113-2 over 150 mm thick and for steels of delivery condition TM to EN 10113-3 over 150 mm thickforlong products and over 63 mm thickforflat products, the minimum Charpy V-notch energy specified in EN 10113 is subject to agreement. For thicknesses up to 150 mm, a minimum value of 27 J is required and 23 J for thicknesses over 150 mm up to 250 mm. The test temperature should be -30°C for KG quality steel and -50°C for KT quality steel.

4)

For steel of quality KG to EN 10113, the specified minimum values of Charpy V-notch energy go down to 40 J at -20°C. The entries in this row assume an equivalent value of 27 J at -30°C.

5)

For full details, refer to informative Annex C of Eurocode 3.

74

[Üble D.2]

Maximum thickness for statically loaded structural elements

Table Π.6

Maximum thickness (mm) for lowest service temperature of

Steel grade and quality

0°C Service condition 4 )

SI

S2

SI

S2

SI

S2

50 145 38 101

140 250

36 94

99 250

28 69

EN 10027

EN 10113 D

S 420 M S 420 ML

S 420 KG 2) S 420 KT 3)

250 250

70 172

162 250

S 460 M S 460 ML

S 460 KG 2) S 460 KT 3)

179 250

53 150

150 250

Service conditions 4 ):

51 52

-20°C

­10°C

either:

. non­welded, or . in compression as welded, in tension

In both cases of service conditions this table assumes loading rate Rl (normal static or slow loading; no impact loading) and consequences of failure condition C2 (fracture critical members or joints with potential complete structural collapse).4) Notes: For steels of delivery condition N to EN 10113­2 over 100 mm thick for steel grade S 460 and over D

150 mm thick for steel grade S 420, and for steels of delivery condition M to EN 10113­3 over 150 mm thick for long products and over 63 mm thick for flat products, the minimum Charpy V­notch energy specified in EN 10113 is subject to agreement. Up to 150 mm thick, a minimum value of 27 J is required and 23 J over 150 mm thick up to 250 mm. The test temperature should be ­30°C for steel qualities S 460 KG and S 420 KG and ­50°C for steel qualities S 460 KT and S 420 KT.

2)

For steel qualities S 460 KG and S 420 KG the specified minimum Charpy V­notch energy in EN 10113 only go down as far as 40 J at ­20°C. The entries in this row assume an equivalent value of 27 J at­30°C.

3)

For steel qualities S 460 KT and S 420 KT the specified minimum Charpy V­notch energy in EN 10113 is 27Jat­50°C.

4)

For full details, refer to informative Annex C of Eurocode 3.

II.h.3

Connecting devices

[3.3]

II.h.3.1 B olts [3.3.2]

(1) The nominal values of the yield strength fyb and the ultimate strength fUb ( to be adopted as characteristic values in calculations) are given in table II.7.

Table IL7

Nominal values of yield strength .fø and ultimate tensile strength/„ft for bolts 4.6

4.8

5.6

5.8

6.8

8.8

10.9

1 fyb (N/mm2)

240

320

300

400

480

640

900

| fub (N/mm2)

400

400

500

500

600

800

1000

Bolt grade

75

II.h.3 2 [3.3.5 (2)]

(1) The specified yield strength, ultimate tensile strength, elongation at failure and minimum Charpy V-notch energy value of the filler metal, shall all be either equal to, or better than, the corresponding values specified for the steel grade being welded.

n.h.4 [3.2.5]

Welding consumables

Design values of material coefficients

(1) The material coefficients to be adopted in calculations for the steels covered by Eurocode 3 shall be taken as follows: Table II.8

Material coefficient :

E=

210 000

N/mm 2

.

G=

80700

N/mm 2

2(1+ v) . coefficient of linear thermal expansion

:

a =

12. IO"6

1/°C

. density

:

P=

7850

kg/m^

. Poisson's ratio

:

V =

0,3

. modulus of elasticity . MICdl IIIUUIUUS

VJ —

"

E

76

III

LOAD ARRANGEMENTS AND LOAD CASES

III.a G eneralities [2.2J5 (l)] [2.25 (2)]

(1) A load arrangement identifies the position, magnitude and direction of a free action. (2) A load case identifies compatible load arrangements, set of deformations and imperfections considered for a particular verification. (3) For the definitions of actions Goad arrangements: F= G, Q,...) and effects of actions (E, S) and for the design requirements it should be referred to chapter La (Basis of design). (4) Flow-chart FC 3.1 presents the general procedure to study structures submitted to actions : all load cases are defined by relevant combinations of characteristic (unfactored) values of load arrangements (Fø, for each load case the global analysis of the structure determines the design values for the effects of actions (Ed = oV,6h, f,... ; Sd = N, V, Μ, σ,...) which shall be checked at SLS (Cd limits) and at ULS (Rd resistances). This general procedure is used in the flow-charts about elastic design of: steel frames (in general) (flow-chart FC 1; see chapter I), braced or non-sway frames (flow-chart FC 4; see chapter IV), bracing system (flow-chart FC 12; see chapter ΧΠ), according to Eurocode 3. Moreover references to those general flow-charts FC 1, FC 4 and FC 12 are specified at the different steps of the general procedure presented in the flow-chart FC 3.1. (5) For braced or non-sway buildings it is explained in chapter I.b.l (flow-chart FC 1) and in chapter IV.a.2 (flow-chart FC 4) that the elastic global analysis of the structure could be based on first order theory. In that case of first order elastic global analysis the principle of superposition is applicable because the effects of actions (E, S) are linear functions of the applied actions (F = G, Q,...) (no Ρ-Δ effects and used material with an elastic linear behaviour). The principle of superposition allows to consider a particular procedure to study structures submitted to actions. This procedure illustrated in flow-chart FC 3.2 could be more practical because it should simplify the decision of which load case gives the worst effect. For each single characteristic (unfactored) value of load arrangement (Fk) the global analysis of the structure determines characteristic (unfactored) values for the effects of actions : Ek = (Ov,6h, f,..)k ; Sk = (N, V, M, a,...)k. All load cases are defined by relevant combinations of the characteristic (unfactored) values for the effects of actions (E^Sk). All these load cases directly furnish the design values for the effects of actions (Ed = δγ,δι,, f,... ; Sd = N, V, M, σ,...) which shall be checked at SLS (Cd limits) and at ULS (Rd resistances).

77

Flow­chart LFC3.1J : Load arrangements and load cases for cenerai global analysis of the structure rows:

\s>^>/

C

rows:

'. "N Determine all load arrangements with characteristic (unfactored) values of actions Fk (Gk, Qk,...) - row 1 of flow-chart FC 1 - row 2 of flow-chart FC 4

Determine all ULS load cases with relevant ULS combinations of load arrangements (Fk) (with partial safety factors 7F = γσ, 7Q,...):

Determine all SLS load cases with relevant SLS combinations of load arrangements (Fk): - row 2 of flow-chart FC 1 and FC 12 - row 4 of flow-chart FC 4

- row 2 of flow-chart FC 1 and FC 12 - row 4 of flow-chart FC 4

yes

3 r*

All ULS load cases analysed ?

All SLS load cases analysed ?

ULS checks

SLS checks

I

yes

Classification of the frame: braced or non­sway frame - rows 5 to 8 of flow-chart FC 1 - rows 8 to 14 of flow-chart FC 4 - rows 5 and 6 of flow-chart FC 12

Global analysis of the structure submitted to the considered load case in order to determine the design values for the ULS effects of actions: Sd = N, V, Μ, σ,...

Global analysis of the structure submitted to the considered load case in order to determine the design values for the SLS effects of actions: Ed = oh, δν, f,...

- rows 11 to 13 of flow-chart FC 1 - row 15 of flow-chart FC 4 - rows 9 to 11 of flow-chart FC 12

- row 4 of flow-chart FC 1 and FC 12 - row 6 of flow-chart FC 4

Determine ULS resistances (Rd):

Determine SLS limits (Cd):

- rows 14 to 21 of flow-chart FC 1 - rows 16 to 22 of flow-chart FC 4 - rows 12 to 19 of flow-chart FC 12

- row 4 of flow-chart FC 1 and FC 12 - row 7 of flow-chart FC 4

»­Í Select stronger section(s) or joint(s) 10

j

Adopt the structure if both ULS and SLS checks are fulfilled V

Note: . for the definition of Fk (Gk, Qk), γρ (JG, γο), Sd. Rd, Ed, Cd : see chapter La (Basis of design). . references are done to flow­chart FC 1 (Elastic design of steel frames according to Eurocode 3), flow­chart FC 4 (Elastic design of braced or non­sway steel frames according to Eurocode 3), and flow­chart FC 12 (Elastic design of bracing system according to Eurocode 3).

78

10

Flow-chart (FC 3.2) .Load arrangements and load cases for tirsi order elastic elobal analysis of the structure rows:

i

rows:

f Determine all load arrangements with characteristic (unfactored) values of actions Fk (Gk, Qk, ...)J

y"/AH load arrangements analysed?

Global analysis of the structure submitted to the considered single load arrangement (Fk) in order to determine characteristic (unfactored) values for the effects of actions : - for ULS checks: Sk = (N, V, Μ, σ, ...)k - for SLS checks: Ek = (δη, δν, f,^)k

1

1

ULS checks

SLS checks

I

i

Determine all ULS load cases with relevant ULS combinations of effects of actions (Sk) (with partial safety factors 7F = 7G, γο,...)

Determine all SLS load cases with relevant SLS combinations of effects of actions (Ek)

(Design values for the effects of actionsPN V. Ed ■ oh. δν, f,... J

Design values for the effects of actions: Sd = N, V, Μ, σ,...

All ULS load cases \ v* analysed? /

yes

All SLS load cases analysed?

Classification of frame: braced or non-sway frame

CDetermine ULS resistances (ftp) 10 11

12

Γ Determine SLS limits (Cd) )

yes

yes

Adopt the structure if both ULS and SLS checks are fulfilled

Τ Γ Select stronger section(s) or joint(s) J-

Note: for the definition of Fk (Gk, Qk), ^F (yc, *fQ), Sd. Rd. Ed, Cd : see chapter La (Basis of design)

79

1

IIl.b

Load arrangements

(1) The following load arrangements are characteristic (unfactored) values of actions (Fk) to be applied to the structure. The characteristic values of load arrangements given hereafter are issued from Eurocode 1 (/l/). (2) The table ΠΙ.1 provides a list of all the load arrangements (Fk) to be taken into account in building design and, the references to the chapters of the handbook where details are given about those load arrangements. Load arrangements Fk for building design according to EC 1

Table ΙΠ.1

Load arrangements (Fk) distributed, g Permanent loads : concentrated, G

1) 2)

Variable loads: Imposed loads on floors and roof: - Wind loads: Snow loads:

ECl 1.5.1 (4)

ECl 1.5.1 (4)

ΠΙ. b. 1

distributed, q concentrated, Q wind pressure, we4 wind force, F w distributed, s

Reference to the handbook ni.b.l

m.b.2.1 ffl.b.2.1 m.b.2.2 m.b.2.2 m.b.2.3

Permanent loads (g and G)

(1) Action which is likely to act throughout a given design situation and for which the variation in magnitude with time is negligible in relation to the mean value, or for which the variation is always in the same direction until the action attains a certain limit value. m.b.2

Variable loads (q, Q, w and s)

(1) Action which is unlikely to act throughout a given design situation or for which the variation in magnitude with time is not negligible in relation to the mean value nor monotonie. m.b.2.1 Imposed loads on floors and roof (q and Q)

ECl 2.1.5.1. (1)

ECl 2.1.6.1. (1)

(1) Categories of areas: areas in offices, housing, warehouses, parkings, dwellings, etc. are divided into six categories according to their specific use: - Category A: areas for domestic and residential activities. - Category B: areas where people may congregate. - Category C: areas susceptible to overcrowding, including access areas. - Category D: areas susceptible to accumulation of goods, including access areas. - Category E: - Category F:

traffic and parking areas for light vehicles, traffic and parking areas for medium vehicles.

(2) The values of imposed loads on floors and roof are given in table ΠΊ.2 according to the category of areas and the loaded areas.

80

Table II1.2

Imposed load (qk, Qk) on floors in buildings

Categories of areas

Loaded areas

qk (kN/m2)

Qk(kN)

Category A;

general stairs balconies

2,0 3,0 4,0

2,0 2,0 2,0

Category B;

general stairs, balconies

3,0 4,0

2,0 2,0

Category C;

with fixed seats other

4,0 5,0

4,0 4,0

Category P;

general

5,0

7,0

Category E:

vehicles weight: Ú 30 kN

2,0

10

Category F;

vehicles weight: 30 ­160 kN

5,0

45

III.h.2.2 Wind loads (weJ, Fw) EC1,6.4P(1)

(1) The wind load is presented either as a wind pressure or a wind force. The action on the structure caused by the wind pressure is assumed to act normal to the surface except where otherwise specified; e.g. for tangential friction forces. ECl, 6.4 (3) (2) The wind action is given by: w wind pressure on a surface (see m.b.2.2.1). Fw resulting wind force: see m.b.2.2.2 or obtained by integrating the wind pressure. Me torsional moment, refer to ECI, part 2.3 Ffr friction force, refer to ECl, part 23 III.h.2.2.1 Wind pressure (wCii) ECl, 6.5.4

(1) The net wind pressure across a wall or an element is the difference of the pressures on each surface taking due account of their signs (Pressure is taken as positive, when directed towards the surface and is negative when represents a suction) (see table ΠΙ.3).

81

Table ΙΠ.3

Pressures on surfaces

Θ

0 Θ:

®:

®

<2C

©r , Θ

^

—*- s

·"·

"*" ^

**

— r=r

0

r©;

—► s —»-

¡^ s

;

, 0

EÉ

:©

ECl, 6.5.2 (2) The wind pressure acting on: . the external surfaces of a structure, w e , shall be obtained from: We=qref-Ce(Ze)-Cpe

. the internal surfaces of a structure, WJ, shall be obtained from: w

ECl, 6.7.1

i=qref-ce(zi)-cpi

where qref is the reference mean wind pressure determined from: Ρ 2

ECl, form. (6.7.1) where

Ρ Vref

ECl, form. (6.7.2)

qref = Tpref is the air density (generally = 1,25 kg/m3) is the reference wind velocity taken as follows v

ref - c DIR- c TEM- c ALT- v ref,0

where vref,o

ECl, 6.8.1 ECl, form. (6.8.1)

basic value of the reference wind velocity at sea level given by the wind maps of the countries (Annex 6.A of ECl). CDIR direction factor to be taken as 1,0 unless otherwise specified in the wind maps. C TEM temporary (seasonal) factor to be taken as 1,0 unless otherwise specified in the wind maps. c ALT altitude factor to be taken as 1,0 unless otherwise specified in the wind maps. where ce(ze) is the exposure coefficient for ζ = ze is defined by: Ce(ze) = C?.C?+7Kr.Cr.Ct where Kr, cr (z), c t (z) are given for more details in [ECl, 6.8.1] For flat terrain (i.e. upwind slope < 5% in the wind direction), c t =1,0. For such conditions the exposure coefficient c e is given in the table III.4.

82

ECl, Fig. 6.8.1 ECl Table 6.8.1

1 Table III.4

Exposure coefficient ce as a function of height ζ above ground

Terrain C ategory: I

Rough open sea, lake shores with at least 2 km fetch upwind and smooth flat country without obstacles. Π Farmland with boundary hedges, occasional small farm structures, houses or trees. ΠΙ Suburban or industrial areas and permanent forests. FV Urban areas in which at least 15% of the surface is covered with buildings and their average height exceeds 15 m.

z(m) 1000 ■ , ,

IV TTT π Τ Ψ

inn 1UVJ —

10 -

Ce( ζ ) 1

_

'

0,1X) where c ECl,table6.10.2.1

Pe

1,130

2,(X)

3,1X)

4,1Χ)

I

5,00

is the external pressure coefficient given in ECl, 6.9, which depend on the size of the effected area A and the shape of the building (see table ΠΙ.5).

Table ΙΠ.5 External pressure Cpe for buildings depending on the size of the effected area A Cpe = Cpei ι

A
Cpe = Cpe, 1 + (Cpe, 10" Cpe, i) l o g i o A

1 m2 < A < 10 m 2

Cpe = Cpe, 10

A > 10 m2

The values of are given in the chapters 6.9.2.2 to 6.9.2.8 of ECI for the different

83

shapes of the buildings. where Ze is the reference height appropriate to the relevant pressure coefficient (see table ΙΠ.6). ECl, Fig. 6.9.2.1

Reference height ze depending on h and b

Table II 1.6

h>2b

b < h < 2b | Ze = h

h
Ze = b

ECl, 6.9.2.2 (4)

Buildings whose height h is greater than 2b shall be considered to be in multiple parts, comprising: a lower part extending upwards from the ground by a height equal to b for which Ze = b; and a middle region, between the upper and lower parts, divided into as many horizontal strips as desired and for which Ze is the height of the top of each strip.

and where Cpi is the internal pressure coefficient. For a homogeneous distribution of openings ECl, 6.10.2.9 the value Cpi = - 0,25 shall be used III.b2.2.2

Wind force (F..)

(1) The global force, F w , shall be obtained form the following expression: ECl, form. (6.6.1)

F

w

-°tref-Ce(ze)-Cf-Aref-cd

. qref is the reference mean wind pressure (see m.b.2.2.1) - ce(ze) is the exposure coefficient for ζ = Ze (see m.b.2.2.1) . Ze is the reference height appropriate to the relevant pressure coefficient (see m.b.2.2.1) . Cf is the force coefficient derived from ECl, part 2.3, chapter 10, if available - Aref is the reference area for Cf - ca is the dynamic factor

HI,b,2,3 Snow loads (s) (1) The snow loads are given by: s = ^.ce.ct.sk where μι Sk ce ct

is the snow load shape coefficient is the characteristic value of the snow load on the ground (kN/mm 2 ) is the exposure coefficient, which usually has the value 1,0 is the thermal coefficient, which usually has the value 1,0

84

111 χ Load cases (1) The following load cases are related to the general procedure to study structures submitted to actions (see flow­chart FC 3.1 and comment (4) in chapter IILa): all load cases are defined by relevant combinations of characteristic (unfactored) values of load arrangements (Fk). [2.3.2.2 (l)] For each load case, design values (Ed, Sd) for the effects of actions shall be detenrtined from global analysis of the structure submitted to the design values of actions (Fd = 7 F · Fk) involved by combination rules as given: ­ in table ΠΙ.7, for SLS ­ in table ΠΙ.8 and table m.9, for ULS (2) In the case of the particular procedure defined in flow­chart FC 3.2 (see also comment (5) in chapter IILa), the characteristic (unfactored) values for the effects of actions (Ek, Sk) are obtained from global analysis of the structure submitted to each single characteristic (unfactored) value of load arrangement (Fk). For each load case, design values (Ed, Sd) for the effects of actions shall be determined from combination rules defined in tables ΠΙ.7 to m.9 where values of load arrangements (Fk = Gk, Qk, g, q, s, w, P) are replaced by the characteristic values for the effects of actions (Ek = (ov,Ôh, f,..)k ; S k = (N, V, M, o,...)k). For instance, in the case of the third example in table m.9, the general load case 1. , (l,35.gk + 1,50 wk) should be replaced by the following particular load case 1. considering the elements or the cross­sections with . their worst effects of actions (for columns: axial force (N)k; for beams: shear force (V)k and bending moment (M)k) and, . their worst combined effects of actions (for beam­columns: (N)k + (M)k ; ...): ­ max N = 1,35 (N)k(due to gk) + l,50.(N)k.max(due to Wk), ­ max V = 1,35 (V)k(due to gk) + l,50.(V)k.max(due to Wk), ­ max M = 1,35 (M)k(due to gk) + l,50.(M)k.max(due to Wk), ­ max N + associated M, ­ max M + associated N,... (3) In the following chapters UI.c.l and ffl.c.2, the proposed combinations of actions are simplifications adapted to building structures (for SLS, [2.3.4 (5)] and for ULS, [2.3.3.1 (5)]). (4) If the limitations imposed at SLS and at ULS are difficult to be respected, more favourable combinations of actions could be used instead of the respective simplified proposals of table m.7 (then see [2.3.4 (2)] of EC 3) or tables ΙΠ.8 and ΠΙ.9 (then see [23.2.2(2)] of EC3). in.c. 1 ECCS n°65 table 2.3

Load cases for serviceability limit states

Table 111.7

Combinations of actions for serviceability limit states

Load combinations to be considered: with only the most unfavourable variable actions (Qicmax): 1. £ G k +Qk.max with all unfavourable variable actions (Qk): 2. £ G k +0,9^Qk

Gk ­ Qk ­

permanent actions, e.g. self weight variable actions, e.g. imposed loads on floors, snow loads, wind loads Qk.max ­the variable action which causes the largest effect

The load combination which gives the largest effect (i.e. deformations, deflections) is decisive

85

m.c.2 ECCSn°65 table 2.1

Load cases for ultimate limit states

Table ΙΠ.8

Combinations of actions for ultimate limit state

Load combinations to be considered: with only the most unfavourable variable actions (Qk.max): ** YG­XGk+YQ­Qk.max l,35*.EG k +l,50**.Q k.max 1. with all unfavourable variable actions (Qk):

YGEGk+0,9YQ.XQk

2.

permanent actions, e.g. self weight Qk­ variable actions, e.g. imposed loads on floors, snow load, wind loads Qk.max ­the variable action which causes the largest effect partial safety factor for permanent YGactions partial safety factor for variable YQactions Gk­

l,35*.]TG k +l,35**.£Q k

* If the dead load G counteracts the variable action Q(meaning a favourable effect of G): YG = LOO ■ ' '' t " M " ♦ windload Q ν , Ι ν ι „ „ ι deadload G

-κ

t πι titt

"if the variable load Q counteracts the dominant loading (meaning a favourable effect of Q): YQ = 0 The load combination which gives the largest effect (i.e.internal forces or moment ) is decisive ECCSn0 65 table 2.2

Examples for the application of the combinations rules in table ΙΠ.8. All actions (g, q, P, s, w) are considered to originate from different sources load cases combinations of actions ŒEUm s 1. l,35.g+l,50.q J I q 2. l,35.g+l,50.s l,35.(g + q + s) 3. A A

Table ΙΠ.9

f α ιρg

LXLTEDq * O i i i Q M D s

ο π *i π

-A

w

g­ q-

P­ s­ w­

ΓΤΤΤ ΊΊ ΕΡΖΕΕΠ q ŒEEEED g

1. 2. 3. 4.

l,35.g+l,50.q LSS.g+LSO.P*) 1,35. g+1,50. s L35.(g+q+s + P*))

1. 2. 3. 4.

l,35.g+l,50.w l,35.g+l,50.q 1,35. g+1,50. s l,35.(g + q + w + s)

) assuming Ρ is independent of g, q, s and w

dead load imposed load Point load snow load wind load

86

IV [5.1.2 (l)]

[5.1.2(2)]

ECCS n° 65 table 5.2

DESIGN OF BRACED OR NON-SWAY FRAME

I V.a Generalities (1) Frames shall be checked : . at Serviceability Limit States: - for horizontal deflections (see chapter IV.f.l) , . at Ultimate Limit States: - for static equilibrium (see chapter IV.b), - for frame stability (see chapter IV.d), - for resistance of cross-sections, members and connections (see chapter IV.g) . (2) When checking the resistance of cross-sections and members of a frame, each member may be treated as isolated from the frame, with forces and moments applied to each end as determined from the frame analysis. The conditions of restraint at each end should be determined by considering the member as part of the frame and should be consistent with the type of analysis and mode failure. IV-a.l Analysis models for frames (1) In general spacial frame structures may be separated into several plane frames that may be considered as laterally supported at the spacial nodes (see table IV. 1, part 1.). In the first step for the inplane loading of these plane frames out-of-plane deflections between the lateral supports are neglected and only the inplane monoaxial action effects are determined. In the second step the individual members of the plane frame between the lateral supports, i.e. the beams and the columns, are separated from the plane frame, to consider lateral buckling and lateral-torsional buckling, under monoaxial bending and compression. Members which are common to two different frames, e.g. columns, may be verified for biaxial bending and compression (see table IV. 1, part 2.). (2) Table IV.2 shows the modelling of connections in the global analysis depending on their rotational stiffness. Table IV.2

Modelling of connections

Type of connection Symbols in the analysis Designed for Pinned connection

tension, compression or shear only

O

moment, shear, tension or compression from an elastic or plastic global analysis

Rigid connection

Design or detail criteria Small restraint to sufficient rotations

Small rotations, sufficient elastic moment and shear strength

ì E

For semi-rigid connections see Eurocode 3, Part 1.1 (J2f) (3) Guidance on assumptions for reliable simplified modelling of buildings is provided in the Annex H of Eurocode 3 Part 1.1 (J2f) which is in preparation: "Modelling of building structures for static analysis".

87

Table IV.l

Modelling of frame for analysis

1. Separation of plane frames from the spacial frame :

FRAME 2

Tflrr

2. Separation of individual members from plane frame:

FRAME 1

ÌK t

t

Ml

cHnW

7Û7T

Isolated beam

Isolated column N1 + N2

88

IV.a.2

Flow-chart FC 4:Elastic global analysis of braced or non-s wax steel frames according to Eurocode 3

(1) The flow-chart FC 4 aims to provide a general presentation of the subject dealt in the present design handbook: elastic global analysis of braced or non-sway steel frames according to Eurocode 3. All the details are given in chapters II to XI of the handbook. (2) The flow-chart FC 4 refers to other flow-charts: - flow-chart FC 1 about elastic global analysis of steel frames in general according to EC 3 (the flow-chart FC 1 is provided in chapter I). - flow-chart FC 12 about elastic global analysis of bracing system according to EC 3 (the flow-chart FC 12 and all the details about bracing system design are given in chapter XII) and, (3) The flow-chart FC 4 is a part of flow-chart FC 1 which gives a general presentation of: - elastic global analysis of braced or non-sway frames (= flow chart FC 4 = path Φ of flow-chart FC 1) and, - elastic global analysis of sway frames which are out of the scope of the present design handbook (= paths (D to (D of flow-chart FC 1). (4) The flow-chart FC 4 is divided in 3 parts: rv.a.2.1 general part (1 page)

rv.a.2.2 detail (1 page) IV.a.2.3 comments (4 pages)

IV.a.2.1 Flow-chart FC 4 general see the following page IV.a.2.2 Flow-chart FC 4 details see the second following page

89

Flow-chart 4ÍFC 4J: Elastic global analysis of braced or non-swav steel frames according to EC 3 rowi (General)

Actions Predesign SLS checks and Classification of the frame for ULS (braced or non-sway frame)

10

11 12

13

ULS global analysis of the frame to determine the internal forces and moments (N, V, M)

IS

16

ULS checks of members

submitted to internal forces and moments (N, V, M)

17

18

19

20

ULS checks of local effects ÜLS checks of connections 90

Flow­chart 4 \FC 4 j : Elastic global analysis of braced

steel frames according to EC 3

or non-swav

Í Assumptions of the frame modelling J Τ [Determination of load arrangements (ECl and EC 8)J

(Details)

row: ι 2

SLS checks [Chap. 4]

ULS checks [Chap. 5]

Τ

JL.

:

Load cases

Load cases for ULS [2.3.3.]

for SLS

[2.3.4.] notfulfilled

Predësign of members: beams & columns => Sections with pinned and/or rigid connections First order elastic global analysis of the frame => 6v, Oh, f,...

t

SLS checks Frame with bracing system

Classification of the frame

notfulfilled

[Chap. 4] Frame without bracing system

1 First order elastic global analysis of the frame submitted to hypothetic horizontal loads: 1) with bracing system => 5b and

/ C h o i c e of criterion **—(of sway / non­sway \ frame

δΣν ηΣΗ

Vsd fcr

±

2) without bracing system => 5u

Vertical loads

Horizontal & vertical loads Design of the bracing system

, Braced frame\ yes/

o

Global imperfections of the frame => equivalent horizontal loads [5.2.4.3]

\no

Ob £ 0,2 5u [5.2.53. (2)]

First order elastic global analysis of the frame for each ULS load case

Non-sway frame

First order elastic global analysis of the frame for all concerned ULS load cases: either, laterally supported if braced frame or, without special lateral boundary conditions if non-sway frame

yes

Non­sway frame [5.2.52.] δΣν

<ο,ι Ο Γ ™ so.i

ηΣΗ

F C 1 J­

Classification of the cross­sections [Chap. 5.3]

±

L b, buckling length of members for non­sway mode [Annex E]

J J

IB

notfulfilled

Checks of the out­of­plane stability: members buckling [Chap. 5.5.] Checks of resistance of cross­sections [Chap. 5.4.]

C

1

Checks of local effects (buckling and resistance of webs) [Chap. 5.6 and 5.7] Checks of connections [Chap. 6 and Annex J]

91

17

notfulfilled

Checks of the in­plane stability: members buckling [Chap. 5 J.]

(

14

Vcr

■ L - -

C

Design of sway frames

19

notfulfilled >

J­ >

notfulfilled notfulfilled

rV.a.2.3 Comments onflow-chart FC 4 comments (1/4) on flow-chart FC 4: * Generalities about Eurocode 3: - All checks of (ULS) Ultimate Limit States and all checks of (SLS) Serviceability Limit States are necessary to be fulfilled. - According to the classification of cross-sections at ULS (row 16; chapter V of the design handbook) Eurocode 3 allows to perform: . plastic global analysis of a structure only composed of class 1 cross-sections when required rotations are not calculated [5.3.3 (4)] or, . elastic global analysis of a structure composed of class 1. 2. 3 or 4 cross-sections assurning for ULS checks, either a plastic resistance of cross-sections (class 1 and 2) or, an elastic resistance of the cross-sections, without local buckling (class 3) or, with local buckling (class 4 with effective cross-section). [5.2.1.2(1)]

- In order to determine the internal forces and moments (N. V. M) in a structure Eurocode 3 allows the use of different types of elastic global analysis either: a) first order global analysis using the initial geometry of the structure or, b) second order global analysis taking into account the influence of the deformation of the structure

[5.2.1.2 (2)]

[Annex H]

- First order global analysis may be used for the elastic global analysis in the cases of braced or non-sway frames (row 15).

* row 1: Assumptions of the frame modelling: examples are provided in the present chapter rv.a. 1 and more details are presented in the [Annex H] of Eurocode 3 ("Modelling of building structures for analysis"). * row 2:

[Chap. 5] [Chap. 4]

EC 1: Draft EC 3: ENV 1993-1-1

Eurocode 1 Eurocode 3

Basis of design and actions on structures Design of steel structures, Part 1.1: general rules and rules for buildings. Design of structures for earthquake resistance

EC 8: Draft

Eurocode 8

* rows 3.4: -ULS -SLS

means Ultimate Limit States means Serviceability Limit States

* row 5: This flow-chart concerns structures using pinned and/or rigid joints. 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 (predesigri, 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.

92

comments (2/4) on flow-chart FC 4: [4.2.1 (5)]

* row 6: For SLS checks, the deflections should be calculated making due allowance for any second order effects, the rotational stiffness of any semi­rigid joints and the possible occurrence of any plastic deformations.

[5.2.5.3 (2)]

»nbraçed frame

The frame is braced if:

δ 0 <0,2δ„

where

δ^,: horizontal displacement of the frame with the bracing system oV horizontal displacement of the unbraced frame, according to first order elastic global analysis of the frame submitted to hypothetic horizontal loads. Note: in the case of simple frames with all beam­column nodes nominally pinned, the frame without bracing would be hypostatic, hence δα is infinite and thus the condition Ob £ 0,2 δ„ is always fulfilled. [5.2.4.3]

* row 12: global imperfections of the frame initial sway imperfections of the frame F2

ζ α *

equivalent horizontal forces F2

0F2

could be applied in the form of

fc1

­J

Fi

φ Fl

i i i i ·

fc

f

φ (Fl + F2)

93

i i i ιι

^β

1

r—

φ (Fi + F2)

comments (3/4) on flow-chart FC 4: * row 14:

[5.2.5.2]

classification of sway or non­swav frame:

A frame may be classified as non-sway if according to first order elastic global analysis of the frame for each ULS load case, one of the following criteria (see row 91 is satisfied: either, al in general : [5.2.5.2 (3)]

^ ­ = — < 0,1 , condition which is equivalent to ï a cr

a C T > 10

"­cr

design value of the total vertical load (see row 10) elastic critical value of the total vertical load for failure in a sway mode ( = π2ΕΙ / L2 with L, buckling length for a column in a sway mode; VCT of a column does not correspond necessarily to V cr of the frame including that column) ac coefficient of critical amplification or coefficient of remoteness of critical state of the frame b) in case of building structures with beams connecting each columns at each storey level:

where Vsa: Vcr:

or, [5.2.5.2(4)]

ο·Σν­δ·(νι­τ­ν2) < 0,1 h.£H h.(H 1 + H 2 ) where H, V: total horizontal and vertical reactions at the bottom of the storey, δ: relative horizontal displacement of top and bottom of the storey, h: height of the storey. Η,ν,δ are deduced from a first order analysis of the frame submitted to both horizontal and vertical design loads (see row 10) and to the global imperfections of the frame applied in the form of equivalent horizontal forces (see comments on row 12). Notes: ­ A same frame could be classified as sway according to a load case (Vsdl for instance) and as non­sway according to another load case ( Vsd2 for instance)(see row 13). V ­ = maximum sdi For multi­storeys buildings the relevant condition is V V cri

condition which is equivalent to where

Λ

sdi

>

V V vcny

or acrj are related to the storey i.

94

otcr = minimum (oten),

comments (4/4) on flow-chart FC 4:

* row 15: At this step of the ULS checks procedure the type of frame is defined as - braced frame and the first order elastic global analysis of the frame should be carried out for all ULS load cases, - or, non-sway frame and the first order elastic global analysis of the frame might have already been done for all concerned ULS load cases when the

syv

criterion —^— has been chosen (rows 9 to 13). h2)H The load cases should consider specific actions in case of braced or non-sway frames as provided in the table below. The global analysis of the frame determines the internal forces and moments (N,V,M) in the members. The first order elastic global analysis of the frame should take into account the horizontal the global the vertical actions loads loads imperfections of the types of frame (row 12)' frames X(b) 1) braced frames ($ 2) non-sway frames (c) 15.253 (3)]

Notes : (a) braced frames are frames which may be treated as fully supported laterally by a bracing system. (b) only the part of horizontal loads which are applied to the frame but not assumed to be transmitted to the bracing system through the floors.

[5.2.5.3(5)]

(c) no special lateral boundary conditions are considered in the frame modelling.

* row 16;

The classification of cross-sections have to be determined before all the ULS checks of members, cross-sections and webs (rows 18 to 21).

[Annex E]

* row 17: Nsd

Lh, buckling length of members for non-sway mode

►c^

Lb

* rows 18Λ19,2Q> 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 + — <Ξ1,0 V nc is the number of columns per plane where n„ is the number of storeys nc [5.2.4.3 (2)] (7) Only those columns which carry a vertical load Nsd of at least 50% of mean value of the vertical load per column in the considered plane, shall be included in nc. [5.2.4.3 (3)] (8) Only those columns which extend through all the storeys included in n s shall be included in nc . Only those floor or roof levels which are connected to all the columns included in nc shall be included when determining n*

[5.2.6.1 (l)] [5.2.6.1 (2)] [5.2.6.1 (3)] [5.2.6.1 (4)]

IV.d Frame stability (1) All frames shall have adequate resistance to failure in a sway mode. However, where the frame is shown to be non­sway, no further sway mode verification is required. (2) All frames including sway frames, shall also be checked for adequate resistance to failure in non­sway modes. (3) A check should be included for the possibility of local storey­height failure mode. (4) Frames with non­triangulated pitched roofs shall also be checked for snap­through buckling.

97

Table IV.4 ECCS n°65 table 5.6

Values for the initial sway imperfections φ

number of columns inplane

nc = 2

η<;=3

nc = 4

nç=5

Τ

number of storeys

I

ι I

n.= 1

1/200

1/220

1/230

1/240

1/280

ns = 2

1/240

1/260

1/275

1/285

1/335

ns=3

1/275

1/300

1/315

1/325

1/385

ns = 4

1/300

1/325

1/345

1/355

1/420

nSs = oo

1/445

1/490

1/515

1/535

1/630

—

ï [5.2.1.1]

[5.2.1.2]

!!<;=,

i

I V.e

First order elastic global analysis

IV.e.l

Methods of analysis

(1) The internal forces and moments in a statically determinate structure shall be obtained using statics. (2) The internal forces and moments in a statically indeterminate structure may generally be determined using either: elastic global analysis plastic global analysis (3) Elastic global analysis may be used in all cases. rv.e.2

Effects of deformations

(1) The internal forces and moments may generally be determined using either: first order theory, using initial geometry of the structure. second order theory, taking into account the influence of the deformation of the structure. (2) First order theory may be used for the global analysis in the following cases: braced frames, non­sway frames, design methods which make indirect allowances for second­order effects. (3) Second order theory may be used for the global analysis in all cases.

98

IV.C.3 [5.2.1.3]

Elastic global analysis

(1) Elastic global analysis shall be based on the assumption that the stress-strain behaviour of the material is linear, whatever the stress level. (2) This assumption may be maintained for both first-order and second-order elastic analysis, even where the resistance of a cross-section is based on its plastic resistance (see chapter V about classification of cross-section). (3) In order to determine the internal forces and moments (N, V, M) in braced or non-sway frames, first order elastic global analysis may be used. (4) Following a first order elastic global analysis, the calculated bending moments may be modified by redistributing up to 15% of the peak calculated moment in any member, provided that: - the internal forces and moments in the frame remain in equilibrium with the applied loads and, - all the members in which the moments are reduced have class 1 or 2 cross-sections (see chapter V). (5) The load cases should consider specific actions in case of braced or non-sway frames as provided in table IV. 5 (issued from comments on row 15 in flow-chart FC 4). Table IV.5

Specific actions for braced or non-sway frames

The first order elastic global analysis of the frame should take into account *^^ actions the horizontal the vertical the global imperfections loads of the frame | types of ^ " ^ ^ ^ ^ ^ loads | frames ^*"""-^^ X(b) X 1) bracedframes (¿) 2) non-sway frames (ς) [5.2.5.3 (3)] [5.2.5.3 (5)]

X

X

X

Notes : (al braced frames are frames which mav be treated as fully supported laterally bv the bracing system. (b) only the part of horizontal loads which are applied to the frame but not assumed to be transmitted to the bracing system through the floors. (c) no special lateral boundary conditions are considered in the frame modelling. (6) In case of first order elastic global analysis the principle of superposition is applicable because the effects of actions (E, S) are linear functions of the applied actions (F = G, Q, ...) (no Ρ-Δ effects and used material with an elastic linear behaviour). The principle of superposition allows to consider a particular procedure to study structure submitted to actions. This procedure illustrated in flow-chart FC 3.2 could be more practical because it should simplify the decision of which load case gives the worst effect (see chapter ΙΠ). For each single characteristic (unfactored) value of load arrangement (Fk) the global analysis of the structure determines characteristic (unfactored) values for the effects of actions : Ek = (δν,δη, f,..)k ; Sk = (N, V, Μ, σ,..\. AU load cases are defined by relevant combinations of the characteristic (unfactored) values for the effects of actions (E/dSk). AH these load cases directly furnish the design values for the effects of actions (Ed = Oy.ôh, f,.·· ; Sd = Ν, V, Μ, σ,...) which shall be checked at SLS (Cd limits) and at ULS (Rd resistances). IV.f Verifications at SLS (1) The limiting values for vertical deflections and vibrations of beams are given respectively in chapters Vin.b. 1 and Vin.b.2 (in chapter Vm about members in bending).

99

[4.2.2 (4)]

ECCS n°65 table 4.3

IV.f. 1 Deflections of frames (1) The limiting values for horizontal deflections of frames given in table IV.6 are illustrated by reference to the multi­storey and single­storey frame. Table IV.6

Recommended limits for horizontal deflections Multi­storey frame διδ2

Single storey frame

δι < hi / 300 δ 2 < h2 / 300 ôo
Portal frame without gantry cranes δ < h / 150 Other buildings δ < h / 300

IV.g Verifications at ULS IV. g. 1 Classification of the frame IV.g.1.1 Hypothesis for braced frame [5.2.5.3]

(1) Examples of bracing system are mentioned in chapter I.b.2 and in chapter ΧΠ. [5.2.5.3 (2)] (2) A steel frame may be classified as braced if the bracing system reduces its horizontal displacements by at least 80 %. (3) For practical presentation of the criterion used to classify a frame as braced reference may be made to comments on row 11 of flow­chart FC 4 (see chapter IV.a.2.3). [5.2.5.3 (3)] (4) A braced frame may be treated as fully supported laterally. (5) As the criterion of braced or unbraced frame classification is related to the stiffness of the frame and on hypothetic horizontal loads, the frame should be classified as braced or not independently of load cases. rv.q.1.2 Hypothesis for non-swav frame (1) Examples of sway frames are mentioned in chapter I.b.2. [5.2.5.2] (2) In order to define the criterion used to classify a frame as sway or non­sway reference may be made to comments on row 14 of flow­chart FC 4 (see chapter IV.a.2.3). (3) As the criterion of sway or non­sway frame classification depends on the total vertical load, a same frame could be classified as sway according to a load case and as non­sway according to another load case. Therefore the criterion of sway or non­sway frame classification should be checked for each load case.

rv.g.2

ULS checks

[5.1.2(1)]

(1) The frames shall be checked at ultimate limit states for the resistances of cross­sections, members and connections. For those ULS checks reference may be made to the following chapters: ­ Classification of cross­sections: see chapter V ­ Members in tension: see chapter VI see chapter VH ­ Members in compression: see chapter VIII ­ Members in bending: see chapter LX ­ Members with combined axial force and bending moments: see chapter X ­ Transverse forces on webs: see chapter XI ­ Connections:

100

V C LASSIFI C ATION OF CROSS-SECTIONS V.a

Generalities

(1) For a designer the usual procedure is to choose a cross­section in such a way that the maximal capacity is not controlled by local buckling but is associated with the bearing load of a particular member of the structure (column, beam, beam­column). Therefore the local buckling plays an important role in the design of structural steel. The critical level over which local buckling appears, is defined by the classification of cross­sections. (2) For the check of cross­sections and members at Ultimate Limit States, the steel cross­ sections shall be classified. The classification of cross­sections allows to evaluate beforehand their behaviour, their ultimate resistance and their deformation capacity, taking into account the possible limits on the resistance due to local buckling of compression elements of cross­sections. (3) The classification of cross­sections permits (see table V.l): to guide the selection of global analysis of the structure (elastic or plastic global analysis), to determine the criteria to be used for ULS checks of cross­sections and members. (4) Four classes of cross­section are defined according to (see chapters V.b and V.c): the slenderness of its compression elements (width­over­thickness ratios of web or flange), the yield strength of the steel and, the applied loading. (5) It is important to precise that the present classification of cross­sections is only based on the distribution of normal stresses across the section due to the following separate or combined axial forces and/or bending moments applied to the cross­section:

é

¿Ρ -

χ -

y"

ϊΡ

Μ z.Sd Ν.x.Sd

,y

Νx.Sd

χ

Μy.Sd

(6) The present classification of cross-sections is not affected by shear forces (Vz.sd.Vy.Sd)· The resistance of webs to shear buckling (induced by V^sd) should be checked in chapter VUI.d.2. (7) The flow-chart FC 5.1 presents the general procedure to classify I cross-section (see the following page) . More details are given in chapters V.b and V.c. (8) The flow-chart FC 5.2 presents a procedure to calculate the effective cross-section properties of class 4 cross-section where local buckling occurs (see the second following page). More details are given in chapter V.c.3.

101

Flow-chart fee 5.lJ : Classification of I cross-section rows:

rows:

1

1

Determine ε = V 235 / fy

I

Division of the cross-section into elements: web and flanges

J

Class of cross-section = highest class of all elements

J

Γ Determine the slenderness of element to classify : d/tw, c/tf,... J (

Type of loading on element to classify

1 τ Bending

I Compression ;

1

1

ί Combined Ν + Μ ι axial load and bending moment ¡

M

Ncomp.

J

Γ Determine the position of neutral axis with plastic distribution of stresses

^ C l a s s 1 or 2 element^ X (*) /

­ ^ C l a s s 1 or 2 element \

Determine the position of neutral axis with elastic distribution of stresses

yes 10 h

11

Class 3 element ?

i lyes s

Class 3 element ? (*♦) no

to*)

Class 4 element .with local buckling

Note :

l>

ς

Class 4 element ith local buckling

(*) see table V.3 (**) see table V.4

102

J

J

2£



X

(**)

f

10

no

( Class 4 element Udth local buckling

u

F C 5 . 2 ) : Calculation of effective cross-section properties of Class 4 cross-section Flow­chart (IFC5.21

Approximate method assuming all elements of the cross­section at Ultimate Limit States: the maximal compressive stress in each element is equal to yield strength (fy). rows:

rows:

f

1

r~ ■

2

ι '

Í

Type of loading on cross­section

-

1

"JL

Combined N + M axial load and bending moment

A Bending M

Compression Ncomp.

τ

I

Only class 4 elements (web and/or fiantes) have effective properties

"f Calculate effective section area Aeff.N (from table V.8) yes/ \

Calculate shift of centroidal axis e ^ (with Acff.M from table V.8)

Bisymmetrical cross­section ? Calculate effective moment of inertia Ieff

7

Calculate shift of centroidal axis βΝ

8

Determine additional bending moment ΔΜ = Ν . e N

10

11

8

Calculate the lowest effective section modulus Wefr

9

Combined (N+M) loading(M Φ 0)?

7

yes

9 10

11

Effective properties: 12

­ for Ν or (N, M) loading: Aeff.N ; e N y ; e N z ­ for M or (N, M) loading: Weff.y ; Weff.z

103

12

[5.3.2]

V.b

Definition of the cross-sections classification

(1) Four classes of cross-sections are defined, as follows: Class 1 cross-sections are those which can form a plastic hinge with the rotation capacity required for plastic analysis. Class 2 cross-sections are those which can develop their plastic moment resistance, but have limited rotation capacity. Class 3 cross-sections are those in which the calculated stress in the extreme compression fibre of the steel member can reach its yield strength, but local buckling is liable to prevent development of the plastic moment resistance. Class 4 cross-section s are those in which it is necessary to make explicit allowances for the effects of local buckling when determining their moment resistance or compression resistance. (2) Table V. 1 recapitulates the characteristics of each class of cross-section in case of simply-supported beam. (3) The ultimate resistance of cross-sections and of members submitted to bending and/or compression, depends on class of cross-sections and is based on the following properties (see table V.l): Cross-section properties for ULS check formulas

ULS partial safety factors

plastic properties (Wp¿)

YMO

Class 3

- elastic distribution - with yield strength reached in the extreme fibres

elastic properties (We/)

YMO

Class 4

- elastic distribution across the effective section taking into account local buckling - with yield strength reached in the extreme fibres.

effective properties (Aeff, eN, Weff)

YM1

Distribution of stresses across the section [5.3.4 (2)]

[5.3.4(3)]

Class 1 or 2 - full plastic distribution - at the level of yield strength

[5.3.5]

[5.3.4(4)] [5.3.4(5)]

(4) When elastic global analysis is used, particular exemptions to these rules may be made for the following specific cases: when yielding first occurs on the tension side of the neutral axis, when the cross-section is composed of class 2 compression flange and class 3 web. Those exemptions are not considered in the handbook and reference may be made to Eurocode 3 Part 1.1 (HI).

104

Table V.l

Definition of the classification of cross-section

1

^qTTjpjjj^

Class

Behaviour model

M Mpt--

PLASTIC across full section

7local^

buckling

M Mpi-

Wtpt Mei

M

ƒ

fy

elastic important

or, plastic

PLASTIC across full section \

local buckling θ

χ-— Xocal

buckling θ

Mpi Met

Design resistance

Available rotation capacity of plastic hinge

Global analysis of structures

I

limited

elastic

ELASTIC across full section

ƒ

fy

none

elastic

none

elastic

ELASTIC across effective section

M local buckling θ

ƒ

105

fy

V.c

Criteria of the cross-sections classification

V.c. 1

Classification of compression elements of cross-sections

[5.3.2(3)]

(1) The classification of a cross-section depends on the proportions of each of its compression elements (width-over-thickness ratios of web or flange), on the yield strength of the material and on the applied loading.

[5.3.2(4)]

(2) Compression elements include every element of a cross-section which is either totally or partially in compression, due to axial force or bending moment, under the load combination considered. (3) In case of combined actions (Nsd and Msd), the limiting proportions for classification of elements are related to the position of plastic or elastic neutral axis (parameters α or ψ in tables V.3 and V.4); that position depends on the stresses distribution across the section in equilibrium with the applied design values of (NSd, MSd). Therefore the classification of an element or a cross-section may be different according to the considered combination of actions (Ν, M). (4) In case of elements submitted to tension (Ntension) local buckling is not expected and the concerned elements shall be class 1. V.C.2

Classification of cross-sections

[5.3.2(5)]

(1) The various compression elements in a cross-section (such as a web or a flange) can, in general, be in different classes.

[5.3.2(6)]

(2) A cross-section is normally classified by quoting the highest (least favourable) class of its compression elements.

[5.3.2(7)]

(3) Alternatively the classification of a cross-section may be defined by quoting both the flange classification and the web classification. For instance, the compression flange of an I-section may be class 1 and its web may be class 3. Then this I-section is class 3. But this I-section may also be defined by quoting its class 1 compression flange and its class 3 web. (4) The determinant dimensions of cross-sections for classification are provided in table V.2. (5) In case oil or Η cross-sections, T-sections and channels ( [ ) , the limiting proportions for classification of elements (webs and flanges) are given : - in table V.3, for class 1 and 2 - in table V.4, for class 3 (6) In case of rectangular and square hollow sections the limiting proportions for classification of internal flanges are given in table V.6 for class 1,2 and 3. For classification of webs of these sections reference may be made to tables V.3 and V.4. (7) In case of angles and tubular sections the limiting proportions for classification of elements are given in table V.7 for class 1,2 and 3. V.c.3

[5.3.2(8)]

Properties of class 4 effective cross-sections

(1) An element of a cross-section (as such a web or a flange) which fails to satisfy the limits for class 3 should be taken as class 4.

106

The limiting proportions for class 3 compression elements should be obtained from tables V.4, V.6 or V.7. [5.34(6)]

(2) When any of the compression elements of a cross-section is class 4 the cross-section shall be designed as a class 4 cross-section.

[5.3.2(2)]

(3) Effective widths may be used in class 4 cross-sections to make the necessary allowances for reductions in resistance due to the effects of local buckling.

[5.3.5]

(4) The effective cross-section properties of class 4 cross-sections (Aeff, en, Weff.y, Weff^) shall be based on the effective widths of the compression elements. The flow-chart FC 5.2 presents an approximate method to determine the effective cross-section properties assuming all elements of the cross-section at Ultimate Limit States : the maximal compressive stress in each element is equal to yield strength, fy. (5) The effective properties of class 4 cross-sections may be obtained from table V.8 or from Eurocode 3 (J2f) for other cases. (6) In general the determination of the effective width of a class 4 element may be carried out as follows (see [5.3.5(3)] of EC3) : a) determination of buckling factor k 0 corresponding to the stress ratio ψ (see [table 5.3.2] and [table 5.3.3] of EC3), b) calculation of the plate slenderness λ ρ ; given by :

in which t kø

ε= b

is the relevant thickness of the elements, is the buckling factor corresponding to the stress ratio ψ, 235 (with f in N/mm2), y

is the appropriate width as follows : b= d for webs, b= b for internal flange elements (except RHS), b= b - 3t for flanges of RHS, b= c for outstand flanges, b= b = h or

c)

for equal-leg angles, for unequal-leg angles.

calculation of reduction factor ρ with the following approximation ([formula (5.11)] ofEC3): . when λ ρ <, 0,673 : ρ = 1 (λρ-0,22) .when λ ρ > 0 , 6 7 3 : p=> _ 2 —'-

d)

determination of the effective width beff

107

(7) For cases proposed in table V.8 the effective cross-sectional data may be determined as follows : a) calculation of λ ρ according to table V.8, b) calculation of ρ according to the formula given in V.c.3(6) c), c) determination of effective zones of class 4 elements according to table V.8. (8) It is important to mention that only class 4 compression elements (web and/or flange) shall have effective width. For instance, HEA 500 cross-section in S 460 steel grade subject to uniform compression, has a class 1 flange and a class 4 web; therefore the effective area (Aeff) issued from table V.8 is composed of full flanges and an effective web. ECCS n°65 (9) Where the stresses Osd from effective cross-sectional data are less than fy, the plate 5.3.5(5)

slenderness λ ρ may be decreased by , which may cause an increase of the effective width.

[5.3.5(6)]

(10) Generally the centroidal axis of the effective cross-section will shift by a dimension e compared to the centroidal axis of the gross cross-section. This should be taken into account when calculating the properties of the effective cross-section. Examples are given in table V. 10.

[5.3.5(7)]

(11) When the cross-section is subject to an axial force, the method given in chapter IX.d.1.4 should be used to take account of the additional moment ΔΜ given by : AM = N e N where eN Ν

is the shift of the centroidal axis when the effective cross-section is subject to uniform compression (single N), is positive for compression.

108

V.d [5.3.1(2)]

Procedures of cross-sections classification for different loadings

(1) Because elastic global analysis is used for braced or non-sway frames (see chapter IV.e), any class of cross-section may be used for the members, provided that the design of the members takes into account the possible limits on the resistance of cross-section due to local buckling (see table V.l). (2) The class of a cross-section may specifically be determined according to the applied loading : - for cross-sections subject to compression, see chapter V.d.l, - for cross-sections subject to bending, see chapter V.d.2, - for cross-sections subject to combined (N, M), see chapter V.d.3. V-d.l

Classification of cross-sections in compression

(1) For cross-sections submitted to uniform compression (Nx.sd) two steps are required for classification: 1) if using the plastic compression resistance of the cross-section, the limiting proportions for class 3 sections shall be met for class 3 flange and web submitted to single Ncompression: see tables V.4, V.6 or V.7; the cross-sectional area A shall be used. 2) if an element of the cross-section fails to satisfy the limits for class 3 it should be taken as class 4. The occurence of local buckling in that element should be considered in calculating the effective cross-sectional area : Aeff (see table V.8). In the case of class 4 monosymmetrical cross-section the shift of the relevant centroidal axis (eN) should also be calculated. V-d.2

Classification of cross-section in bending

(1) For cross-sections submitted to bending moments (My.sd, Mz.sd) three steps are required for classification : 1) if using the plastic moment resistance of the cross-section, the limiting proportions for class 2 sections shall be met for class 2 flange and web submitted to bending moments (single My.sd and/or single M^sd) '· see tables V.3, V.6 or V.7; the plastic section modulus Wpi shall be used. 2) if using the elastic moment resistance of the cross-section, the limiting proportions for class 3 sections shall be met for class 3 flange and web submitted to bending moments (single My.sd and/or single M^sd) : see tables V.4, V.6 or V.7; the elastic section modulus Wei shall be used. 3) if an element of the cross-section fails to satisfy the limits for class 3 sections it should be taken as class 4. The occurence of local buckling in that element should be considered in calculating the effective section modulus of the cross-section when subject only to bending moment about the relevant axis (Weff.y from single My.sd; Weff.z from single Mz.sd) (see table V.8).

109

V­d.3

Classification of cross­sections in combined (NM)

(1) For cross­sections submitted to combined axial load (Nx.sd) and bending moments (My.sd» Mz.sd) three steps are required for classification: 1)

if using the plastic moment resistance of the cross­section, the limiting proportions for class 2 sections shall be met for class 2 flange and web submitted to combined axial load and bending moments ((Ncompression or Ntention) and (My.sd and/or Mz.Sd)) : see table V.3, V.6 or V.7; the cross­secùonal area A and the plastic section modulus Wpi shall be used.

2)

if using the elastic moment resistance of the cross­section, the limiting proportions for class 3 sections shall be met for class 3 flange and web submitted to combined axial load and bending moments ((Ncompression or Ntention) and (My.Sd and/or Mz.Sd)) : see table V.4, V.6 or V.7; the cross­secüonal area A and the elastic section modulus Wei shall be used.

3)

if an element of the cross­section fans to satisfy the limits for class 3 sections it should be taken as class 4. The occurence of local buckling in that element should be considered in calculating the effective section properties (see table V.8) : ­ Aeff : the effective area of the cross­section subject to uniform compression (single Nx.sd); ­ in the case of class 4 monosymmetrical cross­section: e N (= eNy> eNz): the shift of the relevant centroidal axis when the cross­section is subject to uniform compression (single Nx.sd); ­ Weff (=Weff.y, Weff.z) : the effective section modulus of the cross­section when subject only to bending moment about the relevant axis (single My.sd, single Mz.sd)·

(2) Difficulties are met to determine immediately the class of an element submitted to combined (N, M) loading because the classification depends on the design values of the applied axial load Nsd and the bending moment Msd which are obtained from global analysis of the structure. The limiting proportions for classification are related to the position of plastic or elastic neutral axis (parameters α or ψ); that position depends on stresses distribution across the section in equilibrium with those design values of (Nsd, M$d)· Therefore the classification of an element or a cross­section may be different according to the considered combination of actions (Ν, M). Then assumptions of class should be tried and verified with the results issued from the global analysis. (3) The class of cross­section submitted to combined (Nsd* Msd) loading could simply be determined in taking into account more severe loading which allows an easier evaluation of the elements class. If the limiting proportions are met and correspond to a satisfying class, complex calculations (positioning of neutral axis) should have been avoided. Two examples illustrate this proposal : in case of web submitted to Ncompression and My. sd, it is easier to classify firstly the web submitted to Ncompression>(see tables V.4, V.6 or V.7), in case of web submitted to Ntension and My.sd, it is easier to classify firstly the web submitted to single My^sd­(see tables V.3, V.4, V.6 or V.7).

110

(4) In case of I or H-sections submitted to bending about major axis (Mysd) and axial load (Nx.sd). the classification of the web may be determined with table V.9 by comparison of the applied design axial load (Nx.sd) with the given limiting axial load (in compression or in tension). The table V.9 should be used (/9/) : firstly by check of the limiting ratios between the applied axial load Nx.sd and the plastic load of the web (= Aw-fy), to determine if the web is class 1 or class 2 (in this case the ultimate limit state is based on plastic distribution of stresses across the section); and if limits for class 2 are not met, by check of the limiting ratios between the applied axial load Nx.Sd and the plastic load of the full section (= A.fy), to determine if the web is class 3 or class 4 (in this case ultimate limit state is based on elastic distribution of stresses across the section).

111

Determinant dimensions of cross-sections for classification

Table V.2

- Webs (internal elements perpendicular to axis of bending)(see tables V.3 and V.4)

JS Axis of bending t -

J

.__d

*)

_h

1

d_.

^W

í Γ

IW

d = h - 3t (t = tf = t j

Rolled sections

Welded sections

- Outstand flanges (see tables V.3, V.4 and V.5) :

4 ί

^Ή

I *Ê j¿ fc 1

i,

c **)

in —*—

ι

ΓΊ

i

i

1

—*—

-Ί

r

c **)

Welded sections

Rolled sections

- Internal flange elements (internal elements parallel to axis of bending)(see table V.6) :

TT Axis of tending

I

.

.

.1

t . \

Rolled sections

i %

Welded sections

- Circular tubes and angles (see table V.7) :

Ψ -Ml— *) **)

For a welded section the clear web depth d is measured : . between welds for section classification . between flanges for shear calculations (see chapter VIII) For welded sections the outstand dimension c is measured from the toe of the weld.

112

Table V.3 Types of loading

Classification of cross-section : limiting width-to-thickness ratios for class 1 & class 2 I c ross-sec tions submitted to different types of loading Class 1 Class 2 Stresses Web Flange distribution for Web Flange class 1 & class 2 oltt< c/tf£ d/tw* d/tw* I

+

I fy

Ncompression

N

1

Μν

33ε

L

ι

+

ι

Ι

+

Ι

fy

-EEf-7'

R

10ε

R

11ε

38ε

W

9ε

W

10ε

R

10ε

R

11ε

83ε

72ε W

9ε

W

10ε

R

10ε

R

11ε

W

9ε

W

10ε

α > 0,5 : R

10ε

α>0,5

R

11ε

456ε 13α-1

W

10ε

Μ,

ΙΓΓ-ΤΕΓ-Τ -•N.M.

■Ν comp. - My

Έ

Ι

1

fy

"•àdH±i

Ntcns. - My

N

■5

396ε 13α-1

W

9ε

-«S.My

a<0,5

R

10ε

Ψ

9ε

R

10ε

^

36ε α iy

Μ2

Ncomp. " Μ ζ

Ι

­

Ι

α < 0,5 : R

11ε

\

33ε

fy

41,5ε α

W

10ε

Æ

11ε

38ε W

9ε

W

10ε

R

10ε/α

R

Ιΐε/α

Ntens. - Μ ζ

Values of d, t w , c, and tf + : stresses in compression are defined in table V.2 - : stresses in tension fy (N/mm2)

= ^2357ζ

W 9ε/α V^ 10ε / α R = rolled sections ; W = welded sections 235 460 275 355 420

ε(ιίΐ£40ητπι)

0,92

0,81

0,75

0,71

ε (if 40 mm < t < 100 mm)

0,96

0,84

0,78

0,74

113

Table V.4 Types of loading N,compression

Classification of cross­section : limiting width­to­thickness ratios for class 3 I cross-sections submitted to différent types of loading Stresses Class 3 distribution for Web Flange class 3 d / ui-w^ g/tfjj I + I fy R 15ε N 42ε W

14ε

R

15ε

W

14ε

R

23ε Λ /057

W

2^057

R

15ε

W

14ε

ψ<­1 :

R

15ε

62ε(1­ψ) Λ /­ψ

W

14ε

ƒ?

23εΛ/ϋ^~(δ)

W

21εΛσ w

/?

23εβζ(α)

i—E l

l

fv

W

—Γ—

M,

M,

+

~+*sMy

124ε

Η-Ι---Τ ψ>­1 :

■N comp. " M y

42ε (l¥fy|<

Ν)

0,67 + 0,33ψ

( lfy/ψΙ < |fy|) .

d.__

Ntens. ­ M .

i

^ 7fy./V ^

■Ν comp. " M z

» ^ - ^

fl-Ff-5"

H 9 fy,

Ntenc - M ,

N

­*>.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<ΐ<100πιπι)

114

42ε

ψ 2Ì B ^jk^(a) R = rolled sections; W = welded sections ko is defined in table V.5 235 275 355 420 460 0,92 0,81 0,75 0,71 0,96 0,84 0,78 0,74

Buckling factor k0 for outstand flanges

Table V.5 Ψ

kc

-1,0 -0,9 -0,8 -0,7 -0,6 -0,5 -0,4 -0,3 -0,2 -0,1 -0,0

0,85 0,82 0,78 0,75 0,72 0,69 0,67 0,64 0,61 0,59 0,57

+0,0 +0,1 +0,2 +0,3 +0,4 +0,5 +0,6 +0,7 +0,8 +0,9 + 1,0

0,57 0,55 0,53 0,51 0,50 0,48 0,47 0,46 0,45 0,44 0,43

Stress distribution (compression positive)

M

Stress distribution (compression positive)

kc

23,80 20,05 16,64 Compression 13,58 10,86 8,48 6,44 4,74 3,38 2,37 1,70 Compression σι

1,70 1,31 1,07 0,90 0,78 0,69 0,61 0,56 0,51 0,47 0,43

(b)

Compression

(c)

Compression σ

L

J

Η

\

2

, .w

"

\

'l

\

+

ί

\ „ ........................

(d)

G21 £ Ι σι

Note 1

ψ = σ2/σι

Note 2 :

The diagram shows a rolled section. For welded members the outstand dimension c is measured from the toe of the weld (see table V.2).

and

115

;

Table V.6 C lassification of cross-section : limiting width-to-thickness ratios for internal flange elements submitted to different types of loading Type of loading

Stresses distribution classes 1,2 and 3

1 h

+

fy ~Ρ

internal flange ι

Ν

1 1

N compression

R

(b-3tf)/tf

O

b/tf

<42ε

! ι I 1 - ■ !

r

<42ε

class 1

]fy

class 2

internal flange

r>

R α>-3ΐ£)Λί<33ε R (b-3tf)/tf£38e O

M

b/tf

<33ε O

b/tf

<38ε

class 3

+

]fy

internal flange

+/ - * ^

-i-— V

£\ J

R

(b-3tf)/tf

O

b/tf

<42ε <42ε

Values of b and tf are defined in table V.2 + : stresses m compression

R = rolled hollow sections

- : stresses in tension

O = other sections fy (N/mm 2 )

ε = Λ/2357Γ3

275

355

420

460

ε (if t{ < 4 0 m m )

0,92

0,81

0,75

0,71

ε (if 40 mm < tf < 100 mm)

0,96

0,84

0,78

0,74

116

235

Table V.7 : Classification of cross-section : limiting width-to-thickness ratios for angles and tubular sections submitted to different types of loading Angles Note : this table does not apply to angles in continuous contact with other components Type of loading

Stresses distribution

]*

class 1

class 2

class 3

h/t <

h/t <

h / t < 15 ε and

10 ε

11ε

N,compression

b+h 2t

< 11,5 ε

M and,

see table V.3 (classes 1 and 2) and table V.4 (class 3) with limiting

(Ν, M)

width-to-thickness ratios concerning outstand flanges. Tubular sections

Type of loading

class 1

class 2

class 3

Ν compression d/t <

M and, 50 ε2

(N,M) Values of h, b, t and d are defined in table V.2 fy (N/mm2) ε = ^235/f 3

70 ε2

90 ε2

+ : stresses in compression

275

355

420

460

ε (if t £ 40 m m )

0,92

0,81

0,75

0,71

ε (if 40 m m < t < 100 m m )

0,96

0,84

0,78

0,74

ε2 (if t ^40 m m )

0,85

0,66

0,56

0,51

ε 2 (if 40 m m < t < 100 m m )

0,92

0,70

0,60

0,55

117

235

Table V.8 Effective cross-sectional data for symmetrical profiles (class 4 cross-sections) Members in compression (N) gross cross-section

effective cross-section

'Ρ»

V,."®. Φ

b 1 t. ε 56,8 ft !

1 b ί.ε 18,6

μ^ u

s>_

-■ +

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-P
Η

275

355

420

460

0,92 0,96

0,81 0,84

0,75

0,71

0,78

0,74

Limiting values of axial load Nsjfor web classification of I cross-sections 1 subject to axial load NSd and to bending according to major axis Mysd

Coefficient dl(tw.e) 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70

Nsd/(A w .fy)

Nsd/(A w .fy)

Nsd/(A.fy)

for Classi web

for Class 2 web

for Class 3 web

Ζ O HH

CA CA

S cu O

u

~ΊΓ~ 74 76 78 80

83

85 90 95 100 105 110 115 120 "Î24 125 130 135 140 145 150

z o HH

co Ζ

ω |

·)

*)

*)

0,946 0,846 0,757 0,677 0,604 0,538 0,478 0,423 0,372 0,325 0,282 0,242 0,204 0,169 0,136 0,106 0,077 0,050 0,024 0,000 ­0,023 ­0,045 ­0,077 ­0,100 ­0,133 ­0,153 ­0,200 ­0,242 ­0,280 ­0,314 ­0,345 ­0,374 ­0,400 ­0,419 ­0,424 ­0,446 ­0,467 ­0,486 ­0,503 ­0,520

*)

*)

*)

*)

*)

*)

0,908 0,824 0,748 0,679 0,615 0,557 0,503 0,453 0,407 0,363 0,323 0,285 0,250 0,217 0,186 0,156 0,128 0,102 0,077 0,053 0,031 0,000 ­0,024 ­0,078 ­0,126 ­0,170 ­0,210 ­0,245 ­0,278 ­0,308 ­0,331 ­0,336 ­0,362 ­0,385 ­0,407 ­0,428 ­0,447

*)

COMPRESSION

Table V.9

L_

ζ

o

HH

c« Ζ W Η

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

*)

Ζ O HH

CA CC

tí

tu O

I

ζ

oCA Ζ tí

0,931 0,868 0,811 0,758 0,709 0,663 0,621 0,582 0,545 0,511 0,479 0,449 0,421 0,394 0,369 0,345 0,322 0.301 0,280 0,252 0,234 0,192 0,155 0,121 0,091 0,063 0,038 0,015 0,000 ­0,004 ­0,023 ­0,040 ­0,057 ­0,071 ­0,085

Aw = d.tw (web areeι); Α = sectional area

119

Table V. 10 Examples of shift of centroidal axis of effective cross-sections 1. in case of monosvmmetrical class 4 cross-sections submitted to uniform compression \N compression) ·

TIJ

Γ-1 'N

2. in case of class 4 cross-sections submitted to bending (My.Sd)

T II II II

ι

eMi: = ι

t: = :=0

My.Sd

"

e

My.Sd

Mf

=*)

1

Notes : -1-1

centroidal axis of gross cross-section

-2-2

centroidal axis of effective cross-section

- elements : '

r non-effective zone of the element, taking into account the occurence of local buckling.

120

VI

MEMBERS IN TENSION (Ntension)

Vl.a

Generalities

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

r£

¿?

Nx.Sd

.-y

x· -

&

(2) The flow­chart FC 6.1 presents the general procedure to check members in tension at ultimate limit states (see the following page). (3) The flow­chart FC 6.2 presents the particular procedure to check at ultimate limit states angles connected by one leg and submitted to tension (see the second following page). (4) The table VI. 1 provides a list of the checks to be performed at Ultimate Limit States for the member submitted to axial tension (Ntension)· A member shall have sufficient bearing capacity if all the checks (from φ ( 1 ) to φ ( 4 ) ) are fulfilled. Several checks (from φ ( 2 ) to φ ( 4 ) ) concern particular cases with specific conditions. All the checks have both references to Eurocode 3 and to the design handbook.

121

Row-chart (FC 6.l) : Members in tension (Ntension) revs;

C Determine ULS load cases J ULS checks

1

Select stronger section

Έ

Select beam size (A, Anet) and steel grade (fy, fu)

I

J

Determine the design tensile force from global analysis of the structure: Nsd Calculate the design plastic resistance of the gross cross-section : Np£Rd Calculate the design ultimate resistance of the net cross-section (Anet) at holes for fasteners: Nu.Rd

Determine the design tension resistance of the cross-section: Nt.Rd = min (Np£Rd, Nu.Rd)

no

Select stronger section

J

Adopt section

122

Flow­chart (FC 6.2J : /Inpfes connected bv one lee and submitted to tension rows:

\^^^y/

rows:

D

Determine ULS load cases ULS checks

Select stronger section

f—

,

.

Select angle size (A, An«) and steel grade (fy, fu)

J

Determine the design tensile force from global analysis of the structure: Nsd Calculate the design plastic resistance of the gross cross­section : Np£Rd

yes

Angle connected by one leg yes 7

Unequal­leg angle connected by its smaller leg ?

Calculate A* as the gross area of an equivalent equal­leg angle of leg size equal to that of the smaller leg

Bolted connection

10

11 12

ι

' Welded lap joint end connection

Calculate the net section A*net from A*

C

I

13

(

Calculate the design ultimate resistance of the bolted net section or welded gross section:

ï

Determine the design tension resistance of the cross­section: NuRd = min (NpCRd, Nu.Rd) Select stronger section

15

16

UseA*^)

Nu.Rd

Ζ 14

Type of connection

Consider A* equal to the gross area of the angle (A)

C

Adopt section

123

J

»c

16

List of checks to be performed at ULS for the member in tension (Ntension)

Table VI.1

φ Axial tensile force iV^ Sd ■ ** General case: (1) Resistance of gross cross-section to Nxsd : [5.4.3 (1)]

Nx.sd — Np£Rd (design plastic resistance of the gross cross­section)

References :

Vl.b.l (1)

** Particular cases: (2) Resistance of the net cross-section to Nxsd if holes for fasteners : [5.4.3 (1)] [5.4.2.2]

Nx.Sd — N u .Rd

(design resistance of the net cross­section considering the net area of a member or element cross­section, A net )

VI.b.2 (1)

Resistance of net cross-section to Nxsd if angle connected by a single row of bolts in one leg:

(3)

Nx.Sd

[6.5.2.3 (2)]

— N u .R(j (design ultimate resistance of the net cross­section, A„et)

VI.c.l (1)

considering the following cases for determination of Anet: ­ either, if unequal­leg angle connected by its smaller leg: A net = 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) : A net = the net section area of the angle Resistance of cross-section to Nxsd if angle connected by welding in one leg:

(4) [6.6.10(2)] [6.6.10(3)]

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

VI.C.2 (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 VLb

General verifications at ULS

VI.b. 1

Resistance of gross cross­section to Ntension

(1) For members in axial tension the design value of the tensile force Nx.sd at each cross­section shall be checked for gross section yielding : [5.4.3 (1)]

Ν x.Sd < N pf.Rd where

Af, ΎΜΟ

NP£Rd is the design plastic resistance of the gross cross-section, A fy

is the gross cross-section (see table VI.2), is the yield strength (see table II.4),

ΎΜΟ

is a partial safety factor (see table 1.2).

124

vi,b.2

Resistance of net cross-section to Nlcn,1(>n

(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 <^NSd < min(Nby.Rd, Nbz.Rd)^>-

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 <1|

where φ = 0,5[ΐ + α ( λ - 0 , 2 ) + λ 2 ] , α

is an imperfection factor (see table VII.2), depending on the appropriate buckling curve. The buckling reduction factor χ is given in function of λ and the appropriate buckling curve in table VII.6. When λ < 0,2 flexural buckling is not a potential failure mode. Imperfection factors a

Table VH.2 Buckling curve Imperfection factor α

a

ao 0,13

0,21

b 0,34

c

d

0,49

0,76

(4) The appropriate buckling curve of a member depends on the type of cross-section. For hot-rolled I-sections the buckling curve also depends on steel grades (see table VQ.4). (5) The non-dimensional slendernesses (Xy,Xz) shall be taken as:

xy=^VßI and *·*=·?■ VßA where (λ*νy,λ ) are the slendernesses of the member: ' v zζ and

[form.(547)l

where L0.y, LD.Z

are the buckling lengths of the member about y and ζ axes,

iy, iz where

λι βA

are the radius of gyration about the y and ζ axes determined using the properties of the gross cross­section (Iy, Iz and A), is the Euler slenderness for buckling (see table VII. 3), is a factor considering the effect of local buckling if class 4 cross­ section: , for class 1, 2 or 3 cross­sections,

ßA=l D

_ Aeff

, for class 4 cross­sections.

Va ue of Euler slenderness Xj

Table VH.3 Steel grade

S 235

S 275

S 355

S 420

S 460

λ ι = π

93,91

86,81

76,41

70,25

67,12

­ ^

134

[5.5.14(1)] [table 5.5.3]

Selection of buckling curve for a cross-section

Table VIL4 Cross-section

Limits

Buckling about axis

with h/b > 1,2 and : . tf ^ 4 0 mm

Rolled I-sections :

b

. 40
y_-

Buckling curves for steel grades S 235 S 420 S 460 to S 355

yy zz

a b b c

a a b b

ao ao a a

yy zz

b c

b b

a a

yy zz

d d

d d

c c

yy zz

^u with any h/b and tf > 100 mm Welded I-sections ζ

ζ

E

y-

y

if tf <, 40 mm

yy zz

b c

if tf > 40 mm

yy zz

c d

hot finished

any

a

cold formed (using fyb *))

any

generally as (except as below)

any

thick welds and b/tf < 30

yy

c

h/tw < 30

zz

c

Hollow sections :

+

+

Welded box sections : ζ

+

+

Angles, channels, tees and solid sections : L,

f /

iL· ι

* ■ ■s >

any ι

Note : *) fyb is the basic yield strength of the flat steel material before cold forming

135

[5.5.1.5 (i)] (6) The buckling length Lb O^b.y» Lb.z) of a compression member with both ends effectively [5.5.1.5 (2)] held in position laterally may conservatively be taken as equal to its system length L; or alternatively, the buckling length may be determined using informative Annex E of Eurocode 3. Buckling lengths of columns in a non­sway mode are provided in table VII.5 for different boundary conditions.

Table VH.5

Buckling length of column : Lb Buckling length Lb

System

2L x.Sd

x.Sd

N,sd

0,7 L

-H N x.Sd

[5.8.3]

0,5 L

(7) For angles in compression (Nx.sd) connected with appropriate fixity (at least two bolts if bolted) the eccentricities may be neglected if following effective slenderness ratios λ ^ are used to determine the design buckling resistance (Nb.Rd) of compression angles.

Kfí.v =0,35+0,7 λν

buckling about the ν ν axis:

λβΓί.χ = 0,50 + 0,7 Xy

buckling about the yy or zz axis:

Ι λ ε ί ί . ζ = 0 , 5 0 + 0,7λ ζ

where λ ν , λ γ , λ ζ are non-dimensional slenderness ratios respectively about w axis, yy axis and zz axis (axes are defined in table 0.1).

136

[table 5.5.2]

If

Table VH.6

Reduction factors χ = f( λ ) χ for buckling curve

λ

ao

a

b

c

d

0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

1,0000 0,9859 0,9701 0,9513 0,9276 0,8961 0,8533 0,7961 0,7253

1,0000 0,9775 0,9528 0,9243 0,8900 0,8477 0,7957 0,7339 0,6656

1,0000 0,9641 0,9261 0,8842 0,8371 0,7837 0,7245 0,6612 0,5970

1,0000 0,9491 0,8973 0,8430 0,7854 0,7247 0,6622 0,5998 0,5399

1,0000 0,9235 0,8504 0,7793 0,7100 0,6431 0,5797 0,5208 0,4671

1.1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2,0

0,6482 0,5732 0,5053 0,4461 0,3953 0,3520 0,3150 0,2833 0,2559 0,2323

0,5960 0,5300 0,4703 0,4179 0,3724 0,3332 0,2994 0,2702 0,2449 0,2229

0,5352 0,4781 0,4269 0,3817 0,3422 0,3079 0,2781 0,2521 0,2294 0,2095

0,4842 0,4338 0,3888 0,3492 0,3145 0,2842 0,2577 0,2345 0,2141 0,1962

0,4189 0,3762 0,3385 0,3055 0,2766 0,2512 0,2289 0,2093 0,1920 0,1766

2,1 2,2 2,3 2,4 2,5 2,6 2,7 2,8 2,9 3,0

0,2117 0,1937 0,1779 0,1639 0,1515 0,1404 0,1305 0,1216 0,1136 0,1063

0,2036 0,1867 0,1717 0,1585 0,1467 0,1362 0,1267 0,1182 0,1105 0,1036

0,1920 0,1765 0,1628 0,1506 0,1397 0,1299 0,1211 0,1132 0,1060 0,0994

0,1803 0,1662 0,1537 0,1425 0,1325 0,1234 0,1153 0,1079 0,1012 0,0951

0,1630 0,1508 0,1399 0,1302 0,1214 0,1134 0,1062 0,0997 0,0937 0,0882

Vlf,C¿,2

Resistance to torsionnal buckling and to flexural-torsional buckling

[5.5.1.1 (3)] (1) In some cases the torsional or flexural­torsional buckling modes may govern. Reference may be made to the Annex G of Eurocode 3 which is not officially available yet

137

VILd Particular verifications at ULS for class 4 monosymmetrical cross-section (1) This chapter concerns monosymmetrical cross-sections (channels ([), T-sections (T) and angles (L): see table 0.1) which are class 4 in uniform compression. (2) Monosymmetrical class 4 effective cross-section subject to uniform compression induces a shift of the centroidal axis eN (see chapter V). An additional bending moment ΔΜ due to that eccentricity of the centroidal axis eN shall be taken into account: [5.3.5 (7)]

AMSd = Nx.Sd e N (3) The criteria presented in this chapter VILd may be used for uniaxial and biaxial bending. VTLd. 1 Resistance of cross-section to Ncompression

[54.4(3)]

[5.4.8.3]

(1) For members of class 4 monosymmetrical cross-section submitted to axial compression, the design values of the compressive force Nx.sd combined with bending moment AMsd shall satisfy in each cross-section: interaction (NX;Sd,AMy,Sd,AMz.Sd) £ 1 where the interaction formula is given in chapter LX.d. 1.4„ AMy.sd = Nx.sd eNy » is the additional bending moment about major axis due to the eccentricity of the centroidal axis y (eNy) of the effective cross-section subject to uniform compression Nx.sd, AMz.sd = Nx.sd eNz, is the additional bending moment about minor axis due to the eccentricity of the centroidal axis ζ (eNz) of the effective cross-section subject to uniform compression Nx.sdVn.d.2 Stability Of member tO Ncompression (1) For members of class 4 monosymmetrical cross-section submitted to axial compression, the design value of the compressive force Nx.sd combined with bending moment AMsd shall satisfy:

[5.5.4 (5)]

[55.2(7)]

[5.5.4(6)]

interaction (N xSd ,AM y0,4 (see chapter VIILe.2), then lateral-torsional buckling is a potential failure mode and a supplementary check has to be taken into account as follows interaction (N X S d ,AM y Sd ,AM z Sd ) < 1 where the interaction formula is given in table IX.7 (see chapter LX.d.2.2), AMy.sd = Nx.sd eNy (see VILd. 1), AMz.sd = Nx.sd eNz (seeVn.d.l).

138

VILe [54.3 (3)]

Particular verifications at ULS for angle connected by one leg

(1) In these particular cases the effects of eccentricities in the connections may be neglected thanks to the following considerations of chapter VII.e. Those considerations should also be given in a similar way to other types of sections connected through outstands such as T-sections (T) and channels ([). VILe. 1 Connection with a single row of bolts VILe.1.1

Resistance of cross-section to Ncompression

[6.5.2.3 (2)] (1) Angles in compression (Nx.sd) connected by a single row of bolts in one leg may be treated as concentrically loaded with the following requirements: N x.Sd <ΞΝu.Rd

where Nu.Rd is the design ultimate resistance of net cross-section (see chapter VLc. 1). VILe.1.2

Stability of member to Ncompression

[6.5.2.3 (3)] (1) For angles in axial compression connected by a single row of bolts in one leg , the design value of the compressive force Nx.sd shall satisfy: Ν x.Sd < N b.Rd

but Ν b.Rd < N u.Rd

where Nb.Rd is the design buckling resistance of the compression angle (see chapter VII.c.2.1 (2)), where the gross cross-sectional area of the angle (A) is used, Nu.Rd is the design ultimate resistance of net cross-section (see chapter VI.c.l), where the net area of the angle (Anet) is used. VII.e.2 Connection by welding VU.e2.1

Resistance of cross-section to N. compression

[6.6.10 (3)] (1) Angles in compression (Nx.sd) welded by one leg may be treated as concentrically loaded with the following requirements: Ν x.Sd < N u.Rd

where NuRd is the design ultimate resistance of cross-section (see chapter VI.c.2). ΥΠ, e,2,2

Stability of member to Ncompression

[6.6.10 (3)] (1) For angles in axial compression welded by one leg , the design value of the compressive force Nx.sd shall satisfy: Ν x.Sd < N b.Rd where ND.Rd is the design buckling resistance of the compression angle (see chapter Vfl.c.2.1 (2)), where the gross cross-sectional area of the angle (A) is used.

139

VIII

MEMBER S IN BENDING (V ; M ; (V,M))

Vlll.a

Generalities

(1) For each load case (see chapter ΠΓ) the global analysis of the frame (see chapter IV) determines the design values for the following effects of actions which are applied to members in bending and which shall be checked at serviceability limit states and at ultimate limit states : - For SLS : . vertical deflections (δν), . vibrations (f) - For ULS : separate or combined shear forces and bending moments : ζ

r£

M z.Sd &

-y ι

χ -

φ

\

vz.sd

M M, ysd

(2) The flow-chart FC 8 presents the general procedure to check I-section members in bending at SLS and at ULS (see the following page). (3) The table VIII. 1 provides a list of the checks to be performed at Ultimate Limit States for the member in bending (V; M; (V,M)). A member shall have sufficient bearing capacity if all the checks are fulfilled according to the loading applied to that member. For instance, in the case of loading nr φ , all checks from φ ( 1 ) to (D(3) have to be satisfied. Several checks in the table VQI.l concern particular cases with specific conditions. All the checks have both references to Eurocode 3 and to the design handbook. The table VIII. 1 proposes the following loadings applied to the member: φ Shear force Vsd ·' Vy.sd or V^sd Uniaxial bending moment Msd : My.SdOrMz.sd Biaxial bending moments (My Msd )'· (Vz.sd andMy.sd) or (Vy.Sd andM^sd) Interaction of shear forces and biaxial bending moments (Vsd> My.sdt M^sd) '■ (Vz.sd and My.sd) and (Vy.sd and M^sd)

140

Flow-chart (FC 8) : Design of I members in uniaxial bending (Vt:Mv:(VzMv)) or (Vv:Mz:(VvMzì) rows:

Determine SLS load cases

Determine ULS load cases i ULS checks

I —

SLS checks

ïι Select beam size (A, I, We; Wp/) and steel grade (fy) ΐ'

ί

1

1-

ι

Determine the design shear forces (Vz.Sd ; Vy.sd) and design bending moments (My.sd ; Mz.sd) from the global analysis of the structure

1 ~

Select stronger section

}

3

3

Determine vertical deflections and vibrations

4 S

c

6 7

Calculate shear resistance of cross-section ion Vp£Rd J

(Classify the cross-section in bending; if class 4 calculate Weff J yes

no

.Vz.Sd

Calculate Vba.Rd shear buckling resistance of the web]

/tw<( yes.

10 11 12

Calculate design bending moment resistance of cross-section McRd for the class of the cross-section

13 14 |

yes

Consider Mv.Rd = McRd

(i

culate Mv.Rd)

Si

15

s

16

s

17

«8

18

C Calculate Mcy.Rd for the class of the cross-section J

19 20

yes

< y l s d £ 0,5 Vb¡j£>—

no •

Consider Mvby.Rd equal to Mcy.Rd Calculate the slenderness ratio λ ί τ no

f Calculate Mvby.Rd reduced by shear buckling

21 22 23 24 25

yes

Calculate Mb.Rd design lateral-torsional buckling resistance moment

yes

'!·.

-J-

»(Adopt section if both series ULS and SLS checks are fulfilled^ 141

J 29 30

List of checks to be performed at ULS for the member in bending according to the applied internal forces and/or moments(V;M;(V,M)) References : Shear force V v :

Table VIILI (Î)

(1) [54.6 (1)]

V s d — Vpi.Rd (design plastic shear resistance of the cross­section)

(2)

[6.5.2.2(1)] [6.5.2.2(2)]

(3)

[5.6.1 (1)] [5.6.3 (1)]

(5)

[5.4.5.1 (1)] [5.4.5.1 (2)] [55.2(7)]

(2)

[55.2 (1)]

(3)

[5.4.8.1] [5.4.8.2] [5.4.8.3]

(2) [55.4 (1)] [5.5.4 (3)] [5.54(5)1

(3)

[55.2(1)]

Γ55.4 (2)1 [5.5.4(4)] [554(6)]

Resistance of cross-section to Vzsd, if web with a group of table VTII.6 fastener holes near the end of a beam : V z .Sd ^ Veff.Rd (design value of the effective resistance to block shear)

Vm.d.l (3)

Stability of web to Vzsd, ifdltw > 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
[55.2 (7)]

Vm.d.l (1)

Uniaxial bending moment Mw : (1)

[55.2(7)]

Resistance of cross-section to Vsd ·"

(4)

Resistance of cross-section to (Mysd, Mzsd)'·

vm.f.1 (i)

interaction (My.sd , Mz.sd) ^ 1, for class 1 and 2 cross­section for class 3 cross­section for class 4 cross­section

LX.d.1.2 (2)

Stability of member to (My_sd, Mzsd)'·

vm.f.2 (i)

interaction (My.sd » Mz.sd) ^ 1, for class 1 and 2 cross­section for class 3 cross­section for class 4 cross­section

table ΓΧ.4 table LX.5 table LX.6

Stability of member to Mysd ,if λυτ > 0,40 :

Vni.e.2 (3)

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

Vffl.e.2 (4)

rx.d.1.3 (1) LX.d. 1.4(1)

Vni.e.2 (3) Stability of member to (My.sd, Mz.sd), if %>LT > 0,40 (potential lateral-torsional buckling) : VUI.f.2 (2) interaction (My.sd , Mz.sd) ^ 1, for class 1 and 2 cross­section for class 3 cross­section for class 4 cross­section

142

table ΓΧ.4 table IX.5 table ΓΧ.7

List of checks to be performed at ULS for the member iiι bending according to the applied internal forces and/or moments!V;M;(V,M)) References : Œ) Interaction of shear force and uniaxial bending moment (VIA. M*A ):

Table VIILI

vm.d.i (1)

If Vsd ^ 0,5 Vpi.Rd then interaction (Vsd, Msd ) is not considered and

154.7(2)]

checks nr φ and nr @ of this table Vffi. 1 shall be performed, with the following check nr @ (6). vm.g.i (i) vm.g.i.i (i)

If Vsd > 0¿ Vpijid then interaction (Vsd, Msd ) has to be considered

154.7(3)]

and following checks shall be carried out : (1)

Resistance of cross-section to Vsd'· vm.d.i (i)

154.6(1)] V sd ^ Vpi.Rd (design plastic shear resistance of the cross-section) [65.2.2(1)]

(2)

[65.2.2(2)]

[5.45.1 (1)] [54.5.1 (2)] [55.2(7)1

Resistance of cross-section to Vzsd, if web with a group of fastener holes near the end of the beam :

(3)

Resistance of cross-section to Msd'.

(4)

Resistance of cross-section to (Vsd, Msd)'· M sd — MViRd (design plastic resistance moment reduced by shear force)

(6)

Vm.e.2 (4)

vm.g.i.i(i) table Vm.7

Stability of web to (Vzsd, MySd), ifd/tw > 69ε : One of the three following checks ((5.1), (5.2), (5.3)) shall be fulfilled : (6.1) If My.Sd ^ Mf.Rd (design plastic moment resistance of cross-section with the flanges only) then V z .sd ^ V ^ R d (design shear buckling resistance of the web) (6.2) If M y .sd > MtRd and V z . S d <, 0,5 V ^ d then My.Sd — McyJld (design uniaxial bending moment resistance of the cross-section)

[5.6.7.2(3)]

Vm.e.2 (3)

Stability of member to Mysd, if λυτ > 0,40 : My.sd — Mh.Rd (design lateral-torsional buckling resistance moment of the member)

154.7(3)]

[5.6.7.2(2)]

vm.e.i (1)

Msd ίΞ M c .Rd (design uniaxial bending moment resistance of the cross-section)

(5)

[5.6.7.2(1)]

Vffl.d.l.(3)

V^sd ^ Veff.Rd (design value of the effective resistancetoblock shear)

[55.2(1)]

[5.6.1 (1)]

table Vm.6

(6.3) If My.sd > Mfju and V^sd > 0,5 VbaLRd then Mysd ^ design moment resistance reduced by shear buckling (interaction (Vz.sd, My.Sd)) and, My.sd ^ M ^ j ^ and, Vz.sd ^ V^ju

143

Vm.g.2(3)® Vm.d.2 (5) Vm.g.2(3)@ vm.e.i (1) vm.g.2(3)(D Vm.g.2(3)(3) Vm.e.l (1) Vm.d.2 (5)

Table VIILI

List of checks to be performed at ULS for the member in bending according to the applied internal forces and/or moments(V;M;(V,M))

Interaction of shear forces and biaxial bending moments (Vsd, Myjsd, Mz.sd) : [5.4.7 (2)]

References

If Vsd ^ 0,5 Vpiüd then interaction (Vsd, My.sd, Mz.sd) is not considered Vm.d.l (1) and checks nr φ and nr ® of this table VU. 1 shall be performed, with the following check nr (§) (7). vm.g.i(i)

[54.7 (3)]

If Vsd > 0¿ Vpijid then interaction (VSd, My.Sd, Mz.Sd) is to be considered and following checks shall be carried out : (1)

[6.5.2.2 (1)]

(2)

(3) Stability of member to Mysd ,if λυτ > 0,40 :

[55.2 (1)]

(4) [55.4(1)] [5.5.4(3)] [554(5)1 [55.2 (7)]

vm.d.i (3) Vm.e.2 (3)

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

Vm.e.2 (4)

Stability of member to (Mysd, Mz.sd)'·

vm.f.2 (i)

interaction (My.sd » Mz.sd) ^ 1 » for class 1 and 2 cross­section for class 3 cross­section for class 4 cross­section

table IX.4 table ΓΧ.5 table ΓΧ.6

(5)

Stability of member to (My.sd, Mz.sd), if ALT > 0,40 Vm.e.2 (3) (potential lateral-torsional buckling) : Vm.f.2 (2) table LX.4 interaction (My.sd » Mz.sd) ^ 1, for class 1 and 2 cross­section for class 3 cross­section table ΓΧ.5 for class 4 cross­section table LX.7

(6)

Resistance of cross-section to (Vgd, Mysd, Mzsd)'· vm.g.i.2 interaction (My.sd , Mz.sd) ^ 1, for class 1 and 2 cross­section Vm.g.l.2(2) Vffl.g.l.2(3) for class 3 cross­section Vm.g.l.2(3) for class 4 cross­section where design resistance moments are reduced by shear forces but limited by appropriate values of moment resistance according to :

[55.4 (2)] [55.4 (4)] [5.5.4 (6)]

[5.4.8.1] [5.4.8.2] [5.4.8.3]

vm.d.i (i)

Resistance of cross-section to Vsd, if web with a group of fastener table Vm.6 holes near the end of a beam : V s d — Veff.Rd (design value of the effective resistance to block shear)

[65.2.2(2)] [55.2(7)]

Resistance of cross-section to Vzsd'· V z .sd — VpURd (design plastic shear resistance of the cross­section)

[54.6 (1)]

vm.g.i.i (i)

[5.4.7 (3)]

Mv.Rd (design plastic resistance moment reduced by shear force),

vm.g.i.i (i)

[5.45.1 (1)] [54.5.1 (2)]

With My.Rd — M c jRd (design uniaxial bending moment resistance of the cross­section),

VIILe.l (1)

in other words, with Mvy.Rd ^ McyRd and Mvz.Rd ^ Mcz.Rd (checks nr © to be continued)

144

List of checks to be performed at ULS for the member in bending according to the applied internal forces and/or moments(V;M;(V,M))

Table VOLI

[5.6.1 (1)]

[5.6.7.2(1)]

References Interaction of shear forces and biaxial bending moments (continuation) (Vsd, Mysd, Mzjsd) (7) Stability of web (Vzsd, MySd), ifdftw > 69ε : table Vni.7 One of the three following checks ((6.1), (6.2), (6.3)) shall be fulfilled : VULg.2(3)®| (6.1) If Mjf.sd ^ Mf,Rd (design plastic moment resistance of cross­section with the flanges only) t h e n V z .Sd — VbaJld (design shear buckling resistance of the web)

[5.6.7.2(2)]

(6.2) If My.sd > MfJU and V^sd $ 0,5Vba.Rd then My.sd — M C y«d (design uniaxial bending moment resistance of the cross­section)

[5.6.7.2(3)]

(6.3) If My.sd > Mfju and Vz.Sd > 0,5Vba.Rd then My.sd ^ design moment resistance reduced by shear buckling (interaction (V^sd, My.sd)) and, My.sd ^ Mcy­Rd and, Vz.sd ^ Vbajw

Vm.d.2 (5)

VTJI.g.2(3)¿) vm.e.i (1) vm.g.2(3)(D vm.g.2(3)(D vm.e.i (1) Vin.d.2 (5)

VIILI) Verifications at SLS Vlll.b.l Deflections [4.2]

(1) Steel structures and components shall be so proportioned that deflections are within limits agreed between the clients, the designer and the competent authority as being appropriate to the intended use and occupancy of the building and the nature of the materials to be supported. (2) The deflections should be calculated making due allowance for any second order effects, the rotational stiffness of any semi­rigid joints and the possible occurrence of any plastic deformations at the serviceability limit state. (3) The values given in table Vm.2 are empirical values. They are intended for comparison with the results of calculations and should not be interpreted as performance criteria. [4.2.2(1)] to

[4.2.2 (3)]

(4) The design values for the vertical deflections (δν) (see chapters ΙΠ and IV) should be lower limiting values given in table VIII.2. Those limiting values are illustrated by reference to the simply supported beam shown in table VHI.3.

145

Table VIII.2

Recommended limiting values for vertical deflections

ECCS n°65 table 4.2

Conditions

Limits Omax

roofs generally roofs frequently carrying personnel other than for maintenance floors generally floors and roofs supporting brittle finish or non­flexible partitions floors supporting columns (unless the deflection has been included in the global analysis for the ultimate limit state) where omax can impair the appearance of the building

L/200 L/250 L/250 L/250 L/400

L/250 L = span of the beam; for cantilever beams : L = twice cantilever span Discharge of rainwater: slope of the roof less than 5% slope of the roof less than 3%

ECCS n°65 table 4.1

Table Vffl.3

δ2 L/250 L/300 L/300 L/350 L/500 ­

check that rainwater cannot collect in pools additional check that incremental collapse cannot occur due to the weight of water

Vertical deflections to be considered ­Tnax

Omax = δι + 02 ­ δο State 0

δο

li

♦ δο

δι

'max

θ2

146

= the sagging in the final state relative to the straight line joining the supports, = the pre­camber (hogging) of the beam in the unloaded state (state 0), = variation of the deflection of the beam due to permanent loads (G) immediately after loading (state 1), = variation of the deflection of the beam due to the variable loading (Q) (state 2).

[4.3]

ECCS n°65 table 44

Vni.b.2 Dynamic effects ­ vibrations (1) The vibrations of structures on which the public can walk shall be limited to avoid significant discomfort to users. (2) The design values for the effects of actions (vertical deflections (δν) and natural frequency (f)) (see chapters ΙΠ and IV) should be limited by the values given in table Vm.4. Those limiting values may be relaxed where justified by high damping values. Recommended limiting values for floor vibrations

Table VIIL4

f>fe

δν < δι + Ô2

Type of floor

lowest natural frequency U [Hz]

limited total deflection δι + θ2 [mm]

Floors over which people walk regularly (offices, dwellings,...) Floors which are jumped or danced on in a rhythmical manner (gymnasium, dance hall,...)

3

28

5

10

#

fe =

fe

E I L m

α

1 α Í1T

27lWm

[HZ1

natural frequency modulus of elasticity second moment of area span mass per unit length coefficient of frequency of the basis mode vibration

gr^zzzz^ α = 9,869

α = 22,37

α = 3,516

α =15,418

V111 .c C lassification of cross-section (1) At ultimate limit states the resistance of cross­section 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 bending moments (My.sd, Mz.sd) the classification may specifically be determined according to the procedure defined in chapter V.d.2.

147

vm.d

Verifications at ULS to shear force VSd

VIII.d.l Resistance of cross-section to VSd [5.4.6 (1)]

(1) For members submitted to shear force the design value of the shear force V Sd (Vz.sd> Vy.sd) at each cross-section shall satisfy :

[form. (5.20)]

V

z.Sd -

V

pf.z.Rd -

A

vz77ã— ΪΜ0

Vy.sd^Vp,.y.Rd-Avy-^-

where V p£z R d , Vp/;y.Rd vz 'J "* *v y

/ \ y

Z

are the shear areas about ζ and y axes, given in table VHL5,

L

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

YmO

is a partial safety factor (see table 1.2).

y

[5.4.6 (8)]

are the design plastic shear resistances about ζ and y axes,

(2) Fastener holes need not be allowed for in shear verifications provided that:

[form. (5.21)]

where Av fu

is the shear area (see table Vm.5), is the yield strength (see table Π.4), is the ultimate tensile strength (see table Π.4).

When Av.net is less than this limit, an effective shear area of (fu/fy).Av.net may be assumed. [6.5.2.2 (l)] (3) Near the end of a member with a group of fastener holes in webs the "block shear" failure shall be prevented by using appropriate hole spacing. The design value of shear force (Vz.sd) applied to the web shall satisfy : ECCS n°65

z.Sd

form. (5.18)

where Veff.Rd Av.net fu γΜ2


_ 0,6 f u Av.net YM2

is the design value of the effective resistance to block shear, is the effective shear area (see table VIII.6), is the ultimate tensile strength (see table Π.4), is a partial safety factor (see table 1.2).

148

[54.6(2)]

Table VHX5 Cross­sections

Shear area Av for cross­sections Vz.sd

Loading *)

Load parallel to web

A v.7. —

t«,—' L

A ­ 2btf + (tw + 2r)tf

*U

Rolled Load parallel A v .y — to flanges

I and H

y.sd I 1 V Vy­sd

4

2btf + (tw + r) tw

r

¿ür r

tf

-w

|V 2 .Sd

sections

*t4

Load parallel A v . z — to web

(h ­ 2tf) t.

Welded *)

Load parallel Ay y — to flanges

tw,

Load parallel to web

Αγ,ζ

—

A ­ 2btf + (tw + r)tf

t HUf JU

'z.Sd

1

*)

Rolled rectangular hollow sections of uniform thickness

Load parallel to depth

Αγ.ζ

—tf

X

A ­ (h ­ 2tf) tw

*)

Rolled channel sections

lVy.Sd

'z.Sd

Ah b+ h

—

*)

Load parallel Av.y — to breadth

±±+ |Vy.Sd

Ah b+ h

i-^-i *)

Circular hollow sections and tubes of uniform thickness

Vsd

2A

π *)

Plates and solid bars Note : *) A is the total cross­sectional area

149

Vsd

.Vsd

ECCS n°65 table 5.34

Table Vm.6

Determination of Ay.net for block shear resistance

ai Lv a2

Av.net = t ( Lv + Li + L 2 - (n do)) Li = 5,0 do ^ ai L2 = 2,5 do < a2 t = web thickness n = number of fastener holes on the block shear failure path do = hole diameter Vm.d.2 Stability of web to Vz.Sd [5.6.1 (l)] [5.6.1 (4)]

(1) If webs are submitted to shear force Vz.sd and if their ratio

exceeds the limits given

in table VHI.7 then they shall be checked for resistance to shear buckling and transverse stiffeners shall be provided at supports. Table VHI.7 Limiting width-to-thickness ratio related to the shear buckling in web. Potential shear buckling Profiles to be checked if webs have a) For unstiffened webs : tw

± >69ε t.k w

F—r

AL·

b) For stiffened webs :

30e->/k7

The value of kT is defined in table VIII.9 fv (N/mm2) = ^235T

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

150

235

275

355

420

460

0,92 0,96

0,81 0,84

0,75

0,71

0,78

0,74

(2) Nearly all hot-rolled I and H sections do not need to be checked for shear buckling. [5.6.2(1)]

(3) The shear buckling resistance nay be verified using either : - the simple post-critical method, or - the tension field method. The first method is presented hereafter.

[5.6.2(3)]

(4) The simple post-critical method can be used for webs of I-section girders, with or without intermediate transverse stiffeners, provided that the web has transverse stiffeners at the supports. (5) For webs with d/tw exceeding limits of table VHI.7, the design value of the shear force Vz.sd shall satisfy :

15.6.3(1)]

z.Sd

^ V ba.Rd = d t w

where Vba.Rd d tw Xba

Table VHX8

x

ba

ΎΜΙ

is the design shear buckling resistance, is the web depth (see table Vffl.7), is the web thickness, is the simple post-critical shear strength (see table VIII.8). where *yw fv is the yield strength of the web, is the web slenderness. Xw Simple post-critical shear strength τ\,α <0,8

Xw

f

Xba

*yw

V3

0,8
<1,2

- ^ ( 1 , 5 - 0,625Ü)

£yw ΓΛ9 V3 Xw

(6) The web slenderness λw should be determined from :

= ^235/ fy , given in table Vfll.7,

where ε kx

Table VUI.9 a/d

<1

is the buckling factor for shear given in table VIII. 9 where a is the clear spacing between transverse stiffeners Buckling factor for shear kx >1 ^ r f

4+

5,34

W

^s v

5,34 +

Sd

v

W

5,34

Sd

AL

a

151

Vlll.e

Verifications at ULS to bending moment Msd

VIII.e.1 Resistance of cross­section to MSH (1) For members in bending and in absence of shear force, the design value of the bending moment M$d (My.sd, Mz.sd) shall satisfy at each section without holes for fasteners :

Mcjid depending on classes of cross­section : class 1 or 2 class 3 class 4 [5.4.5.2(1)]

My.Sd ^ M c y .Rd

Mz.sd ^ Mcz.Rd

­M

­W"­>f> ­

­M ­

M

pf.z.Rd

­

W

^

M C y ü d , MczJtd M

p£y.Rd, Mpiz.Rd

M e £y.Rd, M e £ z J i d

y

­ ­

Rd

"

YMO W

f y

ei.zfy

= Mef.z.Rd =

­ YMO

where Mc.Rd

Mef

_ M _ ivl efl.y.Rd ­

W

eff­y

_ ­

M M

YMO

eff.z.Rd

_Weff.zfy ­ YMI

is the design moment resistances of the cross­section, are the design moment resistances of the cross­section about major (yy) and minor (zz) axes, are the design plastic moment resistance of the cross­section about y and ζ axes, are the design elastic moment resistance of the cross­section about y and ζ axes,

Wp£y,Wp£Z

Wecy, W e£z

are the elastic section modulus about y and ζ axes,

Weff.y, W e ff.z

are the effective section modulus about y and ζ axes (see chapter V), is the yield strength (see table Π.4),

YMO» YMI

y

YMI

are the design effective moment resistance of the cross­ section about y and ζ axes, are the plastic section modulus about y and ζ axes,

Meff.yJld, M e ff. z .R d

f

are partial safety factors (see table 1.2).

ECCS n°65 (2) In the presence of holes for fastener the following simple approach is proposed : 5.3.2(3) ­ no deduction of holes in the compression zone and, ­ deduction of holes in tension zone. Otherwise Eurocode 3 should be consulted in [5.4.5.3].

152

Vm.e.2 Stability of member to My ci [5.5.2] 153.2(8)]

(1) A beam with full restraint to the compression flange does not need to be checked for lateral­torsional buckling. (2) I and Η­sections, channels, angles, T­sections and rectangular hollow sections are susceptible to lateral­torsional buckling in respect of bending about their major axis (My.sd) but not about their minor axis (Mz.sd)-

[53.2(7)]

(3) For members with appropriate non­dimensional slenderness |λυτ ^0,40| no allowance for lateral­torsional buckling is necessary. The value of Xur is defined hereafter. (4) For laterally unrestrained members in bending, the design value for the bending moment about major axis (My.sd) shall satisfy : MbUd depending on classes of cross­section :

[form. (5.48)]

My.Sd ^ Mbjw

class 1 or 2

class 3

class 4

_ XLI W p f . y f y

_ 5CLT W ef.y f y

_ 3CLT Wrff.y f y

YMI

YMI

YMI

Wp¿y

s the design buckling resistance moment of members in bending, s the reduction factor for lateral­torsional buckling, s the plastic section modulus about major axis (yy),

We£y

s the elastic section modulus about major axis (yy),

Weff.y

s the effective section modulus about major axis (yy) (see chapter V),

fy

s the yield strength (see table Π.4),

YMI

s a partial safety factor (see table 1.2).

where Mb.Rd XLT

(5) The value of χυ for the appropriate non­dimensional slenderness XLT may be determined from : X L T =f(X L T) =

1

1 T2

φτ^Τ+Λφτ^Γ­λτ^Γ

,but

XLT^1

where <|>LT =0,5[l+a LT (X L T ­ 0 , 2 ) + λ υ τ ] CCLT is the imperfection factor for lateral­torsional buckling; OCLT should be taken as : ­ for rolled section OCLT = 0,21 (buckling curve a in table VH.2) ­ for welded section au = 0,49 (buckling curve c in table VII.2). The reduction factor for lateral­torsional buckling XLT is given in function of XLT and the type of section in table Vm.10.

153

(6) The non-dimensional slenderness Xu may be determined from : ΧΙΊ depending on the classes of cross-section class 1 or 2 class 3 class 4 [5.5.2(5)]

_ | w p r . y fy \ Mcr

Χυτ

i

(Wrf.y fy

M CT

1

(W eff .y fy

M CT

where W p£y , W^y, Weff.y

are respectively the plastic, elastic and effective section modulus about major axis (yy), is the yield strength (see table Π.4), fy M cr is the elastic critical moment of the gross cross-section for lateral-torsional buckling. (7) The elastic critical moment MCT for doubly symmetrical cross-sections with in plane end moment loading may be taken as 'Je V [Annex F]

M -C M

cr - M

[form. (F.5)]

π2

Ρ*

72 'LT

1

I w + 0,039 f£ T I t

where Ci

is a factor which may be taken from table VIII. 12 using also table Vm. 11, E is the modulus of elasticity, Iz is the second moment of area about minor axis (zz), CUT — kL is the effective length for out-of-plane (xz) bending (see table VUL 11), L is the length of the member between points which have lateral restraint, k is the effective length factor for out-of-plane (xz) bending (see table Vm. 11), kw is the effective length factor for warping (see table Vm. 11), Iw is the warping constant, It is the torsion constant.

(8) In a member with a system length L, each portion C, between adjacent points with lateral restraint, or from one end to the nearest point with lateral restraint, can be checked separately (see table VIII. 12). (9) For other types of cross-section and for other loading conditions on the member, the Annex F of Eurocode 3 should be consulted.

154

ECCS ηβ65 table 5.25

_

ECCS ne65 table 5.23

= f(Xu) for lateral­torsional buckling

Table VUL 10 Reduction factor χ ' ' '

rolled sections (curve a) welded sections (curve c)

0,4 0,5 0,6 0,7 0,8 0,9 1,0

0,9528 0,9243 0,8900 0,8477 0,7957 0,7339 0,6656

0,8973 0,8430 0,7854 0,7247 0,6622 0,5998 0,5399

1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2,0

0,5960 0,5300 0,4703 0,4179 0,3724 0,3332 0,2994 0,2702 0,2449 0,2229

0,4842 0,4338 0,3888 0,3492 0,3145 0,2842 0,2577 0,2345 0,2141 0,1962

2,1 2,2 2,3 2,4 2,5 2,6 2,7 2,8 2,9 3,0

0,2036 0,1867 0,1717 0,1585 0,1467 0,1362 0,1267 0,1182 0,1105 0,1036

0,1803 0,1663 0,1537 0,1425 0,1325 0,1234 0,1153 0,1079 0,1012 0,0951

Effective length factors : k, kw

Table V m . l l

for different out­of­plane (xz) bending end conditions

Æ 'λ

for different warping end conditions

k =1,0

Ll·

^

■K Λ

k = 0,5

155

a-

4d

ï

kw =1,0

kw = 0,5

ECCS n°65 table 5.24

Table VUI.12

Numerical values for Cj and definition of ψ

-0,75

-0,5

-0,25

0

FSd

FSd

ι

t

0,25

0,5

0,75

FSd = yPSk

ι

Vm.f Verifications at ULS to biaxial bending moment (My.sd> M^sd) Vin.f. 1 Resistance of cross-section to (My «=H. Mz.Sd) (1) For members submitted to biaxial bending moments, the design values of both bending moments shall satisfy in each cross-section : interaction (M y Sd , M z S d ) < 1 where the interaction formula is given : - in IX.d.1.2 (2) for class 1 or 2 cross-sections, - in DC.d.1.3 (1) (using Nx.sd = 0) for class 3 cross-sections and, - in IX.d.1.4 (1) (using Nx.sd = 0) for class 4 cross-sections.

156

Vm.f.2 Stability of member to (My *A. Mz.Sd) (1) For members submitted to biaxial bending moments the design values of both bending moments shall satisfy : interaction (My Sd, Mz.sd) £ 1 where the interaction formula is given : ­ in IX.d.2.2( 1) (table IX.4) (using Nx.sd = 0) for class 1 or 2 cross­sections, ­ in IX.d.2.2 (1) (table IX.5) (using Nx.sd = 0) for class 3 cross­sections and, ­ in IX.d.2.2 (1) (table IX.6) (using Nx.sd = 0) for class 4 cross­sections. (2) If the appropriate non­dimensional slenderness |λυτ >0,40| (see chapterVm.e.2) then lateral­torsional buckling is a potential failure mode and a supplementary check has to be taken into account as follows : interaction (M yS d, M zS d) ^ 1 where the interaction formula is given in : ­ in IX.d.2.2 (1) (table IX.4) (using Nx.sd =0) for class 1 and 2 cross­sections, ­ in IX.d.2.2 (1) (table ΓΧ.5) (using Nx.sd =0) for class 3 cross­sections, ­ in IX.d.2.2( 1) (table DÍ.7) (using Nx.sd =0) for class 4 cross­sections. Vm.g

[5.4.7(2)]

Verifications at ULS to combined f VSd, MSt] )

Vlll.g.l Resistance of cross­section to (VSd, MSd) (1) If the design value of the shear force V,sd^,5Vpi.,Rd and, V y .sd^0,5V p ,.y.Rd where

Vpiz.Rd, VpC.yAd

are the design plastic shear resistance about minor (zz) and major (yy) axes (see table VUL 13),

no reduction needs to be made in the resistance moments. With this condition the design value of bending moment Msd shall be verified according to chapter Vm.e or chapter Villi respectively in case of uniaxial bending or biaxial bending.

[5.4.7(3)]

y¡l!,g,l,l Shear force VSd and uniaxial bending MSd (1) For the resistance of cross­section submitted to combined shear force (V^sd or Vy.sd ) and uniaxial bending moment (My.sd or Mz.sd) if the design value of shear force VSd>0,5Vp(.Rd (high shear), then interaction between shear force and bending moment shall be considered. In this case the design value of bending moment Msd shall satisfy at each cross­section :

[form. (5.22)]

Msd <. M V­Rd ,but where

M V.Rd
is the reduced design plastic resistance moment allowing for the shear force (see table Vffl.13), Mc.Rd is the design plastic moment resistance of the cross­section (see chapter VIII.e.1).

MVJW

157

Table VIII.13 Reduced design plastic resistance moment Myjtd allowing for the shear force If high shear: VSd > 0,5 VptRd

Applied bending moment

/

M V.y.Rd

My.sd ,for cross-section with equal flanges:

Wp,yV

PzAyJ f,

My.sd, for cross-section with unequal flanges:

Mv.y.Rd=(l-Pz)

Mz.sd, for any cross-section:

M

v.z.Rd = ( l - p y )

,s ^lw

J YMO

Wpf.y fy YMO

Wpr.z fy ΎΜΟ

= W pf ——, for class 1 or 2 cross - sections YMO

but M v .Rd ^ M c . R d

= Wei ——, for class 3 cross - section YMO

fv = Weff ——, for class 4 cross - section YMI

where

Wpf is the plastic section modulus of cross-section f

Pz =

Pv =

V

^ V p f. z .Sd ( y.Sd V

Y

pf .y.Sd

withV pi . z . Rd =

Ay.z fy YMO^3 A

-1

■**y V

f V

J

- for shear areas (Av.z, Av.y), see table VIII.5 - tw is the web thickness -fv is the yield strength (see table Π.4) YMO is a partial safety factor (see table 1.2). VIII.g.12 Shear force V Sd and biaxial bending moment MSd (1) For the resistance of cross-section submitted to combined shear forces (Vz.sd and Vy.sd) and biaxial bending moments (My.$d and Mz.sd), if the design value of the shear forces V S d>0.5V p f.Rd

(high shear),

it is proposed that following interactions between shear forces and bending moments shall be satisfied at each cross-section according to the class of cross-section.

158

(2) For class 1 or 2 cross-sections, the proposed interaction formula is ECCS n°65 table 5.15

Mv.Sd

ι«

M V.y.Rd

M z.Sd MV.z.Rd

where Mv.yjw and My.z.Rd

<. 1

aie m e

reduced design plastic resistance moments allowing for shear forces (see table Vm.13), α and β are constants, taken as follows : α = 2, (3=1 - for I and Η sections : α = 2, β = 2 - for circular tubes : - for rectangular hollow sections : α = β = 1,66 α = β = 1,73 - for solid rectangles and plates :

(3) For class 3 and class 4 cross-sections, the proposed interaction formula is :

where My.y.Rd and My.z.Rd are the reduced design plastic resistance moments allowing for shear forces (see table VIH. 13), Vm.g.2 Stability of web to (Vz.Sd, My.Sd) (1) If webs are submitted to combined shear force V^sd and bending moment My.sd and if they have ratio - - exceeding the limits given in table Vm.7 then they shall be checked for resistance to shear buckling. (2) The interaction of shear buckling resistance and moment resistance is shown in table Vm.14 according to the simple post-critical method. Table Vffl.14

Interaction of shear buckling resistance and moment resistance with the simple post-critical method

VplRd·· Vba.Rd-7

0,5Vba.Rd M M

159

f.Rd

M

pl.Rd

(3) The web may be assumed to be satisfactory if one of the three following checks (CD, (D or (3))(according to the loading level of Vz.sd and My.sd) shall be satisfied: (D If the design value of bending moment My.Sd
Mf.Rd is the design plastic moment resistance of a cross­section consisting of the flanges only; proposal for cross­section with equal flanges: class 4

class 1,2 or 3 Mf.Rd "r t beff "en ι.

= btf(h­tf)­2­ =

((b + beff)tf il_^j-((b-b e f f ) tf e M ) ] ^ -

YMO

j

, T^yJ ι ­φ tf

where b, tf, h (see are flange width, flange thickness, height of profile table 0.1), beff is the effective width of the compression flange M e L y Sd lTl£ M )) ' (see chapter V), eM is the shift of the centroidal major axis (yy) when the ­ ­­ ­ cross­section consisting of flanges only is subject to My.sd· then the design value of shear force shall satisfy: V

V

z.Sd ­

where

ba.Rd

Vba.Rd is the design shear resistance buckling of the web according to simple post­critical method (see chapter Vm.d.2).

If the design values of bending moment and shear force My.sd>M f.Rd and V z . Sd <0,50V ba .R d

then the bending moment shall satisfy : M

y.Sd^Mcy.Rd

where Mcy,Rd is the design moment resistance of the cross­section depending on classes of cross­sections (see chapter VEI.e.1). If the design values of bending moment and shear force M

y.Sd>Mf.Rd

and V z . Sd >0,50V ba .R d

then the bending moment and the shear force shall satisfy the three following checks:

where

MP£y.Rd P i ï R d

is the design plastic moment resistance of the cross­section :

"

ΪΜ0

- and, J M y Sd < M c y Rd - and,

z.Sd -

V

baJRd

160

IX

MEMBERS WITH COMBINED AXIAL FORCE AND BENDING MOMENT ((N, M);(N, V, M))

IX.a

Generalities

(1) For each load case (see chapter ΠΓ) the global analysis of the frame (see chapter IV) determines the design values for the following effects of actions which are applied to members with combined axial force and bending moment and which shall be checked at serviceability limit states and at ultimate limit states: ­ For SLS : . vertical deflections (δν), . vibrations (f) different combinations of axial forces, shear forces and bending ­ For ULS moments :

r£

S y" &

Mz.Sd

5

Nx.sd

Λ vz.sd

M

Nx.sd

y­sd

(2) The table IX. 1 provides a list of the checks to be performed at Ultimate Limit States for the member submitted to combined axial force and bending moment (N, M). A member shall have sufficient bearing capacity if all the checks are fulfilled according to the loading applied to that member. For instance, in the case of loading nr (Î), all checks from (J)(l) to (T)(5) have to be satisfied. Several checks in the table IX. 1 concern particular cases with specific conditions. All the checks have both references to Eurocode 3 and to the design handbook. The table IX. 1 proposes the following loadings applied to the member: φ Axial tensile force and uniaxial bending moment about major axis (Nx.sd, My.sd) Axial tensile force and uniaxial bending moment about minor axis (Nx.sd > M^d) Axial compressive force and uniaxial bending moment about major axis (Nxsd MySd) (§) Axial compressive force and uniaxial bending moment about minor axis (Nr MA M7 $¿ ) Axial tensile force and biaxial bending moments (Nx¿d t Mysd> MzSd) Axial compressive force and biaxial bending moments (Nxsd, My.sd, M^sd )

161

List of checks to be performed at ULS for the member submitted to combined axial force and bending moment (N, M)

Table LX.1 φ

References : Axial tensile force and uniaxial bending moment about major axis (Nxsd My.Sd)'(1) Resistanc e of gross cross-section to Nxsd ·'

[5.4.3 (1)]

Nx.Sd — Np£Rd (design plastic resistance of the gross cross-section)

(2)

Resistanc e of the net cross-section to Nx.sd if holes for fasteners: N x .Sd

[5.4.3 (1)] [5.4.2.2]

(3)

— N u .Rd

(design resistance of the net cross-section considering the net area of a member or element cross-section, A ^ )

[5.4.8.1] [5.4.8.2] [5.4.8.3] [55.2 (7)]

VLcl (1) VI.C.2 (1)

Resistanc e of cross-section to (Nx.sd, Mysd)·' interaction (Nx.sd , My.sd) ^ 1 , for class 1 and 2 cross-sections for class 3 cross-section for class 4 cross-section

(5)

VI.b.2 (1)

Resistanc e of cross-section to Nxsd if angle connected by one leg: see table VI. 1 : checks φ ( 3 ) and φ ( 4 )

(4)

Vl.b.l (1)

LX.d.1.1 (1) LX.d.1.3 (2) LX.d.l.4(2)

Out-of-plane (xy) stability of member to (Nxsd > Mysd) if λ LT > 0,40 :

[5.5.3]

Meff.Sd — Mb.Rd

(design lateral-torsional buckling resistance moment of the member)

[5.5.3 (3)] [5.5.3 (4)]

with Meff.sd calculated with (Nx.sd, My.sd)

Vm.e.2 (3) Vm.e.2 (4) LX.d.2.1 (1)

Axial tensile force and uniaxial bending moment about minor axis (Nx.sd>Mz.sd): (1) Resistanc e of gross cross-section to Nxsd ■' [5.4.3 (1)]

[5.4.3 (1)] [5.4.2.2]

Nx.Sd — Np£Rd (design plastic resistance of the gross cross-section)

(2)

(4) [5.4.8.1] [5.4.8.2] [5.4.8.3]

Resistanc e of the net cross-section to Nxsd if holes for fasteners: Nx.Sd

(3)

VI.b.1 (1)

— N u .Rd

(design resistance of the net cross-section considering the net area of a member or element cross-section, Ancl)

VI.b.2 (1)

Resistanc e of cross-section to Nxsd if angle connected by one leg: VLcl (1) see table VI. 1 : checks φ ( 3 ) and φ ( 4 ) VI.C.2 (1) Resistanc e of cross-section to (Nxsd, Mzsd)·' interaction (Nx.sd , Mz.sd) ^ 1, for class 1 and 2 cross-sections IX.d.1.1 (1) for class 3 cross-section LX.d.1.3 (2) for class 4 cross-section LX.d.l.4(2)

162

Table IX. 1 D ($) [54.3(1)]

List of checks to be performed at ULS for the member submitted to combined axial force and bending moment (N, M)

Axial comDressive force and uniaxial bendine moment about maior axis References ; 1 (NxSdMy.Sd)'· (1) Resistance of cross-section to NxsdNx.Sd — Np£Rd (design plastic resistance of the cross-section)

(2) [5.5.1.1 (1)]

In-plane (xz) stability of member to NxsdNx.Sd ^ NbyrJld (design flexural buckling resistance of member)

(3)

Vn.c.2.1 (2)

Out-of-plane (xy) stability of member to NX£¿: Nx.Sd — Nbz.Rd (design flexural buckling resistance of member)

[5.5.1.1 (1)]

Vn.cl (1)

General stability of member to Nxsd ■' Nx.sd ^ design torsional buckling resistance of member and, Nx.sd ^ design flexural­torsional buckling resistance of member

Vn.c.2.1 (2)

(4) [Annex O] [Annex G]

(5)

Resistance of cross-section and stability of member to Nx¿d if class 4 monosymmetrical cross-section: see table VILI : from checks φ ( 3 ) to φ ( 5 )

(6)

Resistance of cross-section and stability of member to Nxsd if angle connected by one leg: see table VILI : from checks φ ( 6 ) to φ ( 9 )

[5.5.2(7)]

(7) Out-of-plane (xy) stability of member to Mysd if λυτ > 0,40 :

[5.5.2(1)]

M y.Sd ίΞ Mb.Rd

(8)

(9)

15-5.2(7)]

15.5.4(2)] 15.5.4(4)] [5-5.4(6)]

Vn.d.l (1) Vn.d.2 (1) Vn.d.2 (2) Vn.e.1.1 (1) Vn.e. 1.2 (1) Vn.e.2.1 (1) Vn.e.2.2 (1) Vni.e.2 (3) Vm.e.2 (4)

Resistance of cross-section to (Nxsd, Mysd)·' interaction (Nx.sd, My.sd) ^ 1 , for class 1 and 2 cross-sections for class 3 cross-section for class 4 cross-section

[5.4.8.1] [5.4.8.2] [5.4.8.3]

15.5.4(1)] [5.5.4(3)J [5.5.4(5)]

(design lateral-torsional buckling resistance moment of the member)

Vn.c.2.2 Vn.c.2.2

In-plane (xz) stability of member to (Nxsd, Mysd)-' interaction (Nx.sd . My.sd) ^ 1 , for class 1 and 2 cross-sections for class 3 cross-section for class 4 cross-section

(10) Out-of-plane (xy) stability of member to (Nxjsd, My^d )

rx.d.i.i (i) LX.d.1.3 (2) LX.d. 1.4 (2) LX.d.2.2(3) table LX.4 table LX.5 table LX.6

LX.d.2.2 (2) if λ w > 0,40 (potential lateral-torsional buckling): Vm.e.2 (3) interaction (Nx.sd » My.sd) < 1 , for class 1 and 2 cross-sections table LX.4 table LX.5 for class 3 cross-section table LX.7 for class 4 cross-section

163

Table LX.l 0

Axial compressive force and uniaxial bending moment about minor axis References : (1)

Resistance of cross-section to Nxsd'·

(Nx.sdMzSd)'·

Nx.Sd — Np£Rd (design plastic resistance of the cross-section)

[5.4.3 (1)]

(2) (3)

N x .Sd — Nb y .Rd (design flexural buckling resistance of member)

General stability of member to Nxsd ·' Nx.sd ^ design torsional buckling resistance of member and, Nx.sd ^ design flexural-torsional buckling resistance of member (5) Resistance of cross-section and stability of member to Nxsd if class 4 monosymmetrical cross-section : see table VILI : from checks φ ( 3 ) to φ ( 5 ) (6)

Resistance of cross-section and stability of member to Nxsd if angle connected by one leg: see table VILI : from checks φ ( 6 ) to φ ( 9 )

(7)

Resistance of cross-section to (Nx.sd, Mzsd)·' interaction (Nx.sd , Mz.sd) ^ 1, for class 1 and 2 cross-sections for class 3 cross-section for class 4 cross-section In-plane (xy) stability of member to (Nxsd, Mzsd)' interaction (Nx.sd , M^sd) ^ 1, for class 1 and 2 cross-sections for class 3 cross-section for class 4 cross-section

[5.4.8.1] [5.4.8.2] [5.4.8.3]

(8) [5-5.4 (1)] [5-5.4(3)] [5-5.4(5)]

Vn.c.2.1 (2)

Out-of-plane (xz) stability of member to Nxsd·'

(4) [Annex G] [Annex G]

Vn.c.1 (1)

In-plane (xy) stability of member to Nx.sdNx.Sd — Nb z .Rd (designflexuralbuckling resistance of member)

[5.5.1.1 (1)] [5.5.1.1 (1)]

List of checks to be performed at ULS for the member submitted to combined axial force and bending moment (N, M)

164

Vn.c.2.1 (2) Vn.c.2.2 vn.c.2.2 Vn.d.l (1)

VII.d.2 (1) Vn.d.2 (2) Vn.e.1.1 (1) VILe. 1.2(1) VII.e.2.1 (1) Vn.e.2.2 (1)

IX.d.1.1 (1) IX.d.1.3 (2) IX.d.1.4 (2) LX.d.2.2 (3) table IX.4 table IX.5 table IX.6

List of checks to be performed at ULS for the member submitted to combined axial force and bending moment (N, M)

Table LX.l (D

Axial tensile force and biaxial bending moments (Nxsd,Mysd,Mz.sd)'· References ; (1) Resistance of gross cross-section to Nxsd ■' Nx.Sd 5Í Np£Rd (design plastic resistance of the gross cross-section)

[54.3 (1)1

(2) [54.3 (1)] [54.2.2]

Resistance of the net cross-section to Nxsd if holes for fasteners: Nx.Sd

(3)

— Nu.Rd

(design resistance of the net cross-section considering the net area of a member or element cross-section, Anc[ )

Resistance of cross-section to Nxsd if angle connected by one leg. see table VI. 1 : checks φ ( 3 ) and φ ( 4 )

[5.5.2(7)]

(4)

Meff.Sd — M b.Rd (design lateral-torsional buckling resistance moment of the member

[5.5.3 (3)] [5.5.3 (4)]

(5) [5.4.8.1] [5.4.8.2] [5.4.8.3]

(6) [5.5.4(1)] [5.5.4(3)] 15-54(5)]

[5-5.2(7)]

(7)

VI.b.2 (1) VLcl (1) VI.C.2 (1)

Out-of-plane (xy) stability of member to (NX£d, Mysd ) if λ L T > 0,40 :

[5.5.3]

VI.b.1 (1)

Vm.e.2 (3) Vm.e.2 (4)

with Meff.sd calculated with (Nx.sd, My.sd)

LX.d.2.1 (1)

Resistance of cross-section to (Nxsd, Mysd, Mzsd )'■ interaction (Nx.Sd, My.Sd, Mz.Sd ) ^ 1 for class 1 and 2 cross­sections for class 3 cross­section for class 4 cross­section

LX.d.l LX.d.1.2 (1) LX.d.1.3 (1)

Stability of member to (Nxsd, Mysd, Mzsd )'■

rx.d.l.4(l) vm.f.2 (i)

interaction (My.sd, Mz.sd)) ^ 1 for class 1 and 2 cross­sections for class 3 cross­section for class 4 cross­section

table LX.4 table IX.5 table LX.6

Stability of member to (Nxsd, Mysd, Mzsd ) if Λ-LT > 0,40 : Vm.e.2 (3) (potential lateral-torsional buckling) Vm.f.2 (2) interaction (My.sd, Mz.sd)) ^ 1 for class 1 and 2 cross­sections for class 3 cross­section for class 4 cross­section

[5.5.4(2)] [5.5.4(4)] [5.54 (6)]

with My.sd reduced to Meff.sd ( as in check φ ( 5 ) )

165

table IX.4 table DÍ.5 table LX.7 LX.d.2.1 (1)

Table ΓΧ.1

List of checks to be performed at ULS for the member submitted to combined axial force and bending moment (N, M)

References : Axial compressive force and biaxial bending moments (Nxsd> My.sd, M^si): (1) Resistance of cross-section to Nxsd ■' Nx.Sd — Np£Rd (design plastic resistance of the cross­section)

[54.3 (1)]

(2) [5.5.1.1]

Vn.c.l (1)

Stability of member to Nxsd' Nx.sd ^ minimum (Nbyjjd, Nbz.Rd)

Vn.c.2.1 (2)

(design flexural buckling resistances of member) [Annex G] [Annex G]

and, Nx.sd ^ design torsional buckling resistance of member and, Nx.sd ^ design flexural­torsional buckling resistance of member (3)

Resistance of cross-section and stability of member to Nxsd if class 4 monosymmetrical cross-section: see table VILI : from checks φ ( 3 ) to φ ( 5 )

(4)

Resistance of cross-section and stability of member to Nxsd if angle connected by one leg: see table VU.l : from checks φ ( 6 ) to φ ( 9 )

[5­5.2 (7)]

(5)

[5.5.2 (1)]

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

(6)

(7)

[5.5.4(2)] [5.5.4 (4)] [5.5.4 (6)]

(8)

VILe. 1.1 (1) VILe. 1.2 (1) VII.e.2.1 (1) VII.e.2.2 (1) Vin.e.2 (3) Vin.e.2 (4)

LX.d. 1.2(1) LX.d. 1.3(1) LX.d. 1.4(1)

Stability of member to (Nxsd, MySd, Mz¿d )'■ interaction (Nx.sd, My.sd, Mz.sd)) ^ 1 for class 1 and 2 cross­sections for class 3 cross­section for class 4 cross­section

[5.5.4(1)] [5.5.4 (3)] [5.54 (5)]

Vn.d.l (1) VII.d.2 (1) VILd.2 (2)

Resistance of cross-section to (NXmsd, Mysd, Mzsd )'· interaction (Nx.Sd, My.Sd, Mz.Sd)) ^ 1 for class 1 and 2 cross­sections for class 3 cross­section for class 4 cross­section

[5.4.8.1] [5.4.8.2] [5.4.8.3]

[5­5.2(7)1

Stability of member to Mysd if < > 0,40 :

vn.c.2.2 VII.c.2.2

IX.d.2.2 (1) table LX.4 table LX.5 table ΓΧ.6

Stability of member to (Nxsd, Mysd, Mzsd ) if %>LT > 0,40 : Vm.e.2 (3) (potential lateral-torsional buckling) interaction (Nx.sd , My.sd, Mz.sd)) ^ 1 for class 1 and 2 cross­sections for class 3 cross­section for class 4 cross­section

166

IX.d.2.2 (2) table LX.4 table ΓΧ.5 table ΓΧ.7

IX.b

Verifications at SLS

IX.b.l

Deflections

(1) About recommended limiting values for vertical deflections reference may be made to chapter Vffl.b.1. IX.b.2

Vibrations

(1) About recommended limiting values for floor vibrations reference may be made to chapter Vm.b.2. IX.C Classification of cross-section (1) At ultimate limit states the resistance of cross-sections may be limited by its local buckling resistance. In order to take into account that limitation the different elements (flange, web) of the cross-sections shall be classified according to the rules defined in chapter V. (2) For cross-sections submitted to combined axial load (Nx.sd) and bending moments (My.Sd. Mz.Sd) the classification may specifically be determined according to the procedure defined in chapter V.d.3. I X.d Verifications at ULS to (N,M) (1) The verification of members submitted to combined axial force and bending moments shall be performed with different (N, M) interaction rules about: 1)

the resistance of the cross-section (see chapter IX.d.l),

2)

the buckling of member (see chapter IX.d.2) and,

3)

the lateral-torsional buckling of the member (if potential)(see chapter K.d.2)

This principle of (N, M) interaction formulas is illustrated in table DÍ.2 in case of uniaxial bending and compression (on the basis of the interpretation of Eurocode 3 explained in the comment IX.d.2.2 (3)). (2) All the (N, M) interaction formulas depend on the class of cross-sections. (3) Uniaxial bending (M y sd or M z .sd) and biaxial bending (My.sd and Mz>sd) combined with axial force N x .sd are presented in the following chapters. IX-d.l Resistance of cross-section to (NSc], Msd) IX.d.1.1 Uniaxial bending of class 1 or 2 cross-sections [54.8.1 (1)] (1) For the plastic resistance of class 1 or 2 cross-sections submitted to combined axial load (Nx.sd) and uniaxial bending moment (My.sd or M z .sd), the following criterion shall be satisfied if the level of axial load n is high:

Msd^M N.Rd

[form. (5.23)]

where

MN.Rd is the reduced design plastic resistance moment allowing for the axial force (MNyjui» MNZJW) (see table IX.3), n is the level of axial load (see table IX.3) n=

N x.Sd

N pf.Rd

_

N x.Sd Afj ΎΜΟ

where Np£Rd is the design plastic resistance of the cross-section [5.4.8.1 (3)] (2) If the level of axial load η is low (see table IX.3, for the limiting values of n), then the reduction of the theoritical plastic resistance moment by the presence of small axial forces is counter-balanced by the strain hardening and may be neglected. In that case of low η reference may be made to chapter Vm.e.l for checking single Msd ·

167

Table IX.2 Principle of interaction formulas between axial force Nsd and bending moment Msd 1. For bending moment about maior axis M., *A without lateral­torsional buckling Γλτ τ < 0,4): 7.

Ν '

L

NcRdi (Nb.Rd)mi 'min

Instability without lateral­ torsional buckling

TnctîiKilitT/

r£



i¿—

χ —

Hl—x

y"

Nx.sd

2

M y.Sd

lack of resistance

Mcy.Rd 2. For bending moment about major axis M y KA with lateral­torsional buckling (λτ τ > 0,4): Ν

ζ

NcRd ' ■

.-y r—χ

χ—

y"

3

N x.Sd

y.Sd

Instability due to lateral­torsional buckling

(Nb.RdX

Mb.Rd

z

Mcy.Rd

3. For bending moment about minor axis M 7 ΖΛ : Ν NcRd f

M z.Sd

Ê

Instability

■ ■ ■ ■ - *

X

(Nb.Rd>'min

—

y" ι I

lack of resistance

MCZ.Rd

168

z

'

^

N x.Sd

Reduced design plastic resistance moment MNjtd allowing for axial load class 1 or 2 cross­sections

Table IX.3 [54.8.1 (4)]

Values of the limit a

Rolled and welded I­sections H

• (η π A - 2 b t f > j L = min 0,25;

:

'£¡L' bjz

. ( __ A - 2 b t Lf a = min n0,50;

Values of the limit a

Hollow sections

a = 0,25

κΉ A-

τ=

a=

A-2bt

- ζ

η

W r —— ΎΜΟ

1,04(1-n^iWp,^ V

;

P

ΪΜ0

M N .R d = 1,26(1 - n ) W p f YMO

M N y jid= L 3 3 ( l - n ) W p r . j ΎΜΟ

M

Nz.Rd =

For a plate without bolt holes Notes :

-(fff)3

—

ΎΜΟ

If high level of axial load Nx.sd: if|n>a|

A-2bt 2A

r A 2b a = min 0 , 2 5 ; - L 2A ) V

-y

MNZJW =

M N .R d =

a = min 0,25;

h^H

1-n^j Wp'-y 1-a,

MNy.Rd =

2A J

V

- ζ

y-

If high level of axial load Nx.sd: if|n>a|

1-n ht Λ Γ 0,5 + — A

MN.Rd = Mp£Rd[l-n 2 ]

_Nx.sd Afy ΎΜΟ

- Limitation of M N J W obtained from this table: MN.Rd ^ M p£Rd (design plastic resistance moment) MNy.Rd^M p f , y .Rd=

in other words, M

Nz.Rd ^ Mpf.z.Rd =

169

W ,

fy

γΜο

Wprzfy γΜ()

ΎΜΟ

IX.d.i.2 B iaxial bending of class 1 or 2 cross-sections [54.8.1(H)] (1) For the plastic resistance of class 1 or 2 cross­sections submitted to combined axial load (Nx.sd) and biaxial bending moments (My.sd and Mz.sd) the following criterion may be used : α M

[form. (5.35)]

y.Sd

M

+

ß z.Sd

<1

M

L^Ny.Rd_

_ Nz.Rd_

where MNy.Rd and MNZ.Rd are reduced design plastic resistance moments allowing for axial load (see table IX.3) α and β are constants taken as follows: ­ for I and Η sections: ; β = 5n, but β > 1 α =2 ­ for circular tubes: α =2 ;ß = 2 1,66 ­ for rectangular hollow sections: α = β = 2,buta=ß < 6 1­1,13η ­ for solid rectangles and plates: α = β = 1,73 + 1,8 η 3 (2) In case of biaxial bending moments without axial load it is proposed to use the following criterion: α

M y .sd Wpi.yfy

ß +

z.sd Wpf.Zfy

[ ΎΜΟ

where Wp£y,Wp/;z

ΎΜΟ

α and β

[5.4.8.2]

M

<1

ΎΜΟ

are plastic section modulus about major axis (yy) and minor axis (zz), is the yield strength (see table II.4) is a partial safety factor (see table 1.2) , are constants taken as follows: - for I and Η sections: - for circular tubes: - for rectangular hollow sections: - for solid rectangles and plates:

α =2 ; β=1 α =2 ;β=2 α =β= 1,66 α = β = 1,73

IX.d.i.3 Bending of class 3 cross-sections (1) For the elastic resistance of class 3 cross-sections submitted to combined axial load (Nx.sd) and biaxial bending moments (My.sd and Mz.sd) the following criterion shall be satisfied:

[form. (5.38)]

(2) In case of uniaxial bending moment combined with axial load ((Nx.sd + My.sd) or (Nx.sd + Mz.sd)) and in case of biaxial bending moments without axial load (My.sd + Mz.sd), it is proposed to use the above criterion (IX.d.1.3 (1)).

170

[54.8.3]

[form. (540)]

IX.d.1.4 Bendino of class 4 cross-sections (1) For the elastic resistance of class 4 cross-sections submitted to combined axial load (Nx.sd) and biaxial bending moments (My.sd and Mz.sd) the following criterion shall be satisfied: N x.sd ^eff

where A^f Weff βΝ

, My-sd + Nx-sd eNy

ΎΜΙ

W eff.y

|

Mz-Sd + N x sd e Nz ^ 1 W eff.z'

ΎΜΙ

YMI

is the effective area of the cross-section when subject to uniform compression (single Nx.sd)· is the effective section modulus of the cross-section when subject only to moment about the relevant axis(single My.sd , single Mz.sd) · is the shift of the relevant centroidal axis (eNy, eNz) when the cross-section is subject to uniform compression (single Nx.sd) ·

(2) In case of uniaxial bending moment combined with axial load ((Nx.sd + My.sd) or (Nx.sd + Mz.sd)) and in case of biaxial bending moments without axial load (My.sd + Mz.sd), it is proposed to use the above criterion (IX.d.1.4 (1)). IX.d.2 Stability of member to (Nsd,Msd) [5.5.3]

ΙΧΛ2.1 Stability of member to (N,ension, Mysd) (1) If the non-dimensional slenderness of the member λτ^τ >0,40 (see chapter Vin.e.2), the member subject to combined major axis bending (My.sd) and axial tension (Nx.sd) shall be checked for resistance to lateral-torsional buckling as follows (if bending moment and axial force can vary independently (vectorial effect)): Meff.Sd
°com.Ed

where Wcom is the elastic section modulus for the extreme compression fibre, <*com.Ed is the net calculated stress (which can exceed fy) in the extreme compression fibre determined from:

Ύ)

ÍMy.Sd^ ψ vee V "com y where \j/Vec is the reduction factor for vectorial effects 'com .Ed

Vvec=0,8.

171

[5.54]

IX.d.2.2 Stability of member to (Ncompression, Msd) (1) For members subject to combined axial compression and biaxial bending moments (Nx.sd + My.sd + Mz.sd) the stability is guaranteed if the requirements (concerning the case © ) described in tables IX.4 to IX.7 are satisfied: - in table IX.4 for class 1 or 2 cross-sections, - in table IX.5 for class 3 cross-sections and, - in tables IX.6 and IX.7 for class 4 cross-sections. (2) As given in the tables IX.4 to IX.7, when the non-dimensional slenderness of the member ^LT >0,40| (see chapter VQI.e.2), supplementary specific formulas also need to be satisfied to take into account the potential failure mode of lateral-torsional buckling of the member. (3) The cases of uniaxial bending moment combined with axial compression ((Nx.sd + My.sd) or (Nx.sd + Mz#sd)) are not fully explained in Eurocode 3. Therefore it is proposed to use the rules for biaxial bending with the buckling reduction factor xmin (%min = minimum (%y, Xz); where (x y , χ ζ ) are the buckling reduction factors about y axis and ζ axis) (see rules concerning the case (2) in tables IX.4 to IX.7).This principle of (Ν, M) interaction formulas is illustrated in table IX.2. (4) According to Eurocode 3 Background Document 5.03 (/8/), another interpretation could be proposed for uniaxial bending combined with axial compression: this proposal may be less conservative because the factor xmin is replaced by the buckling reduction factors Xy or χ ζ according to the relevant bending axis. Moreover the stability out of the bending plane should be also checked (buckling resistance of the member to single axial compression) (see rules concerning the case (3) in tables IX.4 to IX.7).

172

Table IX.4 Internal forces and moments

Interaction formulas for the (NM) stability check of members of class 1 or 2 If X L T > 0 , 4 : potential lateral-torsional buckling needs supplementary checks:

General formulas to be always satisfied:

φ Eurocode 3 formulas for biaxial bending (My.sd, M z .sd) and axial compression N x .sd: k v M Sd ,

Nx.sd

Nx.sd + My.Sd + Mz.sd

nin * ■

ΎΜΙ

W pr.y

k

zMz.Sd

c l

Ν x.Sd

X z A Jy_/„ ΎΜΙ

ΎΜΙ

ΎΜΙ

k

LTMy.sd

k z M z .Sd

w A XurWp/.y

ΎΜΙ

<1

ΎΜΙ

Eurocode 3 formulas for uniaxial bending and axial compression: use the formula for biaxial bending and axial compression (see φ ) introducing the relevant bending moment equal to zero and using Xmin buckling reduction factor. Other proposal of interpretation of Eurocode 3 formulas for uniaxial bending and axial compression (see comments in IX.d.2.2) using buckling reduction factors x y or χ ζ according to the relevant bending axis: Nx.sd f, 3CyA-

Nx.sd + My.Sd

,

ΎΜΙ

and,

k M

y y-Sd L W pf.y

Ν x.Sd f

^

ΎΜΙ

ΎΜΙ

k

LTMy.Sd

XLTWpí.y

f

<1

ΎΜΙ

N x . S d <> N b . z . Rd = χ ζ A

ΎΜΙ

Nx.Sd

Nx.sd

XzA^

+ Mz.sd

ΎΜΙ

and,

,

k M

z z.Sd

w

»

c l

<

N x S d <,Nb.yRd = X y A—*ΎΜΙ

where: x m m = minimum ( χ γ ; χ ζ ), where

χ ν and χ ζ are given in chapter VII.c.2.1 XLj and %LT are given in chapter VHI.e.2

ky = 1 -

μ>

*fSd but k y <, 1,5 ; where \ny = Xy(2ßMy

­ 4) +

Wer.y

*y'"y

^zN*Sd X z Af y

Wpr.y­Wef.y

but k z <, 1,5 ; where μ ζ = λ ζ ( 2 β Μ ζ ­ 4 ) +

Wpf,z­Wef,z^

weC.z

b u t μ y <0,90, but μ ζ < 0,90,

k

LT = l ­ ^ T " * ; S d but k L T £ 1,0; where μ ί Τ = ( 0 , 1 5 . λ ζ . β Μ 1 τ ) - 0 , 1 5 but μ ί Τ ^0,90, 3CzAfy where ßM (ßMy, ßMz) is the equivalent uniform moment factor related to the shape of the bending moment (My.sd, M z .sd):

βΜ=1,8­0,7ψ ­1£ψ$ 1

βΜ=1,3

173

βΜ=1,4

Table ΓΧ.5 Internal forces and moments

Interaction formulas for the (NM) stability check of members of class 3 General formulas to be always satisfied:

IflLT>0,4: potential lateral-torsional buckling needs supplementary checks:

φ Eurocode 3 formulas for biaxial bending (My.sd, M z .sd) and axial compression Nx.sd^ Nx.sd + My.sd + Mz.sd

k„M y»'y.Sd

Ν x.Sd

AA

, k z M Z-Sd

<1

Ν x.Sd

k

LTMy.Sd

~ ™ XurWef.y X z A Ì w eC.z ' YMl ΎΜΙ ΎΜΙ Eurocode 3 formulas for uniaxial bending and axial compression: -min

y

ΎΜΙ

k

+

ΎΜΙ

zM z .sd

<1

Wefz-^ ΎΜΙ

use the formula for biaxial bending and axial compression (see φ ) introducing the relevant bending moment equal to zero and using % m i n buckling reduction factor. Other proposal of interpretation of Eurocode 3 formulas for uniaxial bending and axial compression (see comments in IX.d.2.2) using buckling reduction factors %y or χ ζ according to the relevant bending axis: Nx.sd

Nx.sd

,

ΎΜΙ

and,

y y-Sd

Nx.sd f X z A Ì

^

We'.yr1-

XyA-^

+ My.sd

k M

,

ΎΜΙ

ΎΜΙ

k

LTMy.sd f XurWef.y —™ iï

ΎΜΙ

Nx.Sdz.Rd=xzAΎΜΙ

Nx.sd

Nx.sd %

+ Mz.sd and,

Z

!

A^ ΎΜΙ

Nx-Sd < N b

k M

z z.Sd

we Rd

«^

ΎΜΙ

= χ A—*ΎΜΙ

where: %min = minimum ( %y ; χ ζ ) , where

χ γ and χ ζ are given in chapter VII.c.2.1 X LT and %LT are given in chapter Vm.e.2

k y = 1-!~Z * S d but k y < 1,5 ; where μ γ = Xy (2ß M y ­ 4) but μ γ <0,90, XyAfy _ ι μζΝ, kz = 1_r>z-^sd but ^ < ι , 5 ^ η 6 Γ β μ ζ = λζ(2βΜ2-4)οϋΐμζ<0,90, xy XzZAAI k L T = l ­ ^ T ^ * S d but k L T < l , 0 ; where μ ι τ = ( 0 , 1 5 . λ ζ . β Μ υ Γ ) ­ 0 , 1 5 but μ ^ <0,90, XzAfy where ß ^ (ßMy, ßMz) is the equivalent uniform moment factor related to the shape of the bending moment (My.sd, M z .sd):

βΜ=1,8­0,7ψ ­1<ψ< 1

ßM=l,3

174

ßM=l,4

Table IX.6

General interaction formulas for the (NM) stability check of members of class 4

Internal forces and moments

General formulas to be always satisfied:

(Ï) Eurocode 3 formulas for biaxial bending (My.sd, M z .sd) and axial compression N x .sd: Nx.sd + My.Sd +Mz.Sd

N x.Sd Xmin"· min^eff

|

k

y(My,sd+Nx,SdeNy)

kz(MzSd+N;t.SdeNz)^1

|

W eff.z

Weff-y ^ ΎΜΙ

ΎΜΙ

ΎΜΙ

Eurocode 3 formulas for uniaxial bending and axial compression: use the formula for biaxial bending and axial compression (see CD) introducing the relevant bending moment equal to zero and using Xmin buckling reduction factor. Other proposal of interpretation of Eurocode 3 formulas for uniaxial bending and axial compression (see comments in IX.d.2.2) using buckling reduction factors x y or χ ζ according to the relevant bending axis: Ν x.Sd

Nx.sd + My.Sd

XyA y^eff

τ

k

y( M y.Sd

Nx.sdeNy)

weff.y YMI

ΎΜΙ

and,

+

N x - S d < N b - z . R d = χ ζ A eff -

YMI

k

Nx.sd

Nx.sd + Mz.sd

Xz^eff 2A and,

M

, z( z.Sd + N x S d e N z )

YMI

YMI

Nx.sd < N b . y . R d = Xy A e f f - ^ YMI

where: x m i n = minimum ( Xy ; χ ζ ), where

%y and χ ζ are given in chapter VII.c.2.1 Xu and XLT are given in chapter VHI.e.2

ky = 1 kz =

y

x,

y but ky <, 1,5 ; where μ γ = X y (2ß M y ­ 4 ) but μ γ <0,90, Xy Aeff f y

ι_μζΝΧ.Μ Xz A eff r y

but kz s l 5

. w h e r e μ ζ = Χ ζ ( 2 β Μ ζ ­ 4 ) but μ ζ <0,90,

where ßM (ßMy, ßMz) is the equivalent uniform moment factor related to the shape of the bending moment (Msd + Nx.sd eN):

^P

7

βΜ=1,8­0,7ψ ßM=l,4 ­l^yál where Aeff, Weff.y, Weff.z, eN.y, eN.zare effective properties of cross­section defined in chapter V.

175

Table ΓΧ.7 Supplementary interaction formulas for the (NM) stability check of members of class 4 Internal forces and moments

If λτ^τ > 0,4: potential lateral-torsional buckling needs supplementary checks

CD Eurocode 3 formulas for biaxial bending (My.sd, M z .sd) and axial compression Nx.sd^ Nx.sd + My.Sd + Mz.sd

j kLT(My.sd + N x . Sd e N y )

Nx.sd Xmin Aeff

|

k z (M z . S d + N x . S d e N z ) " W eff.z

XirWeff.y YMI

YMI

ΎΜΙ

Eurocode 3 formulas for uniaxial bending and axial compression: use the formula for biaxial bending and axial compression (see (f)) introducing the relevant bending moment equal to zero and using Xnun buckling reduction factor. Other proposal of interpretation of Eurocode 3 formulas for uniaxial bending and axial compression (see comments in IX.d.2.2) using buckling reduction factors x y or χ ζ according to the major axis: Nx.sd

Nx.sd + My.sd

, kLT(My.Sd+Nx,SdeNy)^i

Xz^-eff" ZA YMI where: Xmùi = minimum ( Xy ; χ ζ ), where

XLTWeff.y-^ YMI

x y and χ ζ are given in chapter VII.c.2.1 XLT and XLT are given in chapter Vm.e.2

ky=lk =1

- ^ but k y <1,5 ; where \iy = Xy(2$My -4) but μ γ <0,90, Xy Aeff f y μ ζ Ν , ,Sd but k < 1,5 ; where μ = λ ( 2 β - 4 ) but μ <0,90, z ζ ζ Μζ ζ Χζ Aeff fy

k

L T = l - ^ T A N x f S d but k L T <1,0; where μ ί Τ = ( 0 , 1 5 Ä z . ß M . L T ) ­ 0 , 1 5 but μ ί τ < 0 , 9 0 , XzAeff t y where ßM (ßMy, ßMz) is the equivalent uniform moment factor related to the shape of the bending moment (Msd + N x .sd e ^ :

VOLLV βΜ=1,8­0,7ψ ßM=l,4 ß M = 1,3 ­1<ψ< 1 where Aeff, Weff.y, Weff.z, en.y, eN.z are effective properties of cross­section defined in chapter V. IX.e Verifications at ULS for (N$d >Vsd) (1) If the design values of shear force Vz.Sd<0,50Vp,z.Rd and, Vy.sd<0,50Vpry.Rd where V p f z jid, VPfy.Rd are the design plastic shear resistances about minor (zz) and major (yy) axes (see table K . 8 ) , no reduction of the tension or compression resistances is needed. With this condition the design value of axial force N x .sd shall be checked separately according to chapter VI (tension) or chapter VII (compression).

176

IX e. 1 [54.9 (3)]

Resistance of cross-section to (NSd,Vsd)

(1) For members submitted to combined axial force Nx.sd and shear force (Vz.sd or Vy.sd) if V M > 0,50 V p i Rd then it is proposed that each cross-section shall satisfy the following criterion: Nx.sd*N V.Rd where Nv.Rd is the reduced design resistance of the cross-section allowing for shear force (see table IX.8). Reduced design resistance Ny.Rd allowing for shear force

Table IX.8 Combined loading

If high shear: Vsd > 0,5.Vpi^d

Nx.sd + V^sd

N Vz.Rd

NX.Sd + Vy.Sd

Ν Vy.Rd 2 _V 2 l Sd—!

where:

k

Py =

Vpfz.Rd

J

y.Sd

-1

pfy.Rd

(A - p z AVtZ)f3 ΎΜΟ

(A - Py Ay.y)f3 YMO

Aν · ζ f y with Vp í z . R d = 7=•iu\r

YMOV3

withV

^

Rd

=

A

f

W5

If (Nx.sd)tension, A = gross cross-section or net section (Anet) (see chapter VI), If (Nx.Sd)compression, A = gross cross-section for class 1,2 or 3 cross-section, or effective cross-section (Aeff) for class 4 cross-section (see chapter VU). IX.f Verifications at ULS to (Nsd ,Vsd,Msd) (1) The verification of members submitted to combined axial force, shear forces and bending moments shall be performed with different (N,V,M) interaction rules about: 1) the resistance of the cross-section (IX.f.l), 2) the stability of web (LX.f.2) (2) All the (N,V,M) interaction formulas depend on the class of cross-sections. (3) Uniaxial bending (My.sd or Mz.sd) and biaxial bending (My.sd and Mz.sd) combined with shear forces (Vz.sd and Vy.sd) and with axial force Nx.sd are presented in the following chapters.

177

DC.f. 1 Resistance of cross­section to (NSd,VSd,MSd) (1) If the design values of shear force V z . S d <0,50V p f z . R d and, V y . S d <0,50V p i y R d where Vp¿z R d, Vpfy.Rd are the design plastic shear resistances about minor (zz) and major (yy) axes (see table ΓΧ.9), no reduction needs to be made in combination of bending moment and axial force. With this condition the members shall be verified to combined (Nsd, Msd) loading according to chapter DC.d. [5.4.9 (3)]

(2) If the design values of shear force VSd > 0,50 V p i Rd (high shear), the design resistance of the cross­section to combinations of moment and axial force should be calculated according to Eurocode 3 with a reduced yield strength (1 ­ p)fy for the shear area (Ay) 2\

where ρ =

2V Sd V. V pi.Rd

­1

The interaction formulas (N,V,M) proposed in the following chapters (IX.f.1.1 to IX.f.1.4) in case of high shear are simplifications replacing f, by (l­p)f, for the sections properties of cross­sections: A, Aeff, Wp£We/­,Weff. IX f.1.1 Uniaxial bending of class 1 or 2 cross-section (1) For the plastic resistance of class 1 or 2 cross­sections submitted to combined axial force (Nx.sd) with shear forces and uniaxial bending moments ((Vz.sd and My.sd) or (Vy.sd and Mz.sd)), if the design values of shear force V z . S d >0,50V p f 2 . R d Vy. S d >0,50V p i y . R d or, (high shear) then relevant interaction between (Nsd,Vsd,Msd) shall be considered. In this case the design value of bending moment Msd shall satisfy the following criterion if the level of axial load η is high: M S d
n= J^*LΝ pf .Rd

Ν x.Sd

Afy ΥΜΟ

where Np¿Rd is the design plastic resistance of the cross­section (2) If the level of axial load η is low (see table IX.9, for the limiting values of n), then the reduction of the plastic resistance moment may be neglected and the applied bending moment Msd combined with shear force Vsd shall be verified according to the rules given in chapter VEI. g. 1.1. On the other hand the axial load Nx.sd shall be verified in combination with shear forces Vsd according to chapter IX.e.

178

[5.4.9]

Table IX.9 Reduced design plastic resistance moment Mfj.yjid allowing for axial load and shear force for class 1 or 2 cross­sections If high level of axial load Nx.sd: Rolled and Values of the limit a if[n~>äl welded I­sections

K^H

b

MN.v.y.Rd = Í ^ ^ ^ ^ W y-í^ P y

• (η o< A ­ 2 b t f ^ = min^0,25;^^J

V

• Γη L = nun 0,50; MN.V.z.Rd= (1­Py) 1 ­ V A j

Hti'

hollow sections

J

1­a

(1­Py) 1­a

r

a = 0,25

η

L

y-

a = min 0,25; -y

u-b.

ζ

J - 3=- - z

a=

MN.v.Rd= 1,04 1 ­ p ­

A-2bt^

MN.VJW=

A-2bt 2A

-n = n

Λ

A-2bt

MN.V^.Rd =

J

U6(l-η-p)Wpf

ht 0,5 + — V A j

MN.VJW

w

n c

pr.y

= MpÉRd [1-n 2 ]

^ A£y YMO

- The values of p z and p y are given on the following page. - Limitation of MN.vjtd obtained from this table: Mw.vjid ^ M pCRd (design plastic resistance moment) M

N.V.y.Rd ^ Mpf.yJtd

or, in other words, M

N.V.z.Rd - Mpf . z . Rd

179

f

W rpt 0.7

_ Wpiyfy γ^— _ W pf . Z f y ΎΜΟ

v

ΎΜΟ

YMO

MN.v.y.Rd= 1 , 3 3 ( 1 - n - p z ) W p r .

For plate without bolt holes notes;

YMO

1,7

(1­P)

S=

WpfX

ν If high level of axial load Nx.sd: if|n~>äl

Values of the limit a

. fA„c

YM0

YMO

—

YMO

Pz =

2-^Sd. pf.z.Rd v

Pv =

-1

V

y.Sd

, withV

f-2-Rd

=

A fly ^v.z

·

'

YMOV3

ι -1

pi.y.Rd

IX f. 1.2 Biaxial bending of class 1 or 2 cross-section [54.8.1(H)] (1) For the plastic resistance of class 1 or 2 cross-sections submitted to combined axial force (Nx.sd), with shear forces and biaxial bending moments ((Vz.sd and My.sd) and (Vy.sd and Mz.sd)), if the design values of shear force V z .sd>0,50Vp fz . Rd and, Vy.sd>0,50V pry . Rd then the following criterion is proposed: ία

My.Sd M,N.V.y.Rd J

r-

M z.Sd

L M N.V.z.Rd .

ß <1

where MN.y.y.Rd and Mjsj.v.z.Rd are the reduced design plastic resistance moment allowing for the axial load and shear force (see table IX.9), α and β are constants taken as follows: ­ for I and Η sections: ­ for circular tubes: ­ for rectangular hollow sections: ­ for solid rectangles and plates: [5.4.8.2]

α = 2 ; ß = 5n, b u t ß > l α=2 ;β=2 1,66 , buta=ß < 6 α 1­1,13η' α = β = 1,73 + 1,8 η 3

IX.f.1.3 B ending of class 3 cross-section (1) For the elastic resistance of class 3 cross­sections submitted to combined axial load (Nx.sd), shear forces (Vz.sd, Vy.sd) and biaxial bending moments (My.sd and Mz.sd) the following proposed criterion shall be satisfied in case of high shear( V Sd > 0,50 Vp[ R d ) :

ECCS n°65 table 5.16

where ρ = maximum value of (pz, py) where p z and p y are given in previous chapter IX.f.1.1 (2) In case of uniaxial bending moment combined with axial load and shear force the following criteria shall be satisfied in case of high shear(VSd > 0,50 V pf R d ): ­ for bending about major axis (Nx
180

for bending about minor axis (Nx.sd, Vy.sd and Mz.sd):

[54.8.3]

IXf.l .4 Bending of class 4 cross-section (1) For the elastic resistance of class 4 cross-sections submitted to combined axial force (Nx.sd), shear forces (Vz.sd, Vy.sd) and biaxial bending moments (Mysd and Mzsd) the following proposed criterion shall be satisfied in case of high shear( V Sd > 0,50 Vp/· R d ): Nx.sd f v A eff/

, My.Sd + Nx.Sd e N y

f

W cc

YMO

1

M s.Sd + N x .sd CNZ < 1 - -p

y

ΎΜΟ

YMO

where ρ = maximum value of (p z , p y ), where p z and p y are given in previous chapter IX.f. 1.1 where Aeff is the effective area of the cross-section when subject to uniform compression (single Nx.sd), is the effective section modulus of the cross-section when subject only to Weff moment about the relevant axis(single My.sd , single Mz.sd) , is the shift of the relevant centroidal axis (eNy, eNz) when the cross-section is subject to uniform compression (single Nx.sd) · (2) In case of uniaxial bending moment combined with axial load and shear force the following criteria shall be satisfied: eN

for bending about major axis (Nx.sd, Vz.Sd and My.sd): and,

- for bending about minor axis (Nx.sd, Vy.Sd and Mz.sd): N x.sd , M z.Sd+N x .s d e Nz —Fy-+ ry—*1-P> L

eff"~

YMO

W

eff.z~

YMO

181

IX.f.2 Stability of web to (Nx.sd, Vz.Sd, My.Sd) [5.6.7.2]

(1) If webs are submitted to combined axial load Nx.sd, shear force Vz.sd and bending moment My.sd and, if they have ratio

exceeding the limits given in table VHI.7, w

w

then they shall be checked for resistance to shear buckling. (2) The interaction of shear buckling resistance and moment resistance is shown in table VUL 14 according to the simple post-critical method. (3) The web may be assumed to be satisfactory if one of the three following checks ((T), (2) or (3)) according to the loading level (Vz.sd, My.sd) shall be satisfied: [5.6.7.2 (i)]

(T) If the design value of bending moment My.Sd g MN.f.Rd where

M N . ^ is the reduced design plastic moment resistance of a cross-section consisting of the flanges only and allowing for axial force; proposal for cross-section with equal flanges:

- for class 1, 2 or 3

M

N.f.Rd=btf(h-tf)

YMO

^tf

-T4

e

N x.Sd "2btffy^ v.

My.sd - for class 4:

M )

MN.f.Rd =

YMO

>

f

((b + beff)tf ^ y L ) - ( ( b - b e f f ) t f eM) fy

YMI

1—

Nx.sd

r(b+b eff )t f f y ^| ^

YMI

JJ

where b, tf, h are flange width, flange thickness, height of profile (see table 0.1), beff is the effective width of the compression flange (see chapter V), eM is the shift of the centroidal major axis (yy) when the cross-section consisting of flanges only is subject to My.sd· then the design value of shear force shall satisfy : V

z.Sd ^

where

V

ba.Rd

Vbajid is the design shear resistance buckling of the web according to simple post-critical method (see chapter Vffl.d.2).

182

[5.6.7.2(2)]

(D //"the design values of bending moment and shear force My.sd > M N.f.Rd and V . s d ^ C U O V ^ d then the bending moment shall satisfy : My.Sd ^ M N . y j R d

where M ^ R J is the redudced design resistance moment of the cross-section allowing for axial load depending on classes of cross-sections (see chapter LX.d.1.1, LX.d.1.3, LX.d.1.4). [5.6.7.2 (3)]

If the design values of bending moment and shear force My.sd > M N.f.Rd and

v^^sov^

then the bending moment and the shear force shall satisfy the three following checks

where MN.p£y.Rd is the reduced design plastic resistance moment of the cross-section allowing for axial load : M

N.pf.y.Rd = MN.y.Rd (see table LX.3)

- and, My sd ^ M N y R d - and,

z.Sd - VbaJld

183

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

χ

Generalities X.a (1) For each load case (see chapter ΙΠ) the global analysis of the frame (see chapter IV) determines the design values for the following effects of actions which are applied to the web of members and which shall be checked at ultimate limit states: transverse forces with separate or combined internal forces and moment acting in the plane of the web:

'U

Fsd

ζ

&

...y

χ -

- -χ

Ρ

Νx.Sd

I

f 'z.Sd

Ν.x.Sd

My.Sd

hd\ [5.7.1(2)]

[5.7.1(1)]

[5.7.1(6)]

(2) The transverse forces Fsd may be applied in different ways: - either, through one flange - or, to one flange and transferred through the web directly to the other flange. (3) The resistance of an unstiffened web to transverse forces applied through a flange, should be cheked for all the three following modes of failure (see table X. 1) : . crushing of the web close to the flange, accompagnied by plastic deformations of the flange (see chapter X.c.2), . crippling of the web in the form of localised buckling and crushing of the web close to the flange, accompagnied by plastic deformation of the flange (see chapter X.d. 1), . buckling of the web over most of the depth of the member (see chapter X.d.2) (4) In addition the effect of the transverse force on the moment resistance of the member should be considered : resistance to local buckling (see chapter X.b) and yield criterion (see chapter X.c.1) Table X.1

ECCS n°65 table 5.36

Failure modes due to load introduction Crippling

Crushing

1

=T ι

1

ι

Buckling

I

I

184

.

I

I

I

.

I

Classification of cross-section (1) The effects of significant transverse compressive stresses on the local buckling resistance of a web shall be taken into account in design. Such stresses may arise from transverse forces on a member and at member intersections. (2) The presence of significant transverse compressive stresses may effectively reduce the maximum values of the depth­to­thickness ratios d/tw for class 1, class 2 and class 3 webs below those given in chapter V, depending on the spacing of any web stiffeners. (3) A recognised method of verification should be used. Reference may be made to the application rules for stiffened plating given in ENV 1993­2 Eurocode 3: Part 2 (which is in preparation). X.b

[5.3.6]

X.C X.c.1

Resistance of webs to (F,N, V,M j Yield criterion to (F,N,V,M)

[54.10]

(1) The web of a member subject to a transverse force in the plane of the web (see table X.2) in addition to any combinations of moment and axial force on the cross­section, shall at all points satisfy the criteria given in table X.3.

[Fig. 5.4.3]

Table X.2

Stresses in web panel due to bending moment, axial force and transverse force | Fsd f

Nx.sd

M

y­sdf

'Γ

A' C.

'Β

*My . S d N

x.Sd

.D Fsd

(a) Layout

σ. ΟΖΕΕΡβ* σ,

ED

f

o*., . a n m * σχ­1 Β

>x.l

öb =: 4

D?

σF^C 2

*· a m p o , ° ^

b) Stresses in element E

(c) Stresses in panel ABCD

185

σχ.2 σ^,η oh (where ab=f3rn.fy) (d) Equivalent stresses

Yield criteria to be satisfied by the web

Table X.3

IfVsd < 0,5.V p £ R d (low shear) [form. (5.42)]

Class 1 or 2 (plastic distribution of stresses)

[form. (5.41)]

Class 3 or 4

"xm.Ed fy Ι ΎΜΟ

-a

»z.Ed

+ f ν Ι ΎΜΟ 2

°x.Ed fy/ΎΜΟ

r

°xm£d f y /ΎΜΟ

-k

>z.Ed f y / ΎΜΟ

-a

°z.Ed fy / ΎΜΟ

°x.Ed T g z.Ed

<1-β m

fy/YMoJLfy/YMO

<1

IfVsd > 0,5.V p £ R d (high shear) [form. (5.44)]

Class 1 or 2 (plastic distribution of stresses)

[form. (5.43)]

CJ

°z.Ed

xm.Ed fy/ΎΜΟ

fy/ΎΜΟ 2

Class 3 or 4

f

'x.Ed y / ΎΜΟ

r

»z.Ed fy/ΎΜΟ

where σχ Ed

σ xm.Ed

JΓ gZ.Ed

ί γ /ΎΜθ1ίLVYM γ /ΎΜθ >x.Ed f y / Ύ MO

I*

Ed ΎΜΟ

^l­ßm­Ρ
is the design value of the local longitudinal stress due to moment and axial force at the point (see table X.2), σ ζ £d is the design value of the stress at the same point due to transverse force (see table X.2), c xm.Ed i s m e design value of the mean longitudinal stress in the web(see table X.2) °x.Ed »

°ZSÂ

an

d G xrn £d ®& taken as positive for compression and as negative for tension

ßm = Mw.Sd/Mp/:w.Rd> where M w Sd is the design value of the moment in the web, M p£w . Rd = 0,25t w d 2 f y /Y M0 . p=(2VSd/Vp£Rd-l)2, and

k f r o for

is obtained as follows : crxmiEd/ azJEd < 0: k = 1 - ß m °xm.Ed/ azEd > 0: if ß m < 0,5: ifß m >0,5:

186

then k = 0,5 (1 + ßm) thenk=l,5(l-ßj

[5.7.3 (i)j

X.C.2 Crushing resistance to F (1) The design crushing resistance Ry.Rd of the web of an I, H or U section (see table X.4) should be obtained from:

[form. (5.71)]

where sg is the length of stiff bearing determined by dispersion of load through solid steel material which is properly fixed in place at a slope of 1:1, (see table X.5); no dispersion should be taken through loose packs, f

Sy is given by :

[form. (5.72)]

l

f

w *yw

>2

n Of.Ed

yf / ΎΜΟ

where

bf £ 25tf, Of.Ed is the longitudinal stress in the flange. (2) At the end of a member sy should be halved.

[5.7.3 (3)]

Load introduction

Table X.4

Fsd

t* •

Msd

1 -

1 1

ι

- -*

\

r

u 1 1

* - ■

J

V

Msd

ss

1

1i d

bf = [Fig. 5.7.2]

=

=

=

^—-

=

Length of stiff bearing, ss

Table X.5

r \

I I

Ss *

Ss

45°

V /

sT

Ss

187

¥

1

r^

\ Ν

1

[5.7.4(1)]

X.d Stability of webs to (F ; (F,M)) X.d.l Crippling resistance to (F : (FM)) X.d.1.1 Crippling resistance to F (1) For S 235 up to S 420 steel grades the design crippling resistance Ra.Rd of the web (see table X.4) should be obtained from:

[form. (5.77)]

where ss tw tf d

E tyw

is the length of stiff bearing from table X.5. buts s /d<0,2, is the thickness of the web, is the thickness of the flange, is the depth of the web between the flanges, is the modulus of elasticity, is the yield strength of the web.

(2) For S 460 steel grade only the design crippling resistance RaRd of the web should be obtained from the formula given X.d. 1.1 (1) but replacing the factor 0,5 by 0,6.

[Annex D]

X,dJ ,2 ÇrjppWng resistance \o (FM) Table X.6

Interaction formula of crippling resistance and moment resistance F ii Ra.Rd -

y s 0,5 R a . R d / /

/ /

ss/ / x s / /

s^>^ / /

V//////, M

0,5 M c . Rd

[5.7.4 (2)]

M c . Rd

(1) Where the member is also subject to bending moments, the following criteria should be satisfied (see table X.6): F

Sd - R aJld

Msd^McJld F

[form. (5.78)]

sd . M Sd ^ 1,5 a.Rd M cJRd

R

where Mcj^d is the design noment resistance of the cross-section (see chapter Vin.e. 1).

188

!

X,d,2 [5.7.5 (i)]

Buckling resistance to F

(1) The design buckling resistance Rbjw of the web of an I, H or U section (see table X.4) should be obtained by considering the web as a virtual compression member with an effective breadth beff obtained from :

[form. (5.79)]

b^f = ­yV+S? The table X.7 gives values of beff for different cases of loads.

[5.7.5 (3)]

(2) The buckling resistance should be determined from chapter VII.c.2.1 using buckling curve c and PA = 1 (table VII.6).

[5.7.5 (4)]

(3) The buckling length of the virtual compression member should be determined from the conditions of lateral and rotational restraint at the flanges at the point of load application.

[figure 5.7.3]

Table X.7

Effective breadth ¿>gryfor web buckling resistance

beff = h

s8 !! ν

Β

-f¿--> 1

'

beff

'

I - -t I =)

=1 I -t-

beff1

a ss H-H Η

a beff

>eff

3

I'

= Vh 2

beff = 2

2

+ a

butb e ff < h

beff=}Vh 2 +s 2 +a+|

I·

189

butbeff
X.e

Stability of webs to compression flange buckling Table X.8

Compression flange buckling in plane of the web

Nf

Nf"1

ΤΠΙΙΙΙΙΙΙΙΓ My.Sd

My.Sd (

)

^--iüüiülüJ Nf"

[5.7.7]

ECCS n° 65 table 5.20

Nf"

(1) To prevent the possibility of the compression flange buckling in the plane of the web (see table IX.8), the thickness ratio d/tw shall be lower than the value given in table X.9. Table X.9 Steel grade of flange d/tw

Maximum width-to-thickness ratio d/tw S 235

S 275

S 355

S 420

S 460

360

300

240

200

185

(2) I and H hot-rolled sections never meet such problem of compression flange buckling in plane of the web.

190

XI

CONNECTIONS

Xl.a

Generalities

[6.1.1 (i)]

(1) All connections shall have a design resistance such that the structure remains effective and is capable of satisfying all the basic design requirements given in chapter La. (2) The partial safety factors TM concern the resistances of bolts (7Mb), of welds (TMw). of members and cross-sections (ΎΜΟ» ΎΜΙ» ΎΜ2) and the slip resistance of preloaded bolts (7Ms.ser)· Their numerical values are provided in table 1.2. [6.1.2 (1)] (3) The forces and moments applied to connections at the ultimate limit state shall be determined by global analysis in conformity with chapter IV. [6.14 (l)] (4) Connections may be designed by distributing the internal forces and moments in whatever rational way is best, provided that: (a) the assumed internal forces and moments are in equilibrium with applied forces and moments, (b) each element in the connection is capable of resisting the forces or stresses assumed in the analysis, and (c) the deformations implied by this distribution are within the deformation capacity of the fasteners or welds and the connected parts. [6.2 (l)] (5) Members meeting at a joint shall normally be arranged with their centroidal axes intersecting at a point. [6.2 (2)] (6) Where there is eccentricity at intersections this shall be taken into account in the design of the joint and the member. [6.2 (3)] (7) In the case of bolted connections of angles and tees with at least two bolts per connection, the setting out lines of the bolts may be regarded as the centroidal axes for the purpose of intersection at joints. Xl.b Bolted connections

[6.5]

[6.5.1.1]

Xl.b. 1

Positioning of holes

(1) The positioning of holes for bolts shall be such as to prevent corrosion and local buckling and to facilitate the installation of the bolts. (2) The minimum and maximum distances between bolts and recommended distances (as used in table XL 6 for the bolt bearing resistances) are given in table XL 1. Those values are valid for structures not exposed to weather or other corrosive influences. XI.b.2

Distribution of forces between bolts

[6.5.4 (l)]

(1) Where the design shear resistance Fvjid of a bolt (see chapter XI.b.5.2.1) is less than the design bearing resistance Fbjtø (see chapter XI.b.5.1), the distribution of internal forces between bolts at the Ultimate Limit State shall be proportional to the distance from the centre of rotation (see table XI.2).

[6.54 (2)]

(2) In other cases of bearing type connections the distribution of internal forces between bolts at the Ultimate Limit State may be plastic (see table XI.3).

191

ECCS n'65 table 6.2

Designation of distances between bolts

Table XLI

1,2 do ^ ei < maximum ( 12t ; 150 mm) 1,5 do ^ e2 ^ maximum ( 12t ; 150 mm) 2,2 do ^ pi ^ maximum ( 14t ; 200 mm) 3,0 do < p2 ^ maximum ( 14t ; 200 mm)

PL Pi ef

Recommended distances Bolts

Recommended distances in mm

shear joint e2

M 12

Pi >P2 40

P2

M 16

55

40

30

M 20

70

50

40

M 24

80

60

50

M 27

90

70

55

M 30

100

75

60

M 36

120

90

70

e2

+—4

ei

pi

tension or compression joint

_Çi

30

e2 25

The designations e2 and p2 also apply when distances measured are not in the direction of stress. In case of smaller values of tq. and p2 see Eurocode 3 Part 1.1 (J2I). [figure 6.5.7]

Linear distribution of loads between fasteners

Table XI.2

Ρ Msd

Ρ Ρ Ρ

0,5 F h.sd

)

Vsd

F h.Sd

F

h.Sd ­

M Sd 5p f

F

v.Sd ­

192

'MSd^2 5p

+

m

ECCS n" 65

table 64

| Table XI.3

Possible plastic distribution of loads between fasteners. Any realistic combination could be used, e.g. —'—*¿—

———

Fv.sdv 1

Ρ Ρ ρ Ρ

MSd t

Γ-Γ l. C l

-—

ψ

Ρ K D.l

—i

)

Vsd

_ FvSH —

h.Sd

v

Sd~rb.Rd

= ^ . ­ 2 Ρ b.Rd , 2p

VFh.Sd + Fv.Sd ^Fb.Rd

[6.5.9 (1)] [Annex J] [Fig. 6.5.8]

XI.h.3 Prving forces (1) Where bolts are required to carry an applied tensile force, they shall be proportioned to also resist the additional force due to prying action, see table XI.4. Prying forces

Table XI.4

N = FN + Q Q.

N = FN + Q

f

J

I [6^.3]

. Q = prying force

2 FΝ

XI.b.4 Categories of bolted connections (1) The design of a bolted connection loaded in shear or in tension shall conform with one of the following categories: see table XI.5.

193

[table 6.5.2]

Table XI.5

Categories of bolted connections Shear connections Remarks Criteria No preloading required. Fv.sd ^ F v .Rd All grades from 4.6 to 10.9. Fv.Sd < Fb-Rd

Category A Bearing type Β Slip-resistant at SLS

Fv.Sd.ser ^

F v . R d.ser

Fv.Sd

^

F v .Rd

Fv.Sd

<

Fb.Rd

Fv.Sd

^

Fs.Rd

Fv.Sd

<

Fb.Rd

C slip-resistant at ULS

Preloaded high strength bolts. No slip at the serviceability limit state. Preloaded high strength bolts. No slip at the ultimate limit state.

Tension connections Category D Non-preloaded

Criteria

E Preloaded Key: Fy.Sd.ser Fy.sd F v Jid Fbjid Fsudser FsRd Ftsd Ft.Rd [6.5.5. (2)]

[6.5.5. (3)]

= = = = = — = =

FtSd

^

FLRd

Ftsd

^

Fuid

Remarks No preloading required. All grades from 4.6 to 10.9. Preloaded high strength bolts.

design shear force per bolt for the serviceability limit state design shear force per bolt for the ultimate limit state design shear resistance per bolt design bearing resistance per bolt design slip resistance per bolt for the serviceability limit state design slip resistance per bolt for the ultimate limit state design tensile force per bolt for the ultimate limit state design tension resistance per bolt

XI.b.5 Design ULS resistance of bolts (1) At the Ultimate Limit States the design shear force Fv.sd on a bolt shall not exceed the lesser of: - the design bearing resistance Fb.Rd (see chapter XI.b.5.1) - the design shear resistance Fv.Rd (see chapter XI.b.5.2) (2) At the Ultimate Limit States the design tensile force Ftsd» inclusive of any force due to prying action, shall not exceed the lesser of: - the design tension resistance FLRd (see chapter Xl.b. 5.3) - the design punching shear resistance Bp.Rd (see chapter XI.b.5.4) (3) At the Ultimate Limit States bolts subject to both shear force and tensile force shall satisfy the interaction criterion of chapter XI.b.5.5.

XI.b.5.1 Bearing resistance [table 6.5.3] (1) The design bearing resistance shall be taken as: b.Rd

b.Rk

(see table XI.6 for Fb.Rk)

Ύινη>

194

ECCS n" 65

table 6.6

Β T a b l e XI.6

Bearing resistance per bolt for recommended detailing for t = 10 m m in [kN]

e2

ffce-2.5af.dt

P2 e2 ei

; _PjL_I ; íub ;l7 o a = mm JEL. 3d0 3d0 4 fu

pi

20

22

24

27

30

13

16 18

22

24

26

30

33

36 39

ei

20

27,5

35

37,5

40

45

50

60

P1.P2

30

40

50

55

60

674

75

90

e2 S 235 S 275

20

25

30

32,5

35

40

45

55

55,4

70,7

60,0

76,6

91,4 99,0

101,8 110,2

110,8 120,0

121,5 131,6

166,2 180,0

S 355

754

104,0

1413 149,8

150,8 153,8 163,1

165,4 168,8 178,9

2262

76,9 81,5

124,4 126,9 134,5

138,5

S 420 S 460

96,2 98,1

136,4 147,7 185,6 189,4 200,8

30

40

50

55

60

70

75

90

40

55

70

75

80

90

100

120

25

30

40

45

50

55

60

70

S 235

83,1

106,7

136,4

151,3

166,2

182,3

204,5

2492

S 275 S 355

90,0 113,1

115,6 145,2

147,7 185,6

163,9 205,9

180,0 226,2

197,4

270,0

248,1

221,6 278,4

S 420

115,4 122,3

148,1 157,0

189,4 200,8

210,1 222,7

230,8 244,6

253,1 268,3

284,1 301,1

3462 366,9

ei

40

55

70

75

80

90

100

120

P1.P2

50

70

85

95

100

115

130

150

e2 S 235 S 275

35

50

60

65

70

80

90

110

108,0 117,0

198,0 214,5 269,5

243,0

270,0

324,0

234,0

263,3

147,0

180,0 195,0 245,0

216,0

S 355

144,0 156,0 196,0

294,0

330,8

292,5 3674

351,0 441,0

S 420

150,0

200,0

250,0

275,0

300,0

337,5

375,0

450,0

S 460

159,0

212,0

265,0

291,5

318,0

357,8

3974

477,0

Bolt diameter d [mm] Hole diameter do [mm]

12

compact detailing

recommended ei P1.P2 values e2

S 460 high bearing

230,8

244,6

3392

- For steel grades greater than S 235 the values of fu are issued from table IL 2 (prEN 10113) and are valid for plate thickness not greater than 40 mm. - For intermediate values of α the value of FbjUc may be determined by linear interpolation. - For different plate thickness t in [mm] multiply the values given in the table by — .

1

195

XI.b.5.2 Shear resistance XI.b.52.1 General case [table 6.5.3] (1) The design shear resistance of a bolt shall be taken as: _ F v.Rk v.Rd ­

(see table XI.7 for Fvjuc)

YMb

ECCS n° 65 table 6.7

Table XI.7

Shear resistance per bolt and per shear plane in [kN]

Γ zip

Fv.Rk ­Ci.f u b.A s where

Ci = 0,6 C2 = 0,5

for strength grades 4.6, 5.6 and 8.8 for strength grades 4.6, 5.8, 6.8 and 10.9

Shear in tl ire adec i portion oftheb olt 13

16 18

20 22

22 24

24 26

27 30

30 33

36 39

84,3

157

245

303

353

459

561

817

20,2

37,7 47,1 75,4

58,8 73,5 117,6

72,7 90,9 145,4

84,7

110,2

105,9 169,4

137,7 220,3

134,6 168,3 269,3

196,1 245,1 392,2

78,5

122,5

151,5

176,5

229,5

280,5

408,5

Bolt diameter d [mm]

12

Hole diameter do [mm] Tensile stress2 area of bolt As [mm ] Shear resistance grade per bolt and per 4.6 5.6 shear plane 8.8 F v.Rk in [kN] 10.9

25,3 40,5 42,2

XI.b.52.2 Long Joints [6.5.10. (1)]

(1) Where the distance Lj between the centres of the end bolts in a joint is more than 15 d, where d is the nominal diameter of the bolts, the design shear resistance Fv.Rd of all the bolts calculated as specified in chapter XI.b.5.2.1 as appropriate shall be reduced by multiplying it by a reduction factor ßLf, given by (see table XL 8) : [form. (6.11)] [Fig. 6.5.10]

ßLf=l PU

Table XI.8

L:­15d 3 but 0,75 < ß L f < 1,0 PU

2 0 0 d

Long joints

I I

I

I

I

I

I I

Lj

15 d

65 d

196

•ι

; I I 1 1 1 I ii I 1 I I I I ; = 3 · Ι

ι

ι

ι

ι

ι

l i l i l í

ι

ι

ι

ι

ι

ι

l i l i l í

ι—i

ΧI.h J.3 Tension resistance [table 6.5.3] (1) The design tension resistance of a bolt shall be taken as follows: [6.5.5. (3)] ECCS ne 65 table 6.8

F

_ Ft.Rk t.Rd -

(see table XI.9 for Ftjik)

YMb

Table XI.9

Tension resistance per bolt in [kN]

: mm-

—

Bolt diameter d [mm]

grade

Tension

4.6 5.6 8.8 10.9

resistance F t.Rk in [kN]

Ft.Rk =0,9.f ub .A s

12

16

20

22

24

27

30

36

30,3 37,9 60,7 75,9

56,5 70,7 113,0 141,3

88,2

109,1 136,4 218,2 272,7

127,1 158,9 254,2 317,7

165,2

202,0 252,5 403,9 504,9

294,1

110,3 176,4 220,5

206,6 330,5 413,1

367,7 588,2 735,3

XI.hS.4 Punching shear resistance [65.5. (4)] (1) When the plate thickness tn is smaller than 0,5.d, the design punching shear resistance of the bolt head and the nut, Bp.Rd shall be checked and evaluated as follows: [form. (65)]

Bp.Rd = 0,6 π dm t.

YMb where tp is the thickness of the plate under the bolt head or the nut dm is the mean of the across points and across flats dimensions of the bolt head or the nut, whichever is smaller, in other words dm is the mean diameter of inscribed and circumscribed circles of bolt head or nut: dm = minimum (dm bolt head» dm nut)· XI.hJ.5 Shear and tension interaction [6.5.5. (5)] (1) Bolts subject to both shear force and tensile force shall in addition satisfy the following criterion which is illustrated in table XI. 10: [form. (6.6)]

v.Sd v.Rd

Ft Sd £1,0 l,4.F t Rd

Table XI. 10 Interaction formula of shear resistance and tension resistance for bolts

197

XI.b.6

[5.4.3 (1)]

[6.5.2.3]

[6.5.2.2] [6.5.8]

ULS resistance of element with bolt holes

XI.b.6.1 Net section ULS resistance see chapter VI.b.2 XI.b.6.2 ULS resistance of angle with a single row of bolt see chapter VLcl XI.b.6.3 Block shear ULS resistance see chapter VDXd.l XI.b.7

High strength bolts in slip-resistant connections at SLS

(1) When the slip resistance is needed at serviceability timit states the design for a preloaded high-strength bolt shall be carried out as given hereafter. In the ultimate limit state the bolt is considered as a bolt in shear and bearing without friction (see chapter XI.b.5). (2) In connections designed for slip-resistance at serviceability limit states the design serviceability shear load should not exceed the design slip resistance V&Rd(3) The design slip resistance of a preloaded high strength bolt shall be taken as: F

_ s.Rd -

r

s.Rk

(see table XI. 11 for Fs.Rk)

YMS. ser

(4) When the slip resistance is needed at ultimate limit state, see chapter [6.5.8] of Eurocode 3 Part 1.1 (121). ECCS n° 65 table 4.5

Table XI.11 Characteristic slip resistance per bolt and per friction interface for 8.8 and 10.9 bolts, where the holes in all the plies have standard nominal clearances *"*.** = 0 ^ f u b A s Bolt diameter

d [mm]

12

Tensile stress area of bolt As [mm2] Fsjik for 8.8 bolts [kN] FsRk for 10.9 bolts [kN] surface class class Α (μ = 0,5)

class Β (μ = 0,4)

μ = 0,2 class D μ = 0,2 class D

20

22

24

27

30

36

84,3 157 245

303

353 459

561

817

9,4

16

17,6 27,4 33,9 39,5 51,4 62,8 91,5

11,8 22,0 34,3 42,4 49,4 64,3 78,5 114,4

description surfaces blasted with shot or grit, with any loose rust removed, no pitting. surfaces blasted with shot or grit, and spraymetallized with aluminium or a zinc-based coating. surfaces blasted with shot or grit, and painted with an alkali-zinc silicate paint

multiplication factor 2,5

2,0

class C (μ = 0,3)

surfaces cleaned by wire brushing or flame cleaning, with any loose rust removed.

1,5

class D (μ = 0,2)

surfaces not treated.

1,0

198

[6.6.2.1]

XI.C

Welded connections

xic.i

Type of weld

(1) Welds are generally be classified as (see table XI. 12): - fillet welds - butt welds (with full or partial penetration) ECCS n° 65 table 6.10

Table XI.12

Common types of welded joints Type of joint

Type of weld Butt joint

Tee-butt joint

Ύ.

I

Lap joint

Fillet weld

Full penetration butt weld

single V

X

double bevel

double V

ï

single U

:

double U Partial penetration butt weld

single bevel '

double J

ΣΏ

double V

I

double U XI.C.2 Fillet weld [6.6.2.2. (l)] (1) Fillet may be used for connecting parts, where the fusion faces form an angle of 60° to 120' [6.6.2.2. (2)] (2) Smaller angles than 60° are also permitted. However, in such cases the weld shall be considered to be a partial penetration butt weld. [6.6.2.2. (3)] (3) For angles over 120°, fillet welds shall not be relied upon to transmit forces.

199

XI.C.3

Design resistance of fillet weld

XI.C.3 J Throat thickness [6.6.5.2. (1)] (1) The throat thickness, a, of a fillet weld shall be taken as the height of the largest triangle which can be inscribed within the fusion faces and the weld surface, measured perpendicular to the outer side of this triangle(see table XI. 13). ECCS n° 65 table 6.13

Table XI.13 (a)

Throat thickness

Design sections of fillet welds

(b)

Design throat thickness aup for submerged arc welding

[6.6.5.2. (2)] (2) The throat thickness of a fillet weld should not be less than 3 mm. [6.6.5.2. (4)] (3) In the case of a fillet weld made by an automatic submerged arc process, the throat thickness may be increased by 20% or 2 mm, whichever is smaller, without resorting to procedure trials. ECCS n°65

6.3.4.2 (4)

ECCS n°65 table 6.14

(4) The design force used for checking fillet welds should be taken as the resultant of the forces to be transmitted by the weld (see table XL 14). Table XI.14

Action effects in fillet welds

Sd

Cw.Sd

Vj_sd

VjTSd

Fw.Sd=VNÌ,Sd + VÌ. S d +V 2 / i Sd

200

Vj_sd

[6.6J.3]

ΧI.c.3.2 Design resistance (1) The design resistance of a fillet weld shall be taken as follows w.Rk

w.Sd ECCS n° 65

table 6.15

(see table DC. 15 for

ΎΜν

FWR±)

Resistance of a fillet weld

Table XI.15

w.Rk

V3.ßv

■a.L

fu ­ nominal ultimate tensile strength of the weaker part joined a ­ throat thickness L ­ weld length ß w ­ correlation factor Weld resistance Fw.Rk in [kN] for 100 mm weld length A Throat thickness H a [mm] S 235 ß w = 0,80 S 275 ß w = 0,85 S 355 ß w = 0,90 S 420 S 460

ß w = 0,95 ß w =l,00

3

4

77,9 79,5 94,3 91,2

103,9

91,8

106,0 125,7 121,5 122,4

5

6

7

129,9 155,9 181,9 132,5 158,9 185,4 157,2 188,6 220,0 151,9 182,3 212,7

8

9

1

10

207,8 233,8 259,8 211,9 238,4 264,9 251,5 282,9 314,3 243,1 273,5 303,9

153,0 183,6 214,2 244,8

275,4 306,0

­ For different weld lengths L in [mm] multiply the values given in the table by I

12 311,8 317,9 377,2 364,6 367,2 J.

­ For steel grades greater than S 235 the values of fu are issued from table Π.2 (prEN 10113) and are valid for plate thickness not greater than 40 mm.

XLc.4

Design resistance of butt weld

[6.6.2.3 (l)] (1) A full penetration butt weld is defined as a butt weld that has complete penetration and fusion of weld and parent metal throughout the thickness of the joint. [6.6.2.3 (2)] (2) A partial penetration butt weld is defined as a butt weld that has joint penetration which is less than the full thickness of the parent material. [6.6.6.1 (l)] (3) The design resistance of a full penetration butt weld shall be taken as equal to the design resistance of the weaker of the parts joined. [6.6.6.2 (1)] (4) The design resistance of a partial penetration butt weld shall be determined as for a deep penetration fillet weld. [6.6.6.2 (2)] (5) The throat thickness of a partial penetration butt weld shall be taken as the depth of penetration that can consistently be achieved.

201

XI.C.5 Joints to unstiffened flanges [6.6.8 (i)] (1) In a tee­joint of a plate welded to an unstiffened flange of an I, H or a box section, a reduced effective breadth shall be taken into account both for the parent material and for the welds(see table XL 16). [6.6.8 (2)] (2) For an I or H section the effective breadth beff should be obtained from: 't w + 2r + 7t f beff = minimum

(3) If beff is less than 0,7 times the full breadth, the joint should be stiffened. (4) For a box section the effective breadth beff should be obtained from: 2tw+5tf beff = minimum·'

[6.6.8 (5)]

ECCS n° 65 table 6.16

, but b eff < b

design strength of plate

Lyp

[6.6.8 (4)]

r.2v f Λ

f v*Py v yp J design strength of member

where [6.6.8 (3)]

t w + 2r + 7

(¿\

(*

K%VJ

y yp J

2t w + 5

\

, but b eff < b

f

(5) The welds connecting the plate to the flange shall have a design resistance per unit length not less than the design resistance per unit width of the flange. Effective breadth of an unstiffened tee joint

Table XI.16

*W|

t l

Τ

W|

' i , \s

4

_

ΊΆ s\ -

'eff

s

s

!

^ V

! I

S ^ J^

ι 1 t ι ;Ι θ , 5 .

•PI

Xl.d [6.5.13]

XLe

Xl.f [6.11] [Annex L]

Pin connections Reference may be made to Eurocode 3 Part 1.1 (121) Beam-to-column connections Reference may be made to Eurocode 3 Part 1.1 (/2/)

[6.9] [Annex J]

Design of column bases Reference may be made to Eurocode 3 Part 1.1 (121)

202

10,5 . [tø ·

b eff

ΧΠ

DESIGN OF BRACING SYSTEM

XILa

Generalities

(1) The definition of bracing system and its braced frame is given in chapter Lb. 1 and in table 1.1. (2) Examples of bracing system and its braced frame are given in table XII.5. XILa. 1 Flow-chart FC 12: Elastic global analysis of bracing system according to EC 3 (1) The flow-chart FC 12 aims to provide a general presentation of elastic global analysis of steel bracing system according to Eurocode 3. (2) The flow-chart FC 12 is nearly similar to the flow-chart FC 1 of chapter I about elastic global analysis of steel frames according to Eurocode 3 because only two items are different: - the bracing system should be designed to resist supplementary loads and supplementary effects of global imperfections issued from the frame which it braces (see the part in comments on FC 12 and FC 1 concerning the "Generalities about Eurocode 3") and, - the classification of sway or non-sway bracing system should be established with the same criteria but with specific conditions (see comments on rows 5 and 6 in the part "Choice of the type of global analysis for ULS" of FC 12). (3) The flow-chart FC 12 is divided in 3 parts: Xn.a.1.1 general part (1 page) Xn.a.1.2 details (1 page) XILa. 1.3 comments (6 pages)

XII.a.1.1

Flow-chart FC 12: general see the following page

XII.a.1.2

Flow-chart FC 12: details see the second following page

203

Flow-chart fFC 12): Elastic global analysis of bracing system according to Eurocode 3 (General)

Actions Predesign SLS checks Choice of the type of global analysis for ULS

ULS global analysis of the bracing system to determine the internal forces and moments (N, V, M)

ULS checks of members

submitted to internal forces and moments (N, V, M)

17

ULS checks of local effects ULS checks of connections 204

Flow­chart [FC 12: Elastic global analysis oí bracing SXStem according to Eurocode 3 (Details) Determination of load arrangements (ECl and EC 8) J

1

Load cases for SLS [2.3.4.]

Load cases for ULS [2.3.3.]

Predesign of members: beams & columns => Sections with pinned ^nd/or rigid connections Τ

notfulfilled

1

ULS checks

notfulfilled

SLS checks

[Chap. 5]

[Chap. 4]

i

J.

ι

,J

k

Global imperfections and global imperfections of the bracing system of the braced frame [5.2.4.4.] [5.2.4.3]

i

S.

Non-sway bracing system yes/Non­sway bracing system [52.5.2.]\no Vsd <0,1

Sway bracing system

1

^Vx>0,5[A.fy/NSd]°­5V^í \ [5.2.4.2. (4)] yes/ 0,1 < ^ ^ 0 , 2 5 ν»£$ Ver [5.2.6.2. (4)] FIRST

O

lORDER ANALYSIS

ι SECOND ORDER ANALYSISi

t

Non­sway mode buckling Sway mode buckling length approach length approach [5.2.6.2(1) a)][5.2.6.2. (7)] : [5.2.6.2(1) b)][5.2.6.2. (8)] : with sway moments with sway moments amplified by factor amplified by factor 1,2 in l/(l­VSd/Vcr) beams & connections [5.2.6.2. (3)]

Çr

Non­sway mode iLb l

±

=W

Mjembers imperfections ι eo,d [5.2.4.5.] [5.2.6.2.(2)]

■0

eo.d where necessary [5.2.4.5.(3)]

'0

™ /members with eo.d

eo.d in all members [5.2.4.5.(2)] yes

Ψ

\ ( Sway mode Lb Non­sway mode Lb _ /

«c,

τ

ï ±

Classification of cross­tsections [Chap. 5ι3]

±

Checks of the in­plane stability: members buckling [Chap. 55.]

notfulfilled (n.f.h

i Checks of the out­of­plane stability: members and/or frame buckling [Chap. 5.5.] Checks of resistance of cross­sections [Chap. 5.4.]

15

η yif.

Checks of local effects (buckling and resistance of webs) [Chap. 5.6 and 5.7] Checks of connections [Chap. 6 and Annex J]

205

Pfl»

_J

XII.a.1.3

Comments on Flow-chart FC 12:

comments (1/6) on flow-chart FC 12:

[5.2.5.3 (7)]

[5.2.1.2(1)]

[5.2.1.2(2)]

[5.2.5.3 (6)]

* Generalities about Eurocode 3: - Definition of a bracing system and its braced frame: see chapter I.b.l (table LI) and chapter XILa. - Where bracing system is a frame or sub-frame, it may itself be either sway or non-sway. - All checks of (ULS) Ultimate Limit States and all checks of (SLS1 Serviceability Limit States are necessary to be fulfilled. - According to the classification of cross-sections at ULS (row 14; chapter V of the design handbook) Eurocode 3 allows to perform: . plastic global analysis of a structure only composed of class 1 cross-sections when required rotations are not calculated [5.3.3 (4)] or, . elastic global analysis of a structure composed of class 1. 2. 3 or 4 cross-sections assuming for ULS checks, either a plastic resistance of cross-sections (class 1 and 2) or, an elastic resistance of the cross-sections, without local buckling (class 3) or, with local buckling (class 4 with effective cross-section). - In order to determine the internal forces and moments (N. V. M) in a bracing system Eurocode 3 allows the use of different types of elastic global analysis either: a) first order analysis using the initial geometry of the structure or, b) second order analysis taking into account the influence of the deformation of the structure - First order analysis (row 9) may be used for the elastic global analysis in the following casei (types of bracing systems): The/irsi order elastic global analysis of the bracing system should take into account the the effects the the global member actions horizontal of global vertical and imperfections imperfections loads imperfections horizontal of the bracing of the bracing from the from the loads of the system system braced frame braced frame jracing system types of (a) (b) (a) bracing system (row 5) (row 10) 1) non-sway bracing systems

(path®) 2) sway bracing systems (c) (paths (2) and (3)) [5.2.5.3 (5)] [5.2.5.3 (6)]

X

Notes : (a) actions issued from the frames which are braced by the analysed bracing system. (b) the horizontal and vertical loads which are directly applied to the bracing system. (c) use of design methods which make indirect allowance for second-order effects.

206

comments (2/6) on flow-chart FC 12: [5.2.1.2(3)]

[5.2.5.3 (6)]

Second order analysis may (row 9) be used in all cases (types of bracing systems): The second order elastic global analysis of the bracing system should take into account the global the the effects the member actions horizontal of global vertical and imperfections imperfections loads imperfections horizontal of the bracing of the bracing system from the from the loads of the system types of braced frame braced frame bracing system (a) (b) (row 5) (row 10) bracing systems (a) 1 ) for sway bracing systems X X (path @ ) X(c) X

(D) 2) for(path bracing systems in general ( path©) W) [5.2.5.3 (5)] Notes : (a) actions issued from the frames which are braced by the analysed bracing system. [5.2.5.3 (6)] [5.2.4.5 (3)]

(b) the horizontal and vertical loads which are directly applied to the bracing system. (c) members imperfections are introduced where necessary. (d) the more complex possibility of second order global analysis of the frame (path©) could be conservative because it allows the bypass of the "sway or non-sway frame" classification and consequently : - either the first order analysis might be sufficient, - or, the introduction of member imperfections would not be necessary in all members. On the other hand, particular care shall be brought to the introduction of member imperfections ( eo,d) which would be imposed for the global analysis in the realistic directions corresponding to the deformations of the members for the failure mode of the frame; that failure mode of the frame is related to the combination of applied external loads; otherwise, with more favourable direction of member imperfections, the second order global analysis might overestimate the bearing capacity of the frame. in the flow-chart FC 12 from path (Î) to path (6) (from left to right) the proposed methods for global analysis become more and more sophisticated.

207

comments (3/6) on flow-chart FC 12: * row 1: ECl: Draft EC 3: ENV 1993-1-1

Eurocode 1 Eurocode 3

EC 8: Draft

Eurocode 8

Basis of design and actions on structures Design of steel structures, Part 1.1: general rules and rules for buildings. Design of structures for earthquake resistance

* rows 2.4: [Chap. 5]

- ULS

means Ultimate Limit States

[Chap. 4]

- SLS

means Serviceability Limit States

* row 3: This flow-chart concerns structures using pinned and/or rigid joints. 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. [4.2.1 (5)]

* row 4: For SLS checks, the deflections should be calculated making due allowance for any second order effects, the rotational stiffness of any semi-rigid joints and the possible occurrence of any plastic deformations. * row 5:

[5.2.4.4]

Global imperfections of the bracing system Bracing system imperfections

initial bow imperfection

equivalent stabilizing force

11

' Τ τ Τ Τ Τ Τ Τ Τ Τ Τ Τ ' '

T

T

T

T

,

'

T

T

T

T

T

k

k

i

k

k

1

1

'

''

1

f

'

ι

XX XX 1

208

^ < r 5q

comments (4/6) on flow-chart FC 12: - Global imperfections of all the frames which are braced by the bracing system: initial sway imperfections of the frame equivalent horizontal forces

[5.24.3]

F2 i 4 t

/ / *

i f could be applied in the form of

Fi

4 *

I

Λ L·

φ (Fi + F2)

φ (Fi + F2)

classification of swav or non­swav bracing system: * row 6: A bracing system may be classified as non-sway if according to first order elastic global analysis of the bracing system for each ULS load case, one of the following

[5.23.2]

criteria is satisfied; either, a) in general : [5.2.5.2 (3)]

Vsd__ ι V, af

< 0,1

aCT > 10

, condition which is equivalent to

design value of the total vertical load elastic critical value of the total vertical load for failure in a sway mode »cr* ( = π2ΕΙ / L2 with L, buckling length for a column in a sway mode; V cr of a column does not correspond necessarily to VCT of the frame including that column). α cr coefficient of critical amplification or coefficient of remoteness of critical state of the frame. The total vertical load includes the vertical loads applied directly to the bracing system and the ones acting on all the frames which it braces.

where Vsd¡

[5.2.5.3 (8)]

or,

bi in case of bracing systems with beams connecting each columns at each storey level:

[5.23.2(4)]

δ.5> ,5.(V1+V2) h­ΣΗ

209

]( ι . ^ + H2)

_ v

>*

comments (5/6) on flow-chart FC 12:

[5.2.5.3 (9)]

where H, V: total horizontal and vertical reactions at the bottom of the storey. δ: relative horizontal displacement of top and bottom of the storey. h: height of the storey. H, V, δ are deduced from a first order analysis of the bracing system submitted to: ­ the horizontal and vertical loads: . applied directly to the bracing system and, . acting on all the frames which it braces, ­ and, the global imperfections applied in the form of the equivalent horizontal forces: . from the bracing system (see comments on row 5) and, . from all the frames which it braces (see below in the comments on row 6). Notes: ­ A same frame could be classified as sway according to a load case (Vsdl for instance) and as non­sway according to another load case (Vsd2 for instance). For multi­storeys buildings the relevant condition is —— = maximum condition which is equivalent to where

Vsdi

aCT = minimum (oten),

^ L or acrj are related to the storey i. cri

5.2.4.2 (4)

* row 7:

λ>0,5

where λ :

Af,

­|0,5

ΝSd

»condition which is equivalent to

N

N Sd > π or equivalent to ε> — 2

;

Νcr·

non­dimensional slenderness ratio calculated with a buckling length equal to the system length yield strength area of the cross­section design value of the compressive force elastic critical axial force ( = π2ΕΙ/ L2, with L = system length)

ε:

factor ( = L , '—Sá., with L = system length)

Nsd

5.2.6.2 (4)

Members imperfections may be neglected except in sway frames in the cases of members which are subject to axial compression and which have moment resisting connections, if :

* row 8: According to the definition of aCT introduced in comment on row 6: Vsd 0,1<—aa.< 0,25

»condition which is equivalent to

4 < aa < 10

* row 9: 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 flow­chart FC 12) in function of the type of bracing system.

210

commente (6/6) on flow-chart FC 12: ♦ rows 10.11.12 : - p a t h © : Sway moments amplified by factor 1,2 in beams and beam­to­column connections and not in the columns. The definition of "sway moments" is provided in [5.2.6.2 (5)]. [5.2A5]

­ paths © and © : the introduction oí member imperfections eo,d should be considered equivalent to the introduction of distributed loads along the members :

e 04

NSd

Nsd

Nsd

ι

τ

τ

?

?

τ

?

J'

Nsd

Ρ"

equivalent to

L ».

M

q = 8.N S d .e 0 , d /L' ÌQ = 4.N S d .e 0 ) d /L

with

Note : the equivalence of en,d and (q, Q) loading is proposed here for a practical point of view but it is not included in Eurocode 3. Verf

* row 11: [Annex E]

For the meaning of the ratio ——, refer to comment on row 6. "cr

* row 13: L ¡,, buckling length of members for sway or non­sway mode NSd

*""

"**

NSd

Lb

* row 14:

* rows

The classification of cross-sections have to be determined before all the ULS checks of members, cross­sections and webs (rows 15 to 18). 15.16.17.18.19:

The sequence of the Ultimate L imit 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 8. [5.5.13(6)]

* row 17: When the member imperfections en,d are used in a second order analysis (paths © or © ) , the resistance of the cross-sections shall be verified as specified in chapter [5.4] but using the partial safety factor ymi in place of γ™

211

ΧII.b Static equilibrium (1) Reference may be made to chapter IV.b. XII.c Load arrangements and load cases Xn.c.l Generalities (1) Load arrangements which may be applied to buildings are provided in chapter ÏÏLb. (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 flow­chart FC 3.1 (chapter ΠΙ) or, a particular procedure presented in flow­chart FC 3.2 (chapter ΙΠ) which is applicable for non­sway 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 ΙΠ.7 for SLS combinations of actions see table ΙΠ.8 for ULS combinations of actions (4) A bracing system should be designed to resist different loads and effects of global imperfections from the braced frame and of the bracing system itself (see comments on flow­chart FC 12 concerning the "generalities about Eurocode 3" (see chapter XILa. 1.3) and see table ΧΠ.1). Load arrangements of the bracing system Table XII.l a~) The horizontal loads from the braced frame:

I I I I II

TT Ρ

c?

θ ^ 7 &

■A

■— ^

s?

b) The effects of global imperfections from the braced frame:

TT

p
A

&7

c) The vertical and horizontal loads of the bracing system:

&,

&,

d) The global imperfections of the bracing system: see chapter XII.c.2

212

XII.C.2 Global imperfections of the bracing system [5.24.3 (ï)] (1) The effects of imperfections shall be allowed for in bracing system design which are required to provide lateral stability within the length of beams or compression members, by means of an equivalent geometric imperfection of the members to be restrained, in the form of an initial bow imperfection, or of the equivalent stabilizing forces according to table ΧΠ.2. (2) The numerical values for the stabilizing force Σ q are given in table ΧΠ.3 according to the following model: k.L e 0 =­ 1 — 500

where

kr=J0,2+

where nr

k

^=J£r< '->

where a =

(but k r £ l ) ,

is the number of members to be restrained 500 δΓ

(3) Practical examples of such global imperfections are given in table ΧΠ.4 which presents the case where the bracing system is required to stabilize a beam.

213

ECCS n°65 table 5.7

Bracing system imperfections

Table ΧΠ.2

initial bow imperfection

X

s

Nl.Sd

.

0 Ni.Sd

/

N2.Sd

N2.Sd

N3.Sd

N3.Sd

/

ECCS n° 65 table 5.8

equivalent stabilizing forces

ie°

μΠΓ

i.

i

4

i

i

i

'r

<1

'

<

I

'

XXXXX »t-δς

>r

Table ΧΠ.3 \

^1

Values for the equivalent stabilizing force Σ q nr=l

nr = 2

nr=3

nr=4

nr=5 Γ ι ι

*

] ι ι

χκζχ EEEE KKKK KZEÉ χζζζ \

XXXCX

ζ ΣΝ8(1 75,1 L ζ ΣΝ 8ά 70,8 L ζ ΣΝ 8ά 64,7 L ζ ΣΝ 8ά 55,2 L

ζ ΣΝ8(1 96,6 L ζ ΣΝ 8ά 89,6 L ζ ΣΝ 8ά 80 L ζ ΣΝ 5α 66 L

J

5q

η Γ = οο


ζ ΣΝ 5α ζ ΣΝ5α 67,2 L 71,8 L ζ ΣΝ 8α ζ ΣΝ8ά 63,8 L 67,9 L ζ ΣΝ 8α ζ ΣΝ5ά 62,2 L 58,8 L ζ ΣΝ 8α ζ ΣΝ5α 53,4 L 50,8 L

ζ N Sd 52,1 L ζ N Sd 50 L ζ N Sd 46,9 L ζ N Sd 41,7 L

ζ ΣΝ 5α 60,3 L ζ ΣΝ 5ά 57,5 L ζ ΣΝ 8ά 53,4 L ζ ΣΝ 8α 46,8 L

2

3

4

m

pw

f*f*m

5

6

7

Wffl PWffl p?
25/24 49/48 9/8 1,0 ι,ο ι,ο ζ δς is the in-plane deflection of the bracing system due to Σq plus any external loads.

214

Bracing system imperfections (examples)

Table XII.4

©

N

\

2Sd

N

\r

N

2Sd \

N

2Sd

2Sd

Φ 1

1

­ * * * ­ .

\

P

1

r

lSd

|P2Sd

,P2Sd

1

Ι

, r P 2Sd

V Iq+w v

XXXX

- S\V—

Ä

ÀV Ν

2Sd

y

(D

A Β

f Η ΜΗ tΗ Η Ι Η tΠ Η Η

215

lSd

Xll.d Bracing system stability (1) Reference may be made to chapter IV.d. XILe First order elastic global analysis (1) Reference may be made to chapter IV .e. ΧΙΙ.Γ

Verifications at SLS

(1) Reference may be made to chapters IV.f.l and VIII. b. XH.g

Verifications at ULS

ΧΠ.g. 1 Classification of the bracing system Xll.g.1.1 Non-sway bracing system [5.2.5.3 (7)] (1) Where bracing system is a frame or sub-frame, it may itself be either sway or non-sway. (2) Examples of sway frames are mentionned in chater I.b.2. (3) In order to define the criterion used to classify a bracing system as sway or non-sway reference may be made to comments on rows 5 and 6 of flow-chart FC 12 (see chapter XILa. 1.3). (4) As the criterion of sway or non-sway bracing system classification depends on the total vertical load, a same bracing system could be classified as sway according to a load case and as non-sway according to another load case. Therefore the criterion of sway or nonsway bracing system classification should be checked for each load case. [5.1.2 (1)]

Xn.g.2 ULS checks (1) The frames shall be checked at ultimate limit states for the resistances of cross-sections, members and connections. For those ULS checks reference may be made to the following chapters: - Classification of cross-sections: see chapter V - Members in tension: see chapter VI - Members in compression: see chapter VH - Members in bending: see chapter VEI - Members with combined axial force and bending moments: see chapter IX - Transverse forces on webs: see chapter X - Connections: see chapter XI

216

APPENDIX A :

List of symbols (1/6)

1.

Latin symbols

a a ad at aup an ai, a2 A

designation of a buckling curve throat thickness of füllet weld geometrical data of the effects of actions geometrical data for the resistance design throat thickness for submerged arc welding designation of a buckling curve distance between fastener holes and edge accidental action; area of building loaded by external pressure of wind; area of gross cross-section effective area of class 4 cross-section effective area of class 4 cross-section subject to uniform compression (single Nx.sd) effective area of class 4 cross-section subject to uniaxial bending (single My.sd or single Mz.sd) net area of cross-section reference area for Cf (wind force) tensile stress area of bolt shear area of cross-section effective shear area for resistance to block shear shear area of cross-section according to yy axis shear area of cross-section according to zz axis designation of a buckling curve; flange width; building width effective breadth design punching shear resistance of the bolt head and the nut designation of a buckling curve; outstand distance altitude factor for reference wind velocity dynamic factor for wind force direction factor for reference wind velocity exposure coefficient for wind pressure and wind force

Aeff Aeff.N Aeff.M Anet Aref A8 Av Ay.net Av.y Av.z b beff BpJld c c ALT cd com ce Cf Cpe cr ct CJEM

Cd Ci, C2 Ci, C 2, C3 d d dm do eN eNy eNz eM eo eo,d ei, β2 E

wind force coefficient external pressure coefficient for wind pressure roughness coefficient for determination of c e topography coefficient for determination of c e temporary (seasonal) factor for reference wind velocity nominal value related to the design effect of actions factors for determination of FyR^ factors for determination of MCT designation of a buckling curve; web depth bolt diameter mean diameter of inscribed and circumscribed circles of bolt head or nut hole diameter shift of relevant centroidal axis of the class 4 effective cross-section subject to uniform compression (single N x .sd) shift of the y centroidal axis of the class 4 effective cross-section subject to uniform compression shift of the ζ centroidal axis of the class 4 effective cross-section subject to uniform compression shift of relevant centroidal axis of the class 4 effective cross-section subject to uniaxial bending (single My.sd or single Mz.sd) equivalent initial bow imperfection design value of equivalent initial bow imperfection distance between hole fastener and edge modulus of elasticity or Young Modulus; effect of actions at SLS

217

List of symbols (2/6) ECCS ECSC EC 1 EC 3 EC 8 Ed Ek fd fe fmin fu fub f, fyb fyb

European Convention for Constructional Steelwork European Community of Steel and Coal Eurocode 1 (/11) Eurocode 3 (/2/) Eurocode 8 (¡3f) design value of the effect of action characteristic value of effects of actions at SLS design natural frequency natural frequency recommended limit of natural frequency ultimate tensile strength nominal value of ultimate tensile strength for bolt yield strength basic yield strength of the flat steel material before cold forming nominal value of yield strength for bolt

F, Fi, F2 FC Fb.Rd Fb.Rk Fd Ffr Fh.sd Fk FpjRd F8d F8k Fs.Rd Fs.Rd.ser Fs.Rk Ft.Rd FtRk FLsd Fv.Rd Fv.Rk Fv.8d Fv.sd.ser Fw Fw.Rk Fw.sd g G Gd Gk h ho H i

action (load, transverse force, imposed deformations,...) flow-chart design bearing resistance per bolt characteristic value of bearing resistance per bolt design value of action friction force force on bolt calculted from Msd and/or Fbjw characteristic value of action design punching shear resistance per bolt design transverse force applied on web through the flange characteristic value of transverse force design slip resistance per bolt at the ultimate limit state design slip resistance per bolt at the serviceability limit state caracteristic slip-resistance per bolt and per friction interface design tension resistance per bolt characteristic value of tension resistance per bolt design tensile force per bolt for the ultimate limit state design shear resistance per bolt characteristic value of shear resistance per bolt and per shear plane design shear force per bolt for the ultimate limit state design shear force per bolt for the serviceability limit state resultant wind force characteristic value of resistance force of fillet weld design force of fillet weld distributed permanent action; dead load permanent action design permanent action characteristic value of permanent action overall depth of cross-section; storey height; building height overall height of structure total horizontal load radius of gyration about relevant axis using the properties of gross cross-section second moment of area A second moment of effective area Aeff (class 4 cross-section) torsional constant warping constant second moment of area about zz axis subscript meaning characteristic (unfactored) value effective length factor factor for lateral-torsional buckling with N-M interaction buckling factor for outstand flanges

fyW

eff

k k kLT k
yield strength of the web

218

List of symbols (3/6) kw Ky» Kz Kr

ί

¿LT

L Lb LTB Lv m max min M Mb.Rd MCT M c .Rd

Me Mef

Mf.Rd MN.Rd MN.V.Rd MN.V.y.Rd MN.V.z.Rd MN.y.Rd MN.z.Rd

Mpr Mp£Rd MpiwJld Mp/:y.Rd Mp£ z Jtd MRd Msd My.Rd Mw.sd My My.Sd Mz M z .sd

n nc nr ns N NAD

Nb.Rd Nb.y.Rd Nb.z.Rd N compression Ncr NcRd

effective length factor for warping end condition factors for N-M interaction roughness factor of the terrain portion of a member effective length for out-of-plane bending system length; span length; weld length buckling length of member lateral-torsional buckling distance between extreme fastener holes mass per unit length maximum minimum bending moment design resistance moment for lateral-torsional buckling elastic critical moment for lateral-torsional buckling design resistance moment of the cross-section torsional moment elastic moment capacity design plastic resistance moment of the cross-section consisting of the flanges only reduced design plastic resistance moment allowing for axial force N reduced design plastic resistance moment allowing for axial force N and by shear force V reduced design plastic resistance moment about yy axis allowing for axial force N and shear force V reduced design plastic resistance moment about zz axis allowing for axial force N and shear force V reduced design plastic resistance moment about yy axis allowing for axial force N reduced design plastic resistance moment about zz axis axial force N plastic moment capacity design plastic resistance moment of the cross-section design plastic resistance moment of the web design plastic resistance moment of the cross-section about yy axis design plastic resistance moment of the cross-section about zz axis design bending moment resistance of the member design bending moment applied to the member design plastic resistance moment reduced by shear force design value of moment applied to the web bending moment about yy axis design bending moment about yy axis applied to the member bending moment about zz axis design bending moment about zz axis applied to the member number of fastener holes on the block shear failure path number of columns in plane number of members to be restrained by the bracing system number of storeys normal force; axial load National Application Document design buckling resistance of the member design buckling resistance of the member according to yy axis design buckling resistance of the member according to zz axis normal force in compression elastic critical axial force design compression resistance of the cross-section

219

List of symbols (4/6) N j . sd Np£Rd

NRd N8d Nt.Rd Ntension N u .Rd N x .Sd Pl»P2 Ρ

q qk qref

Q Qd Qk v¿k.max Γ R Ra,Rd Rb,Rd Rd Rk Ry,Rd S S

Sd Sk Ss

S

sd

Sk SLS tf

h tw U

ULS v Vref Vref.O

V Vba.Rd Vcr V//Sd

v±8d V

p£Rd V p £yJld Vp£zJid

v Rd Vsd Vy Vy.Sd Vz

design value of tensile force applied perpendicular to the fillet weld design plastic resistance of the gross cross­section design resistance for tension or compression member design value of tensile force or compressive force design tension resistance of the cross­section normal force in tension design ultimate resistance of the net cross­section at holes for fasteners design internal axial force applied to member according to xx axis distances between bolt holes Point load imposed variable distributed load characteristic value of imposed variable distributed load reference mean wind pressure imposed variable point load design variable action characteristic value of imposed variable point load variable action which causes the largest effect radius of root fillet rolled sections design crippling resistance of the web design buckling resistance of the web design resistance of the member subject to internal forces or moment characteristic value of Rd design crushing resistance of the web snow load thickness of fillet weld design snow load characteristic value of the snow load on the ground length of stiff bearing effects of actions at ULS design value of an internal force or moment applied to the member characteristic value of effects of actions at ULS Serviceability Limit states design thickness, nominal thickness of element, material thickness flange thickness thickness of the plate under the bolt head or the nut thickness of a plate welded to an unstiffened flange web thickness major axis Ultimate Limit States minor axis reference wind velocity basic value of the reference wind velocity shear force; total vertical load design shear buckling resistance elastic critical value of the total vertical load design value of shear force applied parallel to the fillet weld design value of shear force applied perpendicular to the fillet weld design shear plastic resistance of cross­section design shear plastic resistance of cross­section according to yy axis (// to web) design shear plastic resistance of cross­section according to zz axis (_L to flange) design shear resistance of the member design shear force applied to the member; design value of the total vertical load shear forces applied parallel to yy axis design shear force applied to the member parallel to yy axis shear force parallel to zz axis

220

List of symbols (5/6) Vz.sd w Wd we W Weff Weff.y Weff.ζ Wcf We£y We£z Wpf Wp£y Wp£ 2 x, xx Xk y, yy z, zz Ze

design internal shear forces applied to the member parallel to zz axis wind pressure on a surface design wind load wind pressure on external surface welded sections elastic section modulus of effective class 4 cross­section elastic section modulus of effective class 4 cross­section according to yy axis elastic section modulus of effective class 4 cross­section according to zz axis elastic section modulus of class 3 cross­section elastic section modulus of class 3 cross­section according to yy axis elastic section modulus of class 3 cross­section according to zz axis plastic section modulus of class 1 or 2 cross­section plastic section modulus of class 1 or 2 cross­section according to yy axis plastic section modulus of class 1 or 2 cross­section according to zz axis axis along the member characteristic value of the material properties principal axis of cross section (parallel to flanges, in general) principal axis of cross section (parallel to the web, in general) reference height for evaluation of c e

2.

Greek symbols

α α α ctcr

coefficient of frequency of the basis mode vibration coefficient of linear thermal expansion factor to determine the position of the neutral axis coefficient of critical amplification or coefficient of remoteness of critical state of the frame non­dimensional coefficient for buckling equivalent uniform moment factor for flexural buckling equivalent uniform moment factor for lateral­torsional buckling equivalent uniform moment factor for flexural buckling about yy axis equivalent uniform moment factor for flexural buckling about zz axis non­dimensional coefficient for lateral­torsional buckling correlation factor (for a fillet weld) partial safety factor for force or for action partial safety factor for permanent action partial safety factor for the resistance at ULS partial safety factor for the resistance of bolted connections partial safety factor for the slip resistance of preloaded bolts partial safety factor for the resistance of welded connections partial safety factor for resistance at ULS of class 1,2 or 3 cross­sections (plasticity or yielding) partial safety factor for resistance of class 4 cross­sections (local buckling resistance) partial safety factor for the resistance of member to buckling partial safety factor for the resistance of net section at bolt holes partial safety factor for variable action relative horizontal displacement of top and bottom of a storey horizontal displacement of the braced frame design deflection design vertical deflection of floors, beams,... design horizontal deflection of frames recommended limit of horizontal deflection in plane deflection of the bracing system due to q plus any external loads

βA ßM PM.LT

ß\iy ßvi z ßw ßw YF YG YM YMb YMs.ser YMW YMO YMI YMI YM2 YQ δ 5b 5d 5dv fød OHmax δη

221

List of symbols (6/6) δς ôu ôvd Svmax δο δι δ2 Δ ε θ λ λχ λ Xeff.v Xeff.y Xefí.z λυτ

deflection due to variable load (q) horizontal displacement of the unbraced frame design vertical deflection of floors, beams,... recommended limit of vertical deflection pre­camber (hogging) of the beam in the unloaded state (state 0) svariation of the deflection of the beam due to permanent loads (G) immediatly after loading (state 1) variation of the deflection of the beam due to the variable loading (Q) (state 2) displacement 1235 coefficient = I (with fy in N/mm 2 ) V fy rotation slenderness of the member for the relevant buckling mode Euler slenderness for buckling non­dimensional slenderness ratio of the member for buckling effective non­dimensional slenderness of the member for buckling about vv axis effective non­dimensional slenderness of the member for buckling about yy axis effective non­dimensional slenderness of the member for buckling about zz axis non­dimensional slenderness ratio of the member for lateral­torsional buckling

Ρ

plate slenderness ratio for class 4 effective cross­sections λν non­dimensional slenderness of the member for buckling about w axis Xy non dimensional slenderness ratio of the member for buckling about yy axis λζ non dimensional slenderness ratio of the member for buckling about zz axis μ factor for F s R^ depending on surface class μί snow load shape coefficient μΐ_τ factor for N-M interaction with lateral-torsional buckling \x.y factor for N-M interaction μζ factor for N-M interaction ρ density ρ reduction factor due to shear force V 8 d py reduction factor due to shear force Vy.sd ρζ reduction factor due to shear force Vz.sd σ normal stress Oq numerical values for the stabilizing forces of a bracing system Gx.Ed> tfxm.Ed> design values of normal stresses for web check with Von Mises criteria <*z.Ed

τ υ φ χ XLT Xmin Xy Xz

shear stresss Poisson's ratio initial sway imperfection of the frame reduction factor for the relevant buckling mode reduction factor for lateral-torsional buckling minimum of xy and χ ζ reduction factor for the relevant buckling mode about yy axis reduction factor for the relevant buckling mode about zz axis

222

APPENDIX Β: 0.c Table 0.1 I Table 1.1 Table 1.2 Table 1.3 Table 1.4 Table 1.5 Table 1.6 Table 1.7 Table 1.8 Π Table Π.1 Table Π.2 Table Π. 3 Table Π.4 Table Π.5 Table Π.6 Table Π.7 Table Π.8 ΙΠ Table ΠΙ. 1 Table ΠΙ.2 Table ΠΙ. 3 Table ΠΙ.4 Table ΠΙ.5 Table ΠΙ.6 Table ΙΠ.7 Table ΙΠ.8 Table ΠΙ.9 IV Table IV. 1 Table IV.2 Table IV. 3 Table IV.4 Table IV.5 Table IV.6 V Table V. 1 Table V.2 Table V.3 Table V.4 Table V.5 Table V.6

List of tables (1/3)

SYMBOLS AND NOTATIONS Dimensions and axes of rolled steel sections INTRODUCTION Summary of design requirements Partial safety factor YM for the resistance Definition of framing for horizontal loads Checks at Serviceability Limit States Member submitted to internal forces, moments and transverse forces Planes within internal forces, moments (N8d, V8d» M8d) and transverses forces F8d are acting Internal forces, moments and transverse forces to be checked at ULS for different types of loading List of references to chapters of the design handbook related to all check formulas at ULS STRUCTURAL CONCEPT OF THE BUILDING Typical types of joints Modelling of joints Comparison table of different steel grades designation Nominal values of yield strength fy and ultimate tensile strength fu for structural steels to EN 10025 and EN 10113 Maximum thickness for statically loaded structural elements Maximum thickness for statically loaded structural elements Nominal values of yield strength fyb and ultimate tensile strength fub for bolts Material coefficient LOAD ARRANGEMENTS AND LOAD CASES Load arrangements (Fk) for building design according to ECl Imposed load (qk, Qk) on floors in buildings Pressures on surfaces Exposure coefficient ce as a function of height ζ above ground External pressure Cpe for buildings depending on the size of the effected area A Reference height ZQ depending on h and b Combinations of actions for serviceability limit states Combinations of actions for ultimate limit states Examples for the application of the combinations rules in Table ΙΠ.8. All actions (g, q, P, s, w) are considered to originate from different sources DESIGN OF BRACED OR NON-SWAY FRAME Modelling of frame for analysis Modelling of connections Global imperfections of the frame Values for the initial sway imperfections φ Specific actions for braced or non-sway frames Recommended limits for horizontal deflections CLASSIFICATION OF CROSS-SECTIONS Definition of the classification of cross-section Determinant dimensions of cross-sections for classification Classification of cross-section : limiting width-to thickness ratios for class 1 & class 2 I cross-sections submitted to different types of loading Classification of cross-section : limiting width-to thickness ratios for class 3 I cross-sections submitted to different types of loading Buckling factor k^ for outstand flanges Classification of cross-section : limiting width-to-thickness ratios for internal flange elements submitted to different types of loading

223

Page 6 11 12 23 24 25 26 27 28 30 31 32 33 34 35 35 36 40 41 42 43 43 44 45 46 46 48 47 57 58 59 60 65 72 73 74 75 76

Table V.7 Table V.8 Table V.9 Table V. 10 VI Table VI. 1 Table VI.2 Table VI.3 Table VI.4

vn Table VILI Table Vfl.2 Table Vfl.3 Table VII.4 Table VIL5 Table Vfl.6

vm Table vm.l Table VIII.2 Table νΠΙ.3 Table Vm.4 Table Vni.5 Table Vfll.6 Table VIII.7 Table Vfll.8 Table VIfl.9 Table VIA. 10 Table Vm. 11 Table VIH. 12 Table Vm. 13 Table Vm. 14 LX Table IX. 1 Table IX.2 Table IX.3 Table IX.4 Table IX.5 Table LX.6 Table ΓΧ.7 Table IX.8 Table IX.9

List of tables (2/3) Classification of cross­section : limiting width­to­thickness ratios for angles tubular sections submitted to different types of loading Effective cross­sectional data for symmetrical profiles (class 4 cross­sections) Limiting values of axial load Nsd for web classification of I cross­sections subject to axial load Nsd and to bending according to major axis My.sd Examples of shift of centroidal axis of effective cross­section MEMBERS IN TENSION (Ntension) List of checks to be performed at ULS for the member in tension (Ntension) Gross and net cross­sections Reduction factors ß2 and ß3 Connection of angles

Page 77

MEMBERS IN C OMPRESSION (Ncompression) List of checks to be performed at ULS for the member in compression (NComp.) Imperfection factor α Value of Euler slenderness λι Selection of buckling curve for a cross­section Buckling length of column : Lb Reduction factors χ = f (λ) MEMBERS IN BENDING (V ; M ;( V,M)) List of checks to be performed at ULS for the member in bending according to the applied internal forces and/or moments(V ; M ;( V,M)) Recommended limiting values for vertical deflections Vertical deflections to be considered Recommended limiting values for floor vibrations Shear area A v for cross­sections Determination of A vnet for block shear resistance Limiting width­to­thickness ratio related to the shear buckling in web Simple post­critical shear strength z\,a Buckling factor for shear kT Reduction factor %LT = f (XLT) for lateral­torsional buckling Effective length factors : k, kw Numerical values for Ci and definition of ψ Reduced design plastic resistance moment My.Rd allowing for shear force Interaction of shear buckling resistance and moment resistance with the simple post­critical method MEMBERS WITH COMBINED AXIAL FORCE AND BENDING MOMENT ((N, M) ;(N, V, M)) List of checks to be performed at ULS for the member submitted to combined axial force and bending moment (Ν, M) Principle of interaction formulas between axial force Nsd and bending moment Msd Reduced design plastic resistance moment MNJM allowing for axial load for Class 1 or 2 cross­sections Interaction formulas for the (N,M) stability check of members of Class 1 or 2 Interaction formulas for the (N,M) stability check of members of Class 3 General interaction formulas for the (N,M) stability check of members of Class 4 Supplementary interaction formulas for the (N,M) stability check of members of Class 4 Reduced design resistance Nyjid allowing for shear force Reduced design plastic resistance moment MN.v.Rd allowing for axial load and shear force for Class 1 or 2 cross­sections

224

78 79 80

84 85 86 87 91 94 94 95 96 97 103 107 107 108 110 111 111 112 112 116 116 117 119 120

124 130 131 135 136 137 138 139 141

List of tables (3/3) TRANSVERSE FORCES ON WEBS (F ; (F,N,V,M)) Table Χ. 1 Table X.2 Table X.3 Table X.4 Table X.5 Table X.6 Table X.7 Table X.8 Table X.9

Failure modes due to load introduction Stresses in web panel due to bending moment, axial force and transverse force Yield criteria to be satisfied by the web Load introduction Length of stiff bearing, s s Interaction formula of crippling resistance and moment resistance Effective breadth beff for web buckling resistance Compression flange buckling in plane of the web Maximum width-to-thickness ratio d/tw

XI

CONNECTIONS

Table XL 1 Table XI.2 Table XI.3

Table XL 12 Table XL 13 Table XL 14 Table XL 15 Table XL 16

Designation of distances between bolts Linear distribution of loads between fasteners Possible plastic distribution of loads between fasteners. Any realistic combination could be used, e.g. Prying forces Categories of bolted connections Bearing resistance per bolt for recommended detailing for t = 10 mm in [kN] Shear resistance per bolt and shear plane in [kN] Long joints Tension resistance per bolt in [kN] Interaction formula of shear resistance and tension resistance of bolts Characteristic slip resistance per bolt and friction interface for 8.8 and 10.9 bolts, where the holes in all the plies have standard nominal clearances Common types of welded joints Throat thickness Action effects in fillet welds Resistance of a fillet weld Effective breadth of an unstiffened tee joint

ΧΠ

DESIGN OF BRACING SYSTEM

Table XII. 1 Table XII.2 Table XII. 3 Table XII.4

Load arrangements of the bracing system Bracing system imperfections Values for the equivalent stabilizing force Zq Bracing system imperfections (examples)

Table XI.4 Table XI.5 Table XI.6 Table XI.7 Table XI.8 Table XI.9 Table XL 10 Table XL 11

Page 147 148 149 150 150 151 152 153 153 156 156 157 157 158 159 160 160 161 161 162 163 164 164 165 166 176 178 178 179

APPENDIX D Table D.l

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

225

191

APPENDIX C :

θ

List of flow-charts Chapter Pages

Elastic global analysis of steel frames according to Eurocode 3 General Details Comments (6 pages)

I I

14 15 16 to 21

(FC3A\

Load arrangements & load cases for general global analysis of the structure

HI

38

(FC3.2)

Load arrangements & load cases for first order elastic global analysis of

m

39

IV IV IV

50 51 52 to 55

©

the structure Elastic global analysis of braced or non­sway steel frames according to EC 3 General Details Comments (4 pages)

(FC5.Ï) Classification of I cross­section

62

nFC5.2) Calculation of effective cross­section properties of Class 4 cross­section

ry

63

(FC6.I)

Members in tension (Ntension)

VI

82

(FC62\

Angles connected by one leg and submitted to tension

VI

83

(jFC lj Members in compression (Ncompression)

VU

90

(FC 8) Design of I members in uniaxial bending (Vz;My;(Vz,My)) or (Vy;Mz;(Vy,Mz))

VIII

102

XII XII XII

168 169 170 to 175

ÍFC 12jElastic global analysis of bracing system according to Eurocode 3 General Details Comments (6 pages)

226

H Table D.l

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

at ULS

Typ ; References to Eurocode 3 Part 1.1 for ULS checks Internal forces moments, and Physical phenomena in function of classes of cross­sections ([5.3]) : of class 3 class 4 transverse forces check s classes 1 or 2 | tension resistance (gross & net section) R Γ5.4.3 (1)1 + [5.4.2.2] + [6.5.2.3] + [6.6.10] L Ntension. [5.4.4 (1).(2)] Í5.4.4 (1),(2)1 compression resistance 2. Ncompression R S [5.5.1.1 (1).(3)] [5.5.1.1 (1),(3)1 Ν buckling of members shear and block shear resistances R [3. V [5.4.6 (1)1 + ,6.5.2.2] shear buckling Γ5.6.1 (1)1 + 15.6.3] S uniaxial bending resistance ■ι M Í5.4.5.1 (2)1 [5.4.5.1 (1)1 R 15.4.5.1 (1)1 lateral­torsional buckling (M y ) (LTB) [5.5.2(1)] [5.5.2 (1)] [5.5.2(1)] 1 _JS h . (M y ,M z ) [5.4.8.2(2)] [5.4.8.3 (2)] biaxial bending resistance R [5.4.8.1 (11),(12)]

1

¡6. (V,M) (V z ,M y ) 7. (V,M y ,M z ) (V z , My, M z ) 8. (N,M) (Ntension^y) (Ncomp.. My) (Ncomp.. Mz) 9. (N,My,M Z ) 10. (N, V) 11. (N, V,M) (N,V z ,My) 112. (RV.My.Mz)

f5.5.4 (3H(4)1 [5.5.4 (5)+(6)l S [5.5.4 (1)+(2)1 R [5.4.7(3)] S [5.6.7.2 (1),(2),(3)] [5.4.7 (3)] + formulas for (My. Mz) R formulas for (Vz, M y ) S R ,5.4.8.2(2)1 Γ5.4.8.Π [5.5.3 (2) to (5)] S [5.5.4 (3)+(4)] S [5.5.4 (l)+(2)] [5.5.4(1)] [5.5.4(3)] S

S R

S R Il3. F,(F,N),(F,My), (F,N,My)

lateral­torsional buckling (LTB) N­M buckling + LTB N­M buckling

biaxial bending & axial force resistance (N­biaxial M) buckling + LTB shear and axial load resistance shear buckling uniaxial bending & shear and axial force resistance [5.6.7.2 (1),(2),(3)] + formulas for (Ν,Μ) interaction (N­uniaxial M) resistance & shear buckling [5.4.9 (3)] + formulas for (N,My,Mz) interaction biaxial bending & shear and axial force resistance formulas for (N.V^My) interaction (N­uniaxial M) resistance & shear buckling [5.4.10(2)] [5.4.10(1)] transverse force (+N, +M y ) resistance [5.4.10(1)1

R S

[5.7.3 (1)1 [5.7.4(1)] +[5.7.5 (1),(2),(3)]

S

[5.7.4 (2)] + formulas for M [5.7.7 (1),(2)] [5.7.7 (1),(2)] [5.7.7 (1),(2)]

S 14. (F.VZ),(F,N,VZ), R (F,Vz,My), (F.N,Vz,My) S tvpe of loadine:

[5.5.4 (5)+(6)] [5.5.4 (5)]

uniaxial bending & shear buckling uniaxial bending & axial force resistance

R [5.4.8.1(11) ,(12)] [5.4.8.2 (2)] [5.4.8.3 (2)] Γ5.5.4 (3H(4)1 [5.5.4 (5)+(6)l S Í5.5.4 (1)+(2)1 [5.4.9 (3)] +1"ormulas for (N tension , Ncomp.) R [5.6.7.2] S [5.4.9 (3)] + formulas for (Ν,Μ) interaction R

(N,Vz,My,Mz)

F F (F.My)

Γ5.4.8.3 (2)1 [5.5.3(2)to (5)]

biaxial flexural buckling uniaxial bending & shear resistance uniaxial bending & shear buckling biaxial bending & shear resistance

[5.4.10(5)]

[5.4.10(4)]

[5.4.10(4)]

formulas for (N,V¿.MV) interaction 1. 2. 3. t o ' '. 8. t o l 12. 13. to 14.

= = = = =

crushing crippling + buckling crippling compression flange induced buckling transverse forces + shear V z (+N, +My) resistance (N­uniaxial M) resistance & shear buckling

tension members com pression members men ibers in bend i η men íbers with c o m jined N­M tran¡»verse forces or t webs

R = re sistance of cros s­sections ([5.4] ) 5 = Stiìbility of members ([5.5]) or w e bs ([5.6],[5.7])

227

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European Commission EUR 16839 — Properties and service performance Simplified version of Eurocode 3 for usual buildings P. Chantrain, J.-B. Schleich Luxembourg: Office for Official Publications of the European Communities 1997 — 227 pp. — 21.0 χ 29.7 cm Technical steel research series ISBN 92-828-1485-8 Price (excluding VAT) in Luxembourg: ECU 38

The aim of this ECSC 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 totally conforms 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 were 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 ECSC research projects No SA/312 and No SA/419 also dealing with Eurocode 3: respectively 'Application software of Eurocode 3: EC3-tools' (CTICM, France) and 'Design handbook for sway buildings' (CSM, Italy).

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