Eurocode 3 Simplified

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ISSN 1018-5593

European Commission

t e c h n i c a l s t e e l r e s e a r c h

Propert ies and service performance

Simplified version of Eurocode 3for usual buildings

STEEL RESEARCH


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European Commission

t e c h n i c a l s t e e l r e s e a r c hProperties and service performance

Simplified version of Eurocode 3for usual buildingsP. Chantrain, J.-B. Schleich

ARBED recherchesBP 141L-4009 Esch-sur-Alzette

Contract No 7210-SA/5131 July 1991 to 30 June 1994

Final report

Directorate-GeneralScience, Research and Development1997 EUR 1683 9 E N


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LEGAL NOTICENeither the European Commiss ion nor any person act ing on behal f of the Commiss ionis responsible for the use which might be made of the fo l lowing informat ion.

A great deal of add i t ional informat ion on the European Union is avai lable on the Internet . !I t can be a ccesse d through the E uropa server (ht tp: //europa.eu. int )Cataloguing data can be found at the end of th is publ icat ion.Luxembourg: Of f ice for Of f ic ia l Publ icat ions of the European Communit ies , 1997ISBN 92-828-1485-8 European Com mun i t ies , 1997 [Reproduct ion is author ised prov ided the source is acknowledged.Printed in Luxembo urg


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SIMPLIFIED VER SION OF EIIROCODE 3 FOR USUAL BUILDINGS.ECSC Agreement 7210-SA/513S u m m a r yThe aim of the following E.C.S.C. research is to elaborate a simple but com plete docum ent todesign com monly used buildings in steel construction. This document is completely based onEurocode 3 and each paragraph is totally conform to Eurocode 3. Only the design formulasnecessary to design braced or non-sway buildings are taken into account in this d ocument.Tall buildings (skyscrapers) and halls are not treated. The designers and steel constructorsare able to calculate and erect a com monly used steel building with this design handbook.Therefore also the important load cases from Eurocode 1 will be included in this docum ent.The w orking group of the research project was con stituted of 10 European engineeringoffices. Firstly that working group has carried out different examples of calculation of bracedor non-sway buildings accord ing to Eurocode 3 Part 1.1: check of existing steel structures anddesign of new steel buildings. Afterwards thanks to those examples of calculation the neededdesign formulas of Eurocode 3 was highlighted and general procedure of design wasdetermined. The design handbook "Simplified version of Eurocode 3" is based on thatexperience.The link of the working group to the drafting panel of Eurocode 3 was guaranteed by theProfessor Sedlacek of Aachen University.Liaison has been ensured with both other E.C.S.C. research projects nr SA/312 and nr S A/41 9also dealing with Eurocode 3: respectively, "Application software of Eurocode 3: EC3-tools"(CTIC M , France) and "Design handbook for sway buildings" (CSM -Italy).


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VERSION SIMPLIFIEE DE L'EUROCODE 3 POUR LES BATIMENTS COURANTSAgrment CECA 7210-SA/513S o m m a i r eLe but de cette recherche est d'laborer un docum ent simple mais com plet pour calculer desbtiments courants en construction mtallique. Ce document est entirement bas surl'Eurocode 3 et chaque paragraphe est totalement conforme VEurocode 3. Il n'a t pris encom pte que les formu les ncessaires au calcul de btimen ts contrevents et rigides. L esbtiments trs lancs (gratte-ciel) et les halls industriels n'y sont pas traits. Les bureauxd'tudes et constructeurs mtalliques devront tre capables de calculer et d'riger unbtiment courant en acier avec ce manuel de dimensionnement. Les cas de charges le plusimportants issus de l'Eurocode 1 seront galement inclus dans ce document.Le groupe de trav ail du projet de recherche tait constitu de 10 bureaux d'tudes e urope ns.En premire partie ce groupe de travail a effectu diffrents exemples de calculs de btimentscontrevents et rigides conformment l'Eurocode 3 Partie 1.1: vrification de structures enacier dj existantes et dimensionnement de nouveaux btiments en acier. Grce cesexem ples concrets de calcul, les formules de l'Eurocode 3 utiles au dimensionnement ont tmises en vidence et une procdure gnrale de dimensionnement a t dtermine. Lemanuel de dimensionnement "Version simplifie de l 'Eurocode 3" se base sur cetteexprience.La jonction entre le groupe de travail et le groupe de rdaction de l'Eurocode 3 a t faite parle professeur Sedlacek de l'Universit d'Aix-La-Chapelle.Un e collaboration a t assure avec deux autres projets de recherche CECA N SA/312 e t N SA/419 qui concernent aussi l'Eurocode 3: respectivement, "Logiciel d'application del'Eurocode 3 : EC3 -Tools" (CTICM , France) et "Manuel de dimensionnement de btimentssouples ( nuds dplaables)" (CSM , Italie)


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VEREINFACHTE VERSION DES EUROCODE 3 FR BLICHE GEBUDE.EGKS Zulassung7210-SA/513Z u s a m m e n f a s s u n gDieses EGKS Forschungsprojekt hat zum Ziel, ein einfaches aber vollstndiges Dokum entfr allgemeine (bliche) Stahlbaubemessung auszuarbeiten. Dieses Dokument ist vllig aufEurocode 3 basiert und jeder Paragrap h pat genau zu Eurocode 3. Nur dieBemessungsformeln, die no twendig sind fr ausgesteifte oder unverschiebliche Tragwerke ,werden bercksichtigt. Hochhu ser (Wolkenkratzen) oder Hallen werden nicht behandelt.Die Ingenieurbros und Stahlkonstrukteuren haben die Mglichkeit mit diesem Design-Hand buch einen einfachen Stahlbau zu berechnen und zu bauen. Dafr sind die wichtigstenLastflle von Eurocode 1 in diesem Dokum ent beinhaltet.Die Arbeitsgruppe des Forschungssprojekt bestand aus 10 europischen Ingenieurbros. DieArbeitsgruppe hat , im ersten Teil dieses Forschungsvorhabens, verschiedeneBerechnung sbeispiele mit ausgesteiften oder unverschieblichen Tragw erken nach Eurocode3 Teil 1.1 durchgefhlt : Berechnungs-Nachweis einer existierenden Stahlstruktur undDimensionierung eines neuen Stahlbaus. Anschlieend an diese konkreten Beispiele, wurdendie benutzten Bemessungsformeln nach Eurocode 3 hervorgehoben und ein allgemeinesBemessungsverfahren wurde festgelegt. Das Design-Handbuch "Vereinfachte Version desEurocode 3" basiert auf dieser Erfahrung.Die Verbindung zwischen der Arbeitsgruppe und dem technischen Komitee wurde vonProfessor Sedlacek der Aachener Universitt hergestellt.Eine Zusammenarbeit bestand mit zwei anderen EGKS Forschungesprojekten N SA/312und N SA/419, die auch Eurocode 3 behandeln : "Application software of Eurocode 3:EC 3-tools" (CTICM , France) und "Design handbook for sway buildings" (CSM -Italy).


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


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2 . W o r k i n g g r o u pThe research pro ject was fully managed and carried out by ProfilARBE D-Research (RPSDepartment), with the active support of the following working group which is particularlythanked for th e fruitful collaboration :- the following 10 engineering offices w hich were involved to perform 3 worked exam ples :

ReferenceNumber23467910131416

Engineering officeAdem

Bureau DeltaVarendonck Groep / Steelrrack

Ramboll & HannemanBureau Veritas

SocotecSofresid

Danieli IngegneriaSchroeder & Associs

D3BN

CityMonsLigeGent

CopenhagenCourbevoie

Saint-Quentin-YvelinesMontreuilLivorno

LuxembourgNieuwegein

CountryBelgiumBelgiumBelgiumDenmark

FranceFranceFranceItaly

LuxemburgThe Netherlands

- Professor Sedlacek and assistant from Aachen University (Germany) which guaranteed thelink of this working group to the drafting panel of Eurocode 3 and Eurocode 1,- some other eng ineering offices which participated to the meetings of the full w orking group :

Referencenumber5121819

EngineeringofficeVerdeyen & MoenartAssociate PartnerIngenieur gruppe BauenOve A rup & Partners

E C C S - T C l l

CityBruxellesKarlsruheLondon

Kiel

CountryBelgiumGermanyUnitedKingdomGermany

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-some members of CTICM (France) and SIDERCAD (Italy) involved in complementaryresearch projects about simplified approaches of Eurocode 3 (respectively, "Applicationsoftware of Eurocode 3 : EC3-tools" and "Design handbook for sway buildings") :. w hich participated to the meetings of the full working group,. and with which a general flow-chart (FC1) about elastic global analysis of steel frameaccording to EC3 has been established.3. Part 1 : Worked examplesIn order to find the needed formulae and to familiarise the engineering offices to theEuro codes , it has been decided to perform 3 different exercises (check and design of a steelstructure),

- exercise 1: verification of an existing braced or non-sway steel structure,- exe rcise 2: verification of a non-sway steel wind bracing in a building,- exerc ise 3 : design of a braced or non-sway steel structure,Different d rawings issued from the exercises of the offices are enclosed in the technical repo rtn 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 TR 4);- 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 TR 4);- 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 structureThe flow-chart of figure 1 shows the procedure followed for the verification of an existingbuilding with the Eurocodes 1 and 3. This first exercise aimed to find the needed formulaegiven 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 anexisting braced or non-sway building.The flow-chart of figure 1 is divided into 3 subjects:

a. The "K eywords" 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 standardsEN 10025 and EN 10113.c. The "Object" describing each step of the verification.

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3 .2 . Exe rc i se 2 : Ve r i f i ca t i on of a non-sway wind brac ing i n a bu i l d ingThe non-sway wind bracing consisted of a latticed steel structure. The flow-chart of figure 2gives the procedure of the verification of this wind bracing. This exercise was also not aniterative process .The description of the present flow-chart (figure 2) is the same than in the first examplepresented in the chapter 3.1 (figure 1).3.3. Exe rcise 3: Design of a braced or non-sway structureAfter the two first exercises, the engineering offices were familiarised with the Eurocodes 1and 3. They were able to perform a complete design of a structure by using an iterativeprocedu re. 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. T hepractical design handbook about the simplified version of the Eurocode 3 follows animproved way than the one defined in the initial design procedure. The figure 3 shows thedifferent data for the design and the type of chosen optimisation. The Figu re 4 gives the typeof building to b e designed.4 . P a r t 2 : D e s i g n h a n d b o o kA list of the needed formulae taken from the Eurocode 3 has been established following theinitial procedure defined for the exercises (see figures 5 to 8).This initial design procedure nearly corresponds to the sequence of the chapters of Eurocode3. It had to be adapted to comm on practice.The solved exercises E3 (design of a building) and the experience of each engineering officeallowed to determine a more suitable design procedure which constitutes the frame of thedesign handbook.About that practical design procedure reference may be made to the enclosed designhandbook which is called "Design handb ook a ccording to Eurocode 3 for braced or non-sway steel buildings" (short title : "EC3for non-sway buildings") :

- table of contents- general flow-chart FC1 about elastic global analysis of steel frames accord ing toEuroco de 3 (see chapter I of the design handbook); this flow -chart FC1 constitutes thelink with the 2 other researches about simplified approaches of EC3 : from CTICM andSIDE RC AD (see chapter 2 of the present report),- flow -chart FC 3.1 and FC 3.2 about general procedures to study structures submitted toactions (see chapter of the design handboo k), with load cases w hich are respectivelydefined :. by relevant com binations of characteristic values of load arrangemen ts, (g, q, s, w,...), in general cases,. or, by relevant combinations of characteristic values for the effects of actions (N,V , ; , f,. ..), in case of first order elastic global analysis.- flow -chart FC 4 about elastic global analysis of braced or non-sway steel framesaccording to Eurocode 3 (see chapter IV of the design handbook),- flow -chart FC 12 about elastic global analysis of bracing system according to Eu rocode 3(see chapter of the design handbook)

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In gen eral, for the design of buildings w e need to :- define the analysis model of frames (assumptions of plane frames, b racing systems,connections, m em bers,...)- characterise the load arrangements and load cases,- carry out the elastic global analysis of frames in order to determ ine the effects of actions :

. deformations (), vibrations (f) for Serviceability Lim it States (SLS) and,. internal forces and mom ents (N , V, M ) for U ltimate Limit States (ULS).- check the mem bers at SLS (vertical and horizontal displacements, eigenfrequencies) andat 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 UL S.Especially for members to be checked at ULS specific tables are given in the concernedchapters of the handbook, with list of checks according to different types of loading (separateor combined internal forces and m oments : N , V, M ).The design handbook which is enclosed to this final report of the research project, intends tobe a design aid in supplement to the complete document Eurocode 3 - Part 1.1 in order tofacilitate the use of Eurocode 3 for the design of such steel structures which are usual incom mon practice : braced or non-sway steel structures.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 docum ent Eurocode 3 - Part 1.1,which should be consulted in conjunction with the NAD , in case of doubt or need forclarification.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 therules specified in Eurocode 3 - Part 1.1.The lists of all symbols, tables and flow-charts included in the "Design Handbook" areenclosed to the present appendices.

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1. conceptional rype of structuredifferent braced non sway structures


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1 . conceptiqnal type of structurenon-sway wind bracing in a building(latticed structure ). .2. occupancies

EC 3 : Classificationnon-sway :VSd / VCT b /1 classification

5. action effectsdetermination of the action effects(global and local)

elastic or plastic modelSLS ULS

6. dirnehsioning and verification

EC 1: Load casesEC 3 : Load combinationsEC 3 : ImperfectionsEC 3 : Modelling depending onb /1 classification

1 s t order analysisSLS limits

deformationsvibrationsULS limitsFrame stabilityStatic equilibriumResistance of cross section

- tension - bending moment and shear- compression - bending moment and axial force bending moment - bending moment, shear and axial force- shear - transverse forces on webs

shear bucklingResistance of members (stability)- compression members : buckling- lateral torsional buddin g of beams- bending and axial tension- bending and axial compress ionConnection-joints baae of columns

LegendKeywordsWB

Requirement & ReferencesCObject

Exercise 2.Verification of a non-sway wind bracing in a buildingFigure 2

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1. concep tional type of structureBraced non sway structure (defined)I2 . occupancies

types of occupancy (defined)- office building

3. shapeshape of the building (defined) 1

J4. structural conceptstructural modelGeometric dimensions (defined)Non-structural elements (not defined)Load bearing structure (not defined)Type of join ts (defined)Profiles ( not defined)

Floor structure (not defined)Material properties (not defined)I5. action effectsdetermination of the action effects(global and local)

elastic or plastic modelSLSt ULSt6. dimensioning and verification

SLS limitsdeformationsvibrations

7. optimisation of the weightProfiles:- max 3 different profilesfor the columnsType of joints:- hinged or rigidconnectionsSteel: FeE 23 5or FeE 355or FeE 460 grades

ULS limitsFrame stabilityStatic equilibriumResistance of cross section

and axial forceabear and axial force compression

- sbear bedd ingResistance of members (stability)- cflfupyraHin membera bockung- lateral torsional bedding of beams ^"Hiraj and axial tension* bending and axial c ompresiionConnection j o i n t s- base of columns

Exercise 3.Design of a braced non-sway structureFigure 3

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plane view

lift

front view

ce

ICAC

!

I I

Referencenumber26791013

Engineering officeAdemRambll, Hannemann & HjlundVeritasSocotecSofresidDanieli

n123456

X(m)303050505050

Y(m)101014141818

storeysn =51510152015

JointsRigidRigidHingedHingedRigidHingedExercise 3 : Type of building to be designedFigure 4

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i . C E ur o c o de 3 F o r m ul a e R e fe r e nc e s1. Conceptional type of structure.1.1. non-sway-> C hapter 5.2.5.21.2. braced -> C hapter 5.2.5.31.3 storeys2. Occupancies.2.1. Type of building, (category,...)2.2. Impose d loads on floors and roof (p and P) -> Chapter EC 1 , part 2.4: Imposed load3, 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. Geom etric dim ensions.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. -> E C 1 . - permanent loads: g and G- variable loads: q and Q:- imposed loads: and (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 (2.1 7) and (2.1 8)ULS: -> Chapter 2.3.3 .1 clause (5), formulae (2.11 ) and (2.1 2)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)75.4. Elastic or plastic mod el -> EC3: Chapter 5 . 3 : classification of cross-sections (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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E u r o c o d e 3 F o r m u l a e R e f e r e n c e s6. Verification SLS. -> Chapter 46.1. Global analysis. -> beams, portal f rames,structural frames Calculation for- > bracing system verticaland horizontal6.2. Deformations.6.3. Vibrations.

-> Chapter 4.2.2 clause (1) vertical table 4.1, figure 4.1clause (4) ho rizontal-> Chapter 4.3. (ECCSpublication n65: table4.4;... ;

7. Verification ULS.7.1. Global analysis. = > internal forces: , 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 -> Chapter 5.4.5.3 clause(l) formula(5.19) => A v n e t > -2- , - i - 0.9' Mo(remark: y m factors should be ignored)7.2.4. shear.-> Chapter 5.4.6 clause (1) formula (5.20)

clause (2): AyzAvy: EC CS publication n65: table 5.14clause (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 cross-sections with unequal flanges:M S d Rd + (Mp 1 > R d - M f > R d )1 - VSd'pl ,Rd - 1 ^ M c , R d

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 65: tables 5.15 and 5.16)

Figure 6

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Eurocode 3 Formulae References7.2.8. transverse forces on webs.-> Chapter 5.4.10 clause (3) -> clause (1) formula (5.41)clause (2) formula (5.42) figure 5.4.3or -> 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) 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 5.7.37.2.9. shear buckling. -> Chapter 5.6.1 clause (1) limit condition (present paragraph 5.4 )7.2.10 flange-induced buckling.-> Chapter 5.7.7 ECC S publication n 65: table 5207.3. Resistance of m embers. (->for 1 st order analysis)7.3.1. compression members: bu ckling.-for 1 st order e lastic analysis:-> Chapter 5.5.1.1 clause (1) formula (5.45)-> C hapter 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 5.5.3clause (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 buc kling of beam s.

-> Chapter 5.5.2 clause (1) formula (5.48)clause (2) formula (5.49)clause (3)clause (5)clause (6) Annex Fclause (7) limit conditionclause (8)7.3.3. bending and axial tension.-> Chapter 5.5.37.3.4. bending and axial compression.-> Chapter 5.5.4 -without lateral-torsional buckling:clause (1) formula (5.51) class 1 and 2 cross-sectionsclause (3) formula (5.53) class 3 cross-sections- with lateral-torsional buckling:clause (2) formula (5.52) class 1 and 2 c ross-sectionsclause (4) formula (5.54) class 3 cross-sectionsclause (7) figure 5.5.37.4. Resistance of connections.7.4.1. bolted oints. -> Chapter 6.57.4.1.1. Positioning of holes.-> Chapter 6.5.1 figures 6.5.1 to 6.5.4(ECCSp ublication n65: table 62 )7.4.1.2. Design shear rupture resistance.-> Chapter 6.5.2.2 clause (2) formula (6.1)

clause (3) figu re 6.5.5Figure 7

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Eurocode 3 Form ulae References7.4.1.3. Angles.-> Chapter 6.5.2.3 clause (2) formulae (6.2) to (6.4)clause (3) figure 6.5.67.4.1.4. Categories of bolted connections.-> Chapter 6.5.3 and table 6.5.27.4.1.5. Distribution of forces between fasteners.-> Chapter 6.5.4 figure 6.5.77.4.1.6. Design resistance of bolts.-> Chapter 6.5.5 clause (2) table 6.5.3clause (3)clause (4) formula (6.5)clause (5) formula (6.6)clause (9)clause (10)(ECCSp ublication n65: tables 6.6, 6.7and6.8)7.4.1.7. High stren gth bo lts in slip-resistant connections-> Chapter 6.5.8-> Chapter 6.5.9-> Chapter 6.5.10[-> Chapter 6.5.11[-> Chapter 6.5.12-> Chapter 6.5.13.[7.4.2 Joints with rivets.7.4.3 W elded conn ections.[-> Chapter 6.6.3-> Chapter 6.6.4

-> Chapter 6.6.5.1-> Chapter 6.6.5.2-> Chapter 6.6.5.3

-> Chapter 6.6.8[-> Chapter 6.6.9[-> Chapter 6.6.10

Annex Jclause (1) formula (6.11) and figure 6.5.10clause (2) formula (6.12)7clause (1) formula (6.13)7tables 6.5.6 and 6.5.7, figure 6.5.12-> Chapter 6.5.67-> Chapter 6.6clause (3)7clause (1)clause (4)clause (7)clause (2)clause (2)clause (1) Annex Mclause (3) formula (6.14)clause (4) formula (6.15)clause (5)clause (2) formula (6.16)clause (3)clause (1)7clause (3) formula (6.18)7clause (2)clause (3)7.4.4 Beam-to-column connections. -> Chapter 6.9 and Annex J7.4.5. Column bases.7.5. Fram e stability.-> Chapter 5.2.6.1

7.6. Static equ ilibrium .-> Chapter 2.3.2.4

-> Chapter 6.11 and Annex Lclause (1)clause (3)clause (4)clauses (1) to (12)Figure 8

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1. List of symbols in the "Design Handbook" List of symbols (1/6)1. L a t i n s y m b o l sa de s ign a t i on o f a buck l ing cu rv ea thro a t th ic kn ess of f i ll l e t we lda


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LLbLTBLymmaxminMMb.RdM C TM c R dM Mf.RdMN.RdMN.VJld

MN.V.yJRdMN.V.z.RdMN.y.RdMN.z.RdM p fMpRdMp/iw.RdMpy.RdMptzJRdMRdMsdMv.RdMw.sdMyMy.SdM zMz.sdrien rn8NADN b dNb.yJldN b i J l d compressionN erN c R dNxsdNpCRd

List of symbols (3/6)rough ness factor of the terrainportion of a membereffective length for out-of-plane bendingsystem length; span length; weld lengthbuckling length of memberlateral-torsional bucklingdistance between extreme fastener holesmass per unit lengthmaximumminimumbending m omentdesign resistance moment for lateral-torsional bucklingelastic critical moment for lateral-torsional bucklingdesign resistance moment of the cross-sectiontorsional momentelastic moment capacitydesign plastic resistance moment of the cross-section consisting of the flangesonlyreduced design plastic resistance moment allowing for axial force reduced design plastic resistance moment allowing for axial force and byshearforce Vreduced design plastic resistance moment about yy axis allowing for axial force and shear force Vreduced de sign plastic resistance mom ent about zz axis allowing for axial force and shear force Vreduced design plastic resistance moment about yy axis allowing for axialforce reduced design plastic resistance moment about zz axis axial force plastic moment capacitydesign plastic resistance mom ent of the cross-sectiondesign plastic resistance m oment of the webdesign plastic resistance mom ent of the cross-section about yy axisdesign plastic resistance mom ent of the cross-section about zz axisdesign bending moment resistance of the memberdesign bending moment applied to the m emberdesign plastic resistance moment reduced by shear forcedesign value of moment applied to the webbending m oment about yy axisdesign bending moment about yy axis applied to the memberbending mom ent about zz axisdesign bending moment about zz axis applied to the mem bernumber of fastener holes on the block shear failure pathnumber of columns in planenumber of members to be restrained by the bracing systemnumber of storeysnormal force; axial loadNational Application Documentdesign buckling resistance of the memberdesign buckling resistance of the member according to yy axisdesign buckling resistance of the member according to zz axisnormal force in compressionelastic critical axial forcedesign compression resistance of the cross-sectiondesign value of tensile force applied perpendicular to the fillet w elddesign p lastic resistance of the gross cross-section

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N R dN s dN L R drN tensionN u .R dN x . s dP l P 2qqkqrefQQ dQ kVkmaxrRRa,RdRb,RdR dR kRy,RdSSSdSkS sSSdSkSLSttftptptwUULSvVrefVref.OVVbaJldVerV / / S dV j . s dVpRdVpiyJ ldV p zJldv R dV s dV yVy.Sdv zVZ.Sdw

List of sym bols (4/6)design resistance for tension or com pression mem berdesign value of tensile force or com pressive forcedesign tension resistance of the cross-sectionnormal force in tensiondesign ultimate resistance of the net cross-section at holes for fastenersdesign internal axial force applied to mem ber according to xx axisdistances between bolt holesPoint loadimposed variable distributed loadcharacteristic value of imposed variable distributed loadreference mean wind pressureimposed variable point loaddesign variable actioncharacteristic value of imposed variable point loadvariable action which causes the largest effectradius of root filletrolled sectionsdesign crippling resistance of the webdesign buckling resistance of the w ebdesign resistance of the mem ber subject to internal forces or mom entcharacteristic value of Rddesign crushing resistance of the w ebsnow loadthickness of fillet welddesign snow loadcharacteristic value of the snow load on the groundlength of stiff bearingeffects of actions at ULSdesign value of an internal force or mom ent applied to the membercharacteristic value of effects of actions at ULSServiceability Limit statesdesign thickness, nominal thickness of element, m aterial thicknessflange thicknessthickness of the plate under the bolt head or the nu tthickness of a plate welded to an unstiffened flangeweb thicknessmajor axisUltimate Limit Statesminor axisreference wind velocitybasic value of the reference wind velocityshear force; to tal vertical loaddesign shear buckling resistanceelastic critical value of the total vertical loaddesign value of shear force applied parallel to the fillet welddesign value of shear force applied perpendicular to the fillet welddesign shear plastic resistance of cross-sectiondesign 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 memberdesign shear force applied to the mem ber; design va lue of the total vertical loadshear forces applied parallel to yy axisdesign shear force applied to the mem ber parallel to yy axisshear force parallel to zz axisdesign internal shear forces applied to the mem ber parallel to zz axiswind pressure on a surface

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List o f symbols (5/6)Wd desi gn wind loadw e wind pressure on external surfaceW welded sectionsWeff elas tic sectio n mo du lu s of effective class 4 cross-sectionWeff.y elas tic sect ion mo du lus of effective class 4 cross-section according to yy axisWeff.z elas tic sect ion mo du lu s of effective class 4 cross-section according to zz axisWef elastic section mod ulu s of class 3 cross-sectionWey elas tic sectio n mo du lus of class 3 cross-section according to yy axisWez elastic section mod ulu s of class 3 cross-section according to z z axisWpi plastic section mod ulus of class 1 o r 2 cross-sectionWpy plas tic secti on mo dul us of class 1 o r 2 cross-section according to yy axisWpZ plastic section modulus of class 1 o r 2 cross-section according to z z axisx, x x axis along the memberX k characterist ic value of the material propertiesy, y y principal axis of cross section (parallel to flanges, in general)z, z z principal axis of cross section (parallel to the web, in general)Ze refer ence he igh t for evalu ation of c e2u O r e e k s y m b o l s coefficient of frequency of the basis mode vibration coefficient of linear thermal expansion factor to determine the position of the neutral axisaa coefficient of critical amplification or coefficient of remoteness of critical stateof the framePA non-dimensional coefficient for buckling M equ ivale nt unifor m mo men t factor for flexural buckl ing Ml/ r equi vale nt unifo rm mom ent factor for lateral-torsional buck lingMy equi vale nt unifor m mom ent factor for flexural buckli ng about yy axis equi vale nt unifor m mo me nt factor for flexural buckli ng about zz axis w non -di men sio nal coefficient for lateral-torsional buck ling w correlation factor (for a fillet weld)Y F partial safety factor for force or for actionY G partial safety factor for permanent actionY M partial safety factor for the resistance at ULSYMb par t i a l sa fe ty fac tor for the res i s tanc e of bo l te d co nn ec t ion s7Ms.ser pa rt ia l safety facto r for the s l ip res is ta nc e of pr elo ad ed bo ltsTMW p a r t i a l s a f e t y f a c to r f o r t h e r e s i s t a n c e o f w e l d e d c o n n e c t i o n sYMO par t ia l sa fe ty fac tor for res i s tance a t ULS of c lass 1 ,2 or 3 c ross -sec t ions(p las t ic i ty or y ie ld ing)YM I par t ia l sa fe ty fac tor for res i s tance of c lass 4 c ross -sec t ions( l o c a l b u c k l i n g r e s i s t a n c e ) par t ia l safe ty fac tor for the res i s tance of member to buckl ingYM2 pa rt ia l safety factor for the res ista nc e of ne t sect io n at bo lt ho lesYQ par t ia l safe ty fac tor for var iable ac t ion r e l a t i ve ho r i zo n ta l d i sp l acem en t o f t op and bo t tom o f a s t o r eyOb hor i zon ta l d i sp l a cem en t o f t he b raced f r ame5d de s ig n def lec t io n6dv de s ig n ver t ic a l def lec t ion of f loors, b ea m s, . . . d desi gn horizo ntal deflection of framesOHmax re co mm en de d limit of horizontal deflection in plane deflection of the bracing system due to q plus any external loads

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List of symbols (6/6) deflection due to variable load (q)\, horizo ntal displacement of the unbraced framevd design vertical deflection of floors, be am s,. . .Vmax recommended limit of vertical deflection pre-camber (hogging) of the beam in the unloaded state (state 0) svariation of the deflection of the beam due to permanent loads (G) imm ediatlyafter loading (state 1)2 variation of the deflection of the beam due to the variable loading (Q) (state 2) displacement J 23 5 (with fy in N /mm 2) rotation slenderness of the member for the relevant buckling mode Euler slenderness for buckling non-dimensional slenderness ratio of the mem ber for buckling. effective non-dimensional slenderness of the member for buckling about w axis.y effective non-dimensional slenderness of the mem ber for buckling about yy axis . effective non-dimensional slenderness of the member for buckling about zz axisX LT non-dimensional slenderness ratio of the mem ber for lateral-torsional buckling plate slenderness ratio for class 4 effective cross-sections non-dimensional slenderness of the member for buckling about vv axisy non dimensional slenderness ratio of the member for buckling about yy axis non dimensional slenderness ratio of the mem ber for buckling about zz axis factor for FsjRk depending on surface classHi 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 Vsapy reduction factor due to shear force Vy.sdp z reduction factor due to shear force Vz.sd norm al stressGq numerical values for the stabilizing forces of a bracing systemGxEd,


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2. List of tables in the "Design Handbook" List of tables (1/3)Pages of the HandbookO.cTable 0.1ITable 1.1Table 1.2Table 1.3Table 1.4Table 1.5Table 1.6Table 1.7Table 1.8Table .1Table .2Table .3Table .4Table .5Table .6Tab le .7Tab le .8 Table .1Table .2Table .3Table .4Table .5Table .6Table .7Table .8Table .9IVTable IV. 1Table IV.2Table IV.3Table IV.4Table IV.5Table IV.6Table V.lTable V.2Table V.3

SYMBO LS AND NOTATIONSDimensions and axes of rolled steel sectionsINTRODUCTIONSum mary of design requirementsPartial safety factor for the resistanceDefinition of framing for horizontal loadsChecks at Serviceability Limit StatesMember submitted to internal forces, moments and transverse forcesPlanes within internal forces, moments (Nsd> V$d, Msd) and transversesforces Fsd are actingInternal forces, moments and transverse forces to be checked at U LS fordifferent types of loadingList of references to chapters of the design handbook related to all checkformulas at ULSSTRUCTURAL CONCEPT OF THE BUILDINGTyp ical types of jointsModelling of jointsComp arison table of different steel grades designationNominal values of yield strength f and ultimate tensile strength fu forstructural steels to EN 10025 and EN 10113Maximum thickness for statically loaded structural elementsMaximum thickness for statically loaded structural elementsNominal values of yield strength fyb and ultimatetensile strength fub for boltsMaterial coefficientLOAD ARRANGEMENTS AND LOAD CASESLoad arrangem ents (Ffc) for building design according to EC1Imposed load (qk, Qk) on floors in buildingsPressures on surfacesExposure coefficient c e as a function of height above groundExternal pressure Cpe for buildings depending on the size ofthe effected area AReference height ZQ depending on h and bCombinations of actions for serviceability limit statesCombinations of actions for ultimate limit statesExamples for the application of the combinations rules in Table III.8.All actions (g, q, P, s, w) are considered to originate from different sourcesDESIGN O F BRACED OR NON-SWAY FRAMEModelling of frame for analysisModelling of connectionsGlobal imperfections of the frameValues for the initial sway imperfections Specific actions for braced or non-sway framesRecommended limits for horizontal deflectionsCLASSIFICATION OF CROSS-SECTIONSDefinition of the classification of cross-sectionDeterminant dimensions of cross-sections for classificationClassification of cross-section : limiting w idth-to thickness ratios forclass 1 & class 2 I cross-sections submitted to different types of load ing

465152636465666768

7071727374757576

8081828383848586868887979899100105112113

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Table V.4Table V.5T able V.6T able V.7T able V.8Table V.9T able V.10V ITable VI. 1Table VI.2Table VI.3T able VI.4v nTab le Vn . lTable Vfl.2Table Vfl.3T able VH .4Table Vfl.5T able VH .6v mT a b l e V m. l

List of tables (2/3)Pages of the Handbook

TableTableTableTableTableTableTableTable

vm.2Vni . 3V m . 4vm.5vm.6vm.7Vffl.8Vin .9T able V m . 10T able V m . 1 1T able V m . 12Table VIfl .13T able V m . 14EXTable DC. 1T able DC.2T a b l e K . 3

Classification of cross-section : limiting width-to thickness ratios forclass 3 I cross-sections submitted to different types of loadingBuckling factor k


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Tab le K .4Table D.5T able DC.6T able DC.7Table Di. 8Table D.9

T able X . lT able X .2T able X .3T able X .4T able X .5T able X .6Table X.7T able X .8T able X .9XITable X I. 1T able X I .2T able X I .3T able X I .4Table XI.5T able X I .6T able X I.7T able XI.8T able X I .9Table X I. 10Table X I. 11Table X I. 12Table XL 13T able X L 14T able X L 15Table XL 16XIIT able .1T able .2T able .3T able .4T able D.l

List of tables (3/3)Pages of the H andb 'Interaction formulas for the (N,M) stability check of membersof Class 1 or 2 1 75Interaction formulas for the (NM) stability check of mem bers of Class 3 1 76General interaction formulas for the (N,M) stability check ofmembers of Class 4 1 77Supplementary interaction formulas for the (N,M) stability checkof members of Class 4 1 78Reduced design resistance Ny.Rd allowing for shear force 1 79Reduced design plastic resistance moment M N . V J M allowing for axial loadand shear force for Class 1 or 2 cross-sectionsTRANSV ERSE FORCES ON WEBS (F ; (F,N,V,M))Failure m odes due to load introductionStresses in web panel due to bending moment, axial forceand transverse forceYield c riteria to be satisfied by the webLoad introductionLength of stiff bearing, s sInteraction formula of crippling resistance and moment resistanceEffective breadth beff for web buckling resistanceCompression flange buckling in plane of the webMaximum width-to-thickness ra tio d/twC O N N E C T IO N SDesignation of distances between boltsLinea r distribution of loads between fastenersPossible plastic distribution of loads between fasteners. Any realisticcombination could be used, e.g.Prying forcesCategories of bolted connectionsBearing resistance per bolt for recommended detailingfor t = 1 0 mm in [kN]Shear resistance per bolt and shear plane in [kN]Long jointsTension resistance per bolt in [kN]Interaction formula of shear resistance and tension resistance of boltsCharacteristic sup resistance per bolt and friction interface for 8.8 and 10.bolts, where the holes in all the plies have standard nominal clearancesComm on types of welded jointsThroat thicknessAction effects in fillet weldsResistance of a fillet w eldEffective breadth of an unstiffened tee jointDESIGN OF BRACING SYSTEMLoad arrangements of the bracing systemBracing system imperfectionsValues for the equivalent stabilizing force ZqBracing system imperfections (examples)A P P E N D K DList of references to Eurocode 3 Part 1.1 relatedto all check formulas at ULS

1811871881891901901911921*93193196196197197198199200200201201202203204204205206216218218219

221

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3. List offlow-charts n the "Design Handbook" ChapterElastic global analysis of steel frames according to Eurocode 3GeneralDetails IComm ents (6 pages) I[FC 3 .1] Load arrangements & load cases for general global analysis of m

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

analysis of the structure(FCM)Elastic global analysis of braced or non-sway steel frames

according to E C 3General IVDetails IVComm ents (4 pages) IVFC 5. l Classification of I cross-section V(FC 5.2J Calculation of effective cross-section prope rties of Class 4 r v

cross-section(FC6 . )FC 6.11 Members in tension (Ntension)( F C 6 . 2 ) Ang les connected by one leg and submitted to tension( F C 7 ) M em bers in com pression (Ncompression)

VIVIvnvmFC 8 Design of I members in uniaxial bending (V z;My;(Vz,My)) or(Vy;Mz;(VyJvIz);

FC 1 2Elastic global analysis of bracing system according toEurocode 3General Details Comments (6 pages)

Pages141516 to 213 8

3 9

505152 to 556263

828390102

168169170 to 1 75

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Design handbook accordingto Eurocode 3 forbraced or non-sway steel buildings

Short title: EC 3 for non-sway buildings

Profil ARBED-RecherchesChantrain Ph.Conan Y.Mauer Th.


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TABLE OF CONTENTS0 PRELIMINARIES 41

4141414142424344444444454747

' 47

0.aO . u . l0.a.20.a.3O.a.40.a.5

O.bO.cO.c.lO.c.20.C.30.C.4O.dO.d.10.d.2

ForewordGeneralitiesObjective of this design handbookWarningHow to read this design handbookAcknowledgements

ReferencesSymbols and notationsSymbolsConvention for member axesDimensions and axes of rolled steel sectionsNotations in flow-chartsDefinitions and unitsDefinition of special termsUnits

INTRODUCTION fLa Basis of design ._I.a.1 Fundamental requirements .RI.a.2 Definitions 7I.a.2.1 Limit states ~I.a.2.2 Actions 4 9I.a.2.3 Material properties 4 9I.a.3 Design requirements 50I.a.3.1 General 50I.a.3.2 Serviceability Limit States 50I.a.3.3 Ultima te Limit States 50Lb General flow-charts about elastic global analysis 53I.b .l Flow-chart FC LE lastic global analysis of steel frames according to EC 3 53Lb. 1.1 Flow-chart FC 1: general 53I.b.1.2 Flow-chart FC 1: details 53I. b. 1.3 Comments on flow-chart FC 1 56Le Content of the design handbook 61I.c.1 Scope of the handbook 61I.C.2 Definition of the braced frames and non-sway frames 62

I.C.3 Summary of the table of contents 64I.C.4 Checks at Serviceability Limit States 64I.C.5 Checks of members at Ultimate Limit States 65

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TABLE OF CONTENTS S T R U C T U R A L C O N C E P T O F T H E B U IL D IN G 69n . a Structural model 69n . b Geometric dimensions 69n . c Non structural elements 69n. d Load bearing structure 69n. e Joints ?0n.f Profiles 'J lU.g Floor structure 7 -U.h Ma terial properties 72n. h. 1 Nom inal values for hot rolled steel 7~n. h. 2 Fracture toughnessn. h. 3 Connecting devices \?n .h .3 .1 Bol t s 7 5U.h.3 .2 Welding consumables 76n. h. 4 Design values of material coefficients 76m LOAD ARR ANG EME NT S AND LOAD CASES 77ULa Generalities 77n i. b Load arrangements 80m . b . l Permanent loads (g and G) 80m .b .2 Variable loads (q, Q, w and s) 80III.b.2.1 Impo sed loads on floors and roof (q and Q) 80m .b. 2.2 Wind loads (we,i, F w ) 81m. b.2. 2.1 Wind pressure (we) 81m. b.2. 2.2 Wind force (Fw) 84m .b. 2.3 Snow loads (s) 84ULc Load cases 85m . c . l Load cases for serviceability limit states 85m . c. 2 Load cases for ultimate limit states 86

IV DESIGN O F BRA CED OR NON-SWAY FRAM E 87rV. a Generalities 87IV .a .l Analysis mod els for frames 87IV. a.2 Flow -chart FC 4 :Elastic global analysis of braced or non-sway steel framesaccording to Eurocode 3 89IV.a.2.1 Flow-chart FC 4 general 89rV.a.2.2 H ow-cha rt FC 4 details 89rv. a. 2. 3 Comm ents on flow-chart FC 4 92rv . b Static equilibrium 96rv . c Loa d arrangements and load cases 96IV .c. l Generalities 96IV.C.2 Frame imperfections 96rV.d Fram e stability 97rv . e First order elastic global analysis 98rV .e .l Methods of analysis 98IV. e.2 Effects of deformations 98IV. e.3 Elastic global analysis 99rv . f Verifications at SLS 99rv . f. l Deflections of frames 100rv . g Verifications at ULS 1 0 rv . g . l Classification of the frame *00r v . g . 1.1 H ypothesis for braced frame *00

rv .g . 1.2 H ypothesis for non-sway frame 100rv. g. 2 ULS checks 100

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TABLE OF CONTENTSV CLA SSIFICA TION OF CROSS-SECTIONS V.a Generalities 101V.b Definition of the cross-sections classification 104V.c Criteria of the cross-sections classification 106V.c. 1 Classification of compression elements of cross-sections 106V.C.2 Classification of cross-sections 106V.c.3 Properties of class 4 effective cross-sections 106V.d Procedures of cross-sections classification for different loadings 109V.d. 1 Classification of cross-sections in compression 109V.d.2 Classification of cross-section in bending 109V.d. 3 Classification of cross-sections in combined (N,M) 110V I M E M B E R S I N T E N S I O N (N ten sio n) 121V l.a Generalities 121VL b General verifications at ULS 124Vl.b. 1 Resistance of gross cross-section to Ntension 124VI.b.2 Resistance of net cross-section to Ntension 125

VLc Particular verifications at ULS for angles connected by one leg 126VI.c. 1 Connection with a single row of bolts 126VI.C.2 Connection by welding 128V I I M E M B E R S I N C O M P R E S S I O N (NCO nipression) 129V n. a Generalities 129VILb Classification of cross-sections 132VII.c General verifications at ULS J 33V n .c .l Resistance of cross-section to NcompressionVII.C.2 Stability of mem ber to N comp ression ^V n.c.2 .1 Resistance to flexural buckling 133V n.c .2.2 Resistance to torsionnal buckting and to flexural-torsional buckling 137VILd Particular verifications at ULS for class 4 monosym metrical cross-section J38VILd. 1 Resistance of cross-section to N compression ^ VII.d .2 Stab ility of member to Ncompression ^ 8VIL e Particular verifications at ULS for angle connected by one leg 139VILe. 1 Connection with a single row of bolts 139V n. e. 1.1 Resistance of cross-section to NCOmpression ^ 9V n. e. 1.2 Stability of mem ber to Ncompression 139VII.e.2 Connection by welding 139V n.e.2 .1 Resistance of cross-section to Ncompression 139V n.e .2.2 Stability of mem ber to NCOmpression 139VIII M EM BER S IN BENDING (V ; M ; (V, M)) 140

VHLa Generalities 140VH Lb Verifications at SLS 145V m .b .l Deflections 145V in. b. 2 Dynamic effects - vibrations 147VIII.c Classification of cross-section 147VIILd Verifications at ULS to shear force Vsd 148V in .d . 1 Resistance of cross-section to Vsd 148VIII.d.2 Stability of web to Vz.sd 150V in .e Verifications at ULS to bending mom ent Msd 152V in .e . 1 Resistance of cross-section to Msd 152V m .e.2 Stability of member to My.sd I53V in. f Verifications at ULS to biaxial bending mom ent (My.sd> Mz.sd) 156Vin.f. 1 Resistance of cross-section to (My.sd, Mz.sd) 156V m .f.2 Stability of member to (My.sd, Mz.sd) 157

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161

TABL E OF CONTENTSV m .g Verifications at ULS to combined (Vsd, M sd) 157Vr n.g .1 Resistance of cross-section to (Vsd. Msd ) 157Vin .g . 1.1 Shear force Vsd and uniaxial bending Msd 157V in .g . 1.2 Shear force Vsd and biaxial bending moment Msd 158V m .g.2 Stability of web to (V z.Sd,M y.Sd) 159LX MEM BERS WITH COMBINED AXIAL FORCE ANDBEN DING MO M ENT ((N, M) ; (N, V; M))Di.a Gene ralities 161K . b Verifications at SLS 167LX.b.l Deflections 167LX.b.2 Vib rations 167DC.c Classification of cross-section 167DCd Verifications at ULS to (N,M) 167LX.d. 1 Resistance of cross-section to (Nsd, M sd) 1 7LX.d. 1.1 Uniaxial bending of class 1 or 2 cross-sections 167LX.d. 1.2 Biaxial bending of class 1 or 2 cross-sections 170LX.d. 1.3 Bend ing of class 3 cross-sections 170

LX.d. 1.4 Bend ing of class 4 cross-sections 171LX.d.2 Stability of member to (Nsd,M sd) 171K.d.2.1 Stab ility of member to (Ntension My.sd) 171LX.d.2.2 Stability of member to (Ncompression* M sd) 172DC.e Verifications at ULS for (N$d ,Vsd) 1 7 6LX.e.l Resistance of cross-section to (Nsd.Vsd ) I 7 7JX.f Verifications at UL S to (Nsd ,Vsd,M sd) 1 7 7LX.f.l Resistance of cross-sec tion to (Nsd>Vsd>Msd) ^ 7^LX.f. 1.1 Un iaxial bending of class 1 or 2 cross-section 178LX.f. 1.2 Biaxial bend ing of class 1 or 2 cross-section 180LX.f. 1.3 Bending of class 3 cross-section 180LX.f. 1.4 Bending of class 4 cross-section 181LX.f.2 Stab ility of we b to (N x.Sd, Vz.Sd, My.Sd) 182X TRANSVERSE FORCES ON WEBS (F ; (F, N, V, M)) 18X.a Generalities 184X.b Classification of cross-section 185X.c Resistance of web s to (F,N,V,M) I 8 5X.C.1 Yield criterion to (F,N,V,M) 185X.c.2 Crushing resistance to F 187X.d Stability of webs to (F ; (F, M)) 188X.d .l Crippling resistance to ( F ;( F , M)) 188X.d. 1.1 Crippling resistance to F 188X.d. 1.2 Crippling resistance to (F,M) 188X.d.2 Buckling resistance to F 189X.e Stability of webs to compression flange buckling 190XI CO NNE CTIO NS 191XLa Generalities 191XI.b Bolted connections 191XLb. 1 Positioning of holes 191XI .b.2 Distribution of forces between bolts 191XI.b.3 Prying forces 193XI .b.4 Categories of bolted connections 193XI .b.5 Design ULS resistance of bolts 194XI.b.5.1 Bearing resistance 194XI.b.5 .2 Shear resistance 196XI.b.5.2.1 General case 196

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TABLE OF CONTENTSX I.b.5.2.2 Long jointsX I.b.5.3 Tension resistanceX I.b.5.4 Punching shear resistanceX I.b.5.5 Shear and tension interactionX I.b.6 ULS resistance of element with bolt holesX I.b.6.1 Net section ULS resistanceX I.b.6.2 ULS resistance of angle with a single row of boltX I.b.6.3 Block shear ULS resistanceX I.b.7 High strength bolts in slip-resistant connections at SLSX I.c Welded connectionsXI .c . 1 Type of weldX I.C.2 Fillet weldX I.C.3 Des ign resistance of fillet weldX I.C.3.1 Throat thicknessX I.c.3.2 Design resistanceX I.C.4 Design resistance of butt weldXI.c . 5 Join ts to unstiffened flangesX l.d Pin connectionsX I.e Beam-to-column connectionsX l.f Design of column basesXII DESIGN OF BRACING SYSTEMX ILa GeneralitiesX ILa. 1 Flow-chart FC 12:Elastic global analysis of bracing system according toX ILa. 1.1 Flow-chart FC 12: generalX D.a.1.2 Flow-chart FC 12: detailsX ILa. 1.3 Com ments on flow-chart FC 12X ll.b Static equilibriumX II.c Load arrangements and load casesX II.c.l Generalities

X II.C.2 Global imperfections of the bracing systemX ILd Bracing system stabilityX ILe First order elastic global analysisX ILf Verifications at SLSX ll.g Verifications at ULSX ll.g. 1 Classification of the bracing systemX ll.g. 1.1 Non-sw ay bracing systemX II.g.2 ULS checksAPPENDIX A : List of symbols

EC 3

APPENDIX APPENDIX CAPPENDIX D

List of tablesList of flow-chartsList of references to Eurocode 3 Part 1.1 related toall check formulas at ULS

196197197197198198198198198199199199200200201201202202202202203203203203203206212212212213216216216216216216216217223226227

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PRELIMINARIESO.a Foreword0-a.l Generalities(1) The Eurocodes are being prepared to harmonize design procedures between countrieswhich 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 prospectiveEuropean Standard for provisional application).(3) The national authorities of the members states have issued National ApplicationDocum ents (NA D) to make Eurocode 3 - Part 1.1 operative whilst it has EN V-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 completedocum ent Eurocode 3 - Part 1.1 in order to facilitate the use of Eurocode 3 for the designof such steel structures which are usual in common practice : braced or non-sway steelstructures.(2) Therefore, the "Design handbook according to Eurocode 3 for braced or non-sway steelbuildings" 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 beself-sufficient it does not substitute in any case for the com plete docum ent Eurocode 3 -Part 1.1, which should be consulted in conjunction with the NA D, in case of doubt o r needfor 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 therules specified in Eurocode 3 - Part 1.1.

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O.a.4 Ho w to read this design handbook(1) Exam ple of numbering of chapters and paragraphs : VIE . a . 1 . 2(2) Layout of pages :

| Ref. EC 3 for non-sway buildings - VI Members in tension Page 68 \ fleft column short titlefor references of the handbook tconcerned chapter tnumber of the page

Referencesk Main text with a following example about layout of chapters:(...) STRUCTURAL CONCEPT OF THE BUILDING(...)ILh(...)n.h.3(...)II.h.3.2

Material propertiesConnecting devices

(...) Welding consumables

(3) In the left co lumn of each page (Ref.): references to Eurocode 3 are always includedbetween brackets [...]; the other references are specified without brackets; the word"form." means "formula"(4) References to Eurocod e 3 are also given in the text between brackets [...]O.a. 5 Ackno wledgem ents(1) Particular thanks for fruitful collaboration are addressed to:

. 15 engineering offices : Adem (Belgium), Bureau Delta (Belgium), VarendonckGroep /Steeltrak (B elgium), VM Associate Partner (Belgium), Rambll,Hannem ann & Hjlund (Denmark), Bureau Veritas (France), Socotec (France),Sofresid (France), CPU Ingenieurbro (Germany), IGB-Ingenieurgrappe Bauen(Germany ), Danieli Ingegneria (Italy), Schroeder & Associs (L uxemburg),D3B N (the Netherlands), Ove Arup & Partners (United Kingdom), ECCS / TC 11(Germany),. RWTH : Steel Construction Department from Aachen University with ProfessorSEDLACEK G. and GROTMAN N D.,. SIDERCAD (Italy) with MM . BA ND INIM . and CATTANEO F.,. C n C M (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 researchn P2724(contract n 7210 - SA/513),. the F6 executive committee which has followed and advised the working g roupof the research,. anyone w ho has contributed to the work: MM. CON AN Y ves, MAUER Thierry,GERARDY LC.

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O.c Sym bols and notations

O.e.! Symbols[1.6] (1) Se e Ap pen dix A for a list of symb ols used in this design han dbo ok. Th ose symb olsare conform to Eurocode 3.

Q . C . 2 Convention for member axes[1.6.7] (1) Fo r steel me mb ers , the conven tions used for cross-sectio n axes are:

xx - alon g the memb er. generally:

yy - cross-s ection axis paralle l to the flangeszz - cross-s ection axis perp endic ular to the flanges or paral lel to the we b. for angle sections:

yy - axis parallel to the smalle r legzz - axis perpen dicula r to the smaller leg

. where necessary:uu - major axis (whe re this doe s not coin cide with the yy axis)vv - mino r axis (whe re this doe s not coin cide 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 ybe cau se it acts abou t the cross-sectio n axis parallel to the flanges.

0.C.3 Di men sio ns and axes of rolled steel sections(1) "asymmetrical" (I and D ) and "monosymmetrical" ( [, and L) rolled steel sectionsare shown in table 0. 1.

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0-C.4 Notations in flow-charts(1 ) AU the flow-charts appearing in the present design handbook should be read accordingto 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 tobe selected.- convention for flow-charts:

(FC ) Flow-chart number (x)Title,___L__,[ Assumption j Action: determination, calculation,

4 " > 2where : non-dimensional slenderness ratio calculated with a buckling length equalto the system lengthfv,: yie ld strengthA: area of the cross-sectionNsd' design value of the compressive forceN c r: elastic critical axial force ( = 2 / L 2, with L = system length)

: factor (= Li I, with L = system length)EI* ro w 10 : According to the definition of occr introduced in comment on row 8

.condition w hich is equivalent to, l < - ^ - < 0,25 4 < acr < 10* ro w 11:The actions to be considered in first order elastic global analysis and in second orderelastic global analysis are listed in the "generalities about Eurocode 3" (see the firstcom ments on flow-chart 1) in function of the type of frame.* rows 12.13.14 :

- path @: Sway moments amplified by factor 1,2 in beams and beam-to-columnconnections 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 mem ber imperfections eo,d should beconsidered equivalent to the introduction of distributed loadsalong the members :eo,dNsd Nsd

equivalent toqNsd

w i m i q = 8.NSd.e0,d/L2| Q = 4 . N S d . e 0 < d /LNote : the equivalence of eo,d and (q, Q) loading is proposed here for a practical point ofview but it is not included in E urocode 3.

Nsd , ;i

Q

i ', L ,0

6 0


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[Annex J] Semi-rigid connections may be used, provided that they can be dem onstrated to prov idesufficient reliable rotational stiffness (see [6.9.4]) to satisfy the requirements for sway-modeframe stability (see [5.2.6]).(2) Fram ing for resistance to the horizontal loads and to sway. Tw o examp les are given intable 1.3:

[5.2.5.3 (i)] a) typical exa mp le of a frame with "bracing syste m" , wh ich could be sufficientlystiff:. for the frame to be classified as a "bracedframe". and, to assume that all in-plane horizontal loads are resisted by the bracingsystem.

[5.2.5.3 (2)] The criterion of classification as braced or unbraced frames is explained inchapter IV.g. 1.1.[5.2.5.2 (l)] b) example of an unbraced frame which could have sufficiently stiff moment-resist ing joints between the beams and the colum ns:. for the frame to be classified as a "non-sway frame". and, to neglect any additional internal forces or moments arising fromin-plane horizontal displacements of the nodes of the frame.

[5.2.5.2 (3). (4)] The criteria of classification as sway or non-sway frames are detailed inchapter IV .g. 1.2.[Annex H] Table L3 Definition of framing for horizontal loads

1) With b racing s ystem :

wmm w,

ir m

f\ A LA L

i ' i ' " '

F R A M E W I T H B R A C I N G =2) Non-sway frames :

wWT iiflv wftrrB R A C E D F R A M E + B R A C I N G S Y S T E M

r y r r

* m

f l

w m

i lw n

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T.c.3 Sum marv of the table of contents- chapter I : . Limit States (SLS, UL S), design requirements;. flow-chart about elastic global analysis of steel frames according to EC 3.. scope, definitions;. tables of SLS and ULS checks;- chapter : com plete 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 chap ter I.c.4).

. ULS classifications of frames . braced frame condition and,. non-sway frame condition

- chap ter 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 colum ns,...) submitted to internalforces and mom ents (N, V, M) considering the resistance of cross-sections, the overall buckling of mem bers (buckling, lateral-torsionalbuck ling) 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 inducedbuckling): see chapter I.c.5- chapter X I : ULS and SLS checks of connections.- chapter : design of steel bracing system

I.c.4 Checks at Serviceability Limit States(1) The table 1.4 pre sents the different checks which shall be fulfilled by beams and framesat Serviceability Limit Stateswith references to the design handbook:|| Tab le 1.4 Checks at Serviceability Limit States

Type of checksBeamsFrames

Vertical deflectionsof beamsChapter Vm.b.lChapter Vin.b.l

Horizontaldeflections of frames_

Chapter IV .f.l

Vibration of floorsChapter VlII.b.2Chapter VIII.b.2

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II STRUCTURAL CONCEPT OF THE BUILDING

(1) Th is chapter intends to list the data of the analysed building concerning the types ofstructure, members and joints, the geometry and the material properties. The loadarrangements 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 ofthe project (office building, housing, sport or exhibition hall, parking areas,....) should bedefined.

Il l) Geom etric dimensions(1) The geometry of the building should be defined:- the height, the width and the length of the structure, the num ber of storeys of thebuilding and the dimensions of the architectural element.- definition of storeys: plane frame with 3 storeys :

II.C Non structural elemen ts(1) All the elemen ts of the building which do not bear any loads have to be considered in theevaluation 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, beam s, column s, bracingsystem, concrete core,....

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

Table IL2T ype of joint

Modelling of jointsModelling Behaviour

RIGID Joint

M1 1

Mu

SEM I-RIGID Joint

PINNED Joint

K>M

i S S v - S l* -

7 1


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III LOAD ARRANGEMENTS AND LOAD CASESIII.a Generalities

[2.2J5 (l)] (1) A load arrangement identifies the position, magnitude and direction of a free action.[2.25 (2)] (2) A load case identifies compatible load arrangem ents, set of deformations andimperfections considered for a particular verification.(3) For the definitions of actions Goad arrangemen ts: F= G, Q,...) and effects of ac tions (E , S)and for the design requiremen ts it should be referred to chapter La (Basis of design) .(4) Flow-ch art 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 arrangem ents (F,for each load case the global analysis of the structure determines the design valuesfor the effects of actions (Ed = oV ,6h, f,... ; Sd = N, V , , ,...) which shall bechecked at SLS (Cd limits) and at ULS (Rd resistances).This general procedure is used in the flow-cha rts about elastic design of:steel frames (in general) (flow-chart F C 1; see chapter I) ,braced or non-sway frames (flow-chart FC 4; see chapter IV),bracing system (flow-chart FC 12; see chapter ),according to Eurocode 3. Moreover references to those general flow-charts FC 1, FC 4and FC 12 are specified at the different steps of the general procedure presen ted in theflow-chart FC 3 .1.(5) For braced or non-sway buildings it is explained in chapter I .b.l (flow-chart FC 1) and inchapter IV .a.2 (flow-chart FC 4) that the elastic global analysis of the structure could bebased on first o rder theory. In that case of first order elastic global analysis the principle ofsuperposition is applicable because the effects of actions (E, S) are linear functions of theapplied actions (F = G, Q,...) (no - effects and used ma terial with an elastic linearbehaviour).The principle of superposition a llows to consider a particular procedure to study structuressubmitted to actions . This procedure illustrated in flow-chart FC 3.2 could be m orepractical because it should simplify the decision of which load case gives the w orst effect.For each single characteristic (unfactored) value of load arrangement (Fk) the globalanalysis of the structure determines characteristic (unfactored) values for the effects ofaction s : 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 designvalues for the effects of actions (Ed = ,,, f,... ; Sd = N, V , M, ,...) which shall bechecked at SLS (Cd limits) and at ULS (Rd resistances).

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IIl.b Load arrangem ents(1) The following load arrangements are characteristic (unfactored) values of actions (Fk) tobe applied to the structure. The characteristic values of load arrangements given hereafterare issued from Eurocode 1 (/l/).(2) The table .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 thoseload arrangements.

Table .1 Load arrangements Fk for building design according to EC 1Load arrangem ents (Fk) Reference to the handbook

1 ) Permanent loads : distributed, gconcentrated, G ni .b . l2) Variable loads:

Imposed loads on floors and roof:- Wind loads:

Snow loads:

distributed, qconcentrated, Qwind pressure, w e4wind force, F wdistributed, s

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

ECl1.5.1 (4)

ECl1.5.1 (4)

ECl2.1.5.1. (1)

ECl2.1.6.1. (1)

. b. 1 Permanent loads (g and G)(1) Action which is likely to act throughout a given design situation and for which thevariation in magn itude with time is negligible in relation to the mean value, or for w hich

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 thevariation in magn itude w ith time is not negligible in relation to the m ean value normonotonie.m.b.2.1 Imposed loads on floors and roof (q and Q )(1) Categories of areas: areas in offices, housing, warehouses, parkings, dw ellings, etc. aredivided into six categories according to their specific use:

- Category A:- Category B :- Category C:- Category D:- Category E:- Category F:

areas for domestic and residential activities.areas w here people may congregate.areas susceptible to overcrowding, including access areas.areas susceptible to accumulation of goods, including access areas.traffic and park ing areas for light vehicles,traffic and parking areas for m edium vehicles.

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

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ECl,Fig. 6.8.1EClTable 6.8.1

1 Table III.4 Exposure coefficient ce as a function of height above groundTerrain Category:

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

z(m)1000 , ,

inn -1UVJ

10 -

1 _0,1

X) 1,130 2,(X) 3,1

IV TTT

X) 4,1C e(' I

) 5,00 )

where cECl, able6.10.2.1

Peis the external pressure coefficient given in ECl, 6.9, wh ich d ep en d o n thesize of the effected area A and the shape of the building (se e table .5 ).

Table .5 External pressure Cpe for buildings depending on the sizeof the effected area ACpe = Cpei

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

A < l m 21 m 2 < A < 10 m 2

A > 10 m 2

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

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m . c. 2 Load cases for ultimate limit statesECCSn65table 2.1 Table .8 Combinations of actions for ultimate limit state

Load combinations to be considered:with only the most unfavourable variableactions (Qk.max): * *1. YG-XGk+YQ-Qk.maxl,35*.EGk+l,50**.Qk.maxwith all unfavourable variable actions (Qk):Y GE Gk+0,9YQ.XQ k2. l , 3 5 * . ] T G k + l , 3 5 * * . Q k* If the dead load G counteracts the variableaction Q(meaning a favourable effect of G):YG = LOO

' '' t " M " , windload Qdeadload Gt itt -

"if the variable load Q counteracts the dom inantloading (meaning a favourable effect of Q):YQ = 0

G k -Q k -

Qk.maxY G -

Y Q -

permanent actions, e.g. self weightvariable actions, e.g. imposed loadson floors, snow load, wind loads-the variable action wh ich causes thelargest effectpartial safety factor for permanentactionspartial safety factor for v ariableactions

T he load com bination w hich gives the largest effect (i.e.internal forces or mom ent ) is decisiveECCSn0 65table 2.2 Table .9 Examples for the application of the combinations rules in table .8.All actions (g, q, P, s, w) are considered to originate from different sourcesEUmsqJA A

L X L T E D q* O i i i Q M D s * i g-A

load cases1 .2.3 .1 .2.3 .4 .

combinations of actionsl,35.g+l,50.ql,35.g+l,50.sl,35.(g + q + s)l,35.g+l,50.qLSS.g+LSO.P*)1,35. g+1 ,50. sL 3 5 . ( g + q + s + P* ))

qw E E E E D g

1 .2.3 .4 .

l,35.g+l,50.wl,35.g+l,50.q1,35. g+1 ,50. sl,35.(g + q + w + s)g -q -P -s -w -

dead loadimposed loadPoint loadsnow loadwind load

) assuming is independen t of g, q, s and w

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T a b l e I V . l Modelling of frame for analysis1. Separation of plane frames from the spacial frame :

FRAME 2

Tflrr

2. Separation of individual members from plane frame:

FRAME 1K t t

M lcHnWIsolated beam 77TIsolated column

N1 + N2

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[5.2.5.2]comm ents (3/4) on flow -chart FC 4 :* row 14: classification of sway or non-swav frame:A frame may be classified as non-sway if according to first order elastic global analysisof 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)]

or,[5.2.5.2(4)]

where Vsa:V cr :

a c

^ - = < 0,1 acr "-cr , condition which is equivalent to aCT> 10design value of the total vertical load (see row 1 0)elastic critical value of the total vertical load for failure in a sway mode( = 2 / L2 with L, buckling length for a column in a sway mode; VCT ofa column does not correspond necessarily to V c r of the frame including thatcolumn)coefficient of critical amplification or coefficient of remoteness of criticalstate of the fram eb) in case of building structures with beams connecting each columns at each storey level:

- ( - - 2 )h . H h . ( H 1 + H 2 ) < 0,1

wh ere H , V: total horizontal and vertical reactions at the bottom of the storey,: relative horizontal displacement of top and bottom of the storey,h: height of the storey. , , are deduced from a first order analysis of the frame submitted to bothhorizon tal and vertical design loads (see row 10) and to the globalimperfections of the frame applied in the form of equivalent horizontalforces (see comments on row 1 2).Notes:- A same frame could be classified as sway according to a load case (Vsd l forinstance) and as non-sway according to another load case ( Vsd2 for instance)(seerow 13). V - = maximum sdiFor m ulti-storeys buildings the relevant condition iscondition which is equivalent to otcr = minimum (oten),V Vcri

where>sdi

VV v c n y or acrj are related to the storey i.

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comm ents (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 shouldbe 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 thes y vcriterion ^ has been chosen (rows 9 to 13).h2)HThe load cases should consider specific actions in case of braced or non-sw ay framesas 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

actionstypes offrames

the verticalloads the horizontalloads the globalimperfections of theframe(row 12)'1) braced frames ($ X(b)2) non-sway frames (c)

15.253 (3)]

[5.2.5.3(5)]

Notes : (a) braced frames are frames which may be treated as fully supported laterally by abracing system.(b) only the part of horizontal loads which are applied to the frame but not assumedto be transmitted to the bracing system through the floors.(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 checksof memb ers, cross-sections and webs (rows 18 to 21).[Annex E] * row 17: Lh, buckling length of members for non-sway mode

Nsd c ^Lb

* rows 18 19,2Q> 2h 22;The sequence of the Ultimate Limit States checks is not imposed an d it is up to thedesigner to choose the order of the ULS checks which are anyhow all necessary tobe fulfilled. On the contrary , the sequence of steps to define the assum ptions forthe global analysis (row IS) is well fixed and defined in rows 8 to 14.

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I V.b Static equilibrium[2.3.2.4] (1) For the verifica tion of static equ ilibrium , destab ilizing (unfavourab le) actions shall berepresented by upper design values and stabilizing (favourable) actions by lower designvalues.

(2) For s tabilizing effects, only those actions which can reliably be assumed to be present inthe situation considered shall be included in the relevant combination.(3) Variable actions should be applied where they increase the destabilizing effects butom itted w here they w ould increase the stabilizing effects (> = 0, in table III.8 ).(4) Acco unt should be taken of the possibility that non-structural elements m ight be om ittedor removed.(5) For building structures, the normal partial safety factor given in table .8 of chapter apply to permanent actions (YG = 1,0 if favourable actions).(6) W here uncertainty of the value of a geom etrical dimension significantly affects theverification of static equilibrium, this dimension shall be represented in this verificationby the most un favourable value that it is reasonably possible for it to reach.I V.c Load arrangem ents and load casesrv.cl General i t ies(1) Load arrangem ents which may be applied to buildings are provided in chapter ULb.(2) Load cases (see chapter ni .c) m ay be established according to two procedures to studystructures subm itted to actions:

a general procedu re presented in flow-chart FC 3.1 (chap ter ) or,a particular procedure presented in flow-chart FC 3.2 (chapter ) which isapplicable for braced or non-sway buildings because such structure may be studiedby first order elastic global analysis.

(3) Tw o 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 .7 for SLS combinations of actionssee table .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 (seechapter X II).(2) In case of non-sway frame global imperfections are needed for the design of the frame.

[5.2.4.1 (l)] (3) Ap prop riate allow ances shall be incorporated to cover the effects of practicalimperfections, including residual stresses and geometrical imperfections such as lack ofvertically, lack of straightness due to welding or lack of fit and the unavoidable m inoreccentricities p resent 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 or,- equivalent horizontal forces according to table IV.3, either method is perm issible.

(5) As shown in table IV.3 the initial sway imperfections of a frame are directly proportionateto the relevant applied vertical loads of each load case.Therefore global imperfections of a frame should be calculated for each load case.

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Table IV .3 Global imperfections of the frameECCS 65table 5 J

Initial sway imperfections of the fram e equivalent horizontal forcesF2 2

Fi

tel

'

1 i i i F il i l i -

y ^ ' (Fi + F2) (Fi + F2)

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

where = 5 5 'k c= J o , 5 + < 1,0 andV n rk g = j 0 , 2 +


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[4.2.2 (4)]

ECCS n65table 4 .3

IV.f. 1 Deflections of frames(1) The limiting values for horizontal deflections of frames given in table IV.6 areillustrated by reference to the multi-storey and single-storey fram e.Table IV.6 Recommended limits for horizontal deflections

Multi-storey frame2

< hi / 300 2 < h2 / 300 o < h 0 / 5 0 0

Single storey frame

Portal fram e w ithoutgantry cranes < h / 150Other buildings < h / 3 00

[5.2.5.3]

IV .g V erifications at ULSIV. g. 1 Classification of the frameIV.g.1.1 Hypothesis for braced frame(1 ) Exam ples of bracing system are mentioned in chapter I.b.2 and in chapter .

[5.2.5.3 (2)] (2) A steel fram e may be classified as braced if the bracing system reduces its horizontaldisplacements by at least 80 %.(3) For practical presentation of the criterion used to classify a frame as braced referencemay b e made to comments on row 11 of flow-chart 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 theframe and on hypothetic horizontal loads, the frame should be classified as braced or notindependen tly of load cases.rv.q.1.2 Hypothesis for non-swa v frame(1) Exam ples 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 non-sway referencemay b e made to comments on row 14 of flow-chart FC 4 (see chapter IV.a .2.3 ).(3) As the criterion of sway or non-sway frame classification depends on the total vertical

load, a same frame could be classified as sway according to a load case and as non-swayaccording to another load case. Therefore the criterion of sway or non-sway frameclassification should be checked for each load case.rv. g. 2 ULS checks(1) T he frames shall be checked at ultimate limit states for the resistances of cross-sections,mem bers and connections. For those ULS checks reference may be m ade to the followingchapters:- Classification of cross-sections:- M embers in tension:- Members in compression:- Members in bending:

- M embers with combined axial force and bending mom ents:- Transverse forces on webs:- Connections:

[5.1.2(1)]

see chapter Vsee chapter VIsee chapter VHsee chapter VIIIsee chapter LXsee chapter Xsee chapter X I

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

1

10 h

11

Determine = V 235 / fy

Irows:

1

Division of the cross-section into elements:web and flanges JClass of cross-section =highest class of all elements J

De term ine the slenderness of elem ent to classify : d/tw, c/tf,... J( Ty pe of loading on elem ent to classify J1 1I Compression ;Ncomp. BendingM

ye s

1 Combined + axial load and bending moment Determine the position of neutral axiswith plastic distribution of stresses

Class 3 element ?to*)Class 4 element.with local buckling

^ C l a s s 1 or 2 e l e m e n t ^X (*) /

J

i lyes s Class 3 element ?(*)no l> Class 4 elementith local buckling

- ^ C l a s s 1 o r 2 e le m en t \

Determine the position of neutral axiswith elastic distribution of stresses J2X (**) fno 10

( Class 4 elementUd th local buckling u

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

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( F C 5 . 2 ) :low-chart IFC5.21 : Calculation of effective cross-sectio

Eurocode 3 Simplified

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