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Frame design according to the European design code of practice (Eurocode 3)
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ISSN 1018-5593
European Commission
technical steel research
Properties and service performance
Simplified version of Eurocode 3 for usual buildings
STEEL RESEARCH
European Commission
technical steel research Properties and service performance
Simplified version of Eurocode 3 for usual buildings
P. Chantrain, J.-B. Schleich ARBED recherches
BP 141 L-4009 Esch-sur-Alzette
Contract No 7210-SA/513
1 July 1991 to 30 June 1994
Final report
Directorate-General Science, Research and Development
1997 EUR 16839 EN
LEGAL NOTICE
Neither the European Commission nor any person acting on behalf of the Commission is responsible for the use which might be made of the following information.
A great deal of additional information on the European Union is available on the Internet. ! It can be accessed through the Europa server (http://europa.eu.int)
Cataloguing data can be found at the end of this publication.
Luxembourg: Office for Official Publications of the European Communities, 1997
ISBN 92-828-1485-8
European Communities, 1997 [ Reproduction is authorised provided the source is acknowledged.
Printed in Luxembourg I
SIMPLIFIED VERSION OF EIIROCODE 3 FOR USUAL BUILDINGS. ECSC Agreement 7210-SA/513
Summary
The aim of the following E.C.S.C. research is to elaborate a simple but complete document to design commonly used buildings in steel construction. This document is completely based on Eurocode 3 and each paragraph is totally conform to Eurocode 3. Only the design formulas necessary to design braced or non-sway buildings are taken into account in this document. Tall buildings (skyscrapers) and halls are not treated. The designers and steel constructors are able to calculate and erect a commonly used steel building with this design handbook. Therefore also the important load cases from Eurocode 1 will be included in this document.
The working group of the research project was constituted of 10 European engineering offices. Firstly that working group has carried out different examples of calculation of braced or non-sway buildings according to Eurocode 3 Part 1.1: check of existing steel structures and design of new steel buildings. Afterwards thanks to those examples of calculation the needed design formulas of Eurocode 3 was highlighted and general procedure of design was determined. The design handbook "Simplified version of Eurocode 3" is based on that experience.
The link of the working group to the drafting panel of Eurocode 3 was guaranteed by the Professor Sedlacek of Aachen University.
Liaison has been ensured with both other E.C.S.C. research projects nr SA/312 and nr S A/419 also dealing with Eurocode 3: respectively, "Application software of Eurocode 3: EC3-tools" (CTICM, France) and "Design handbook for sway buildings" (CSM-Italy).
VERSION SIMPLIFIEE DE L'EUROCODE 3 POUR LES BATIMENTS COURANTS Agrment CECA 7210-SA/513
Sommai re
Le but de cette recherche est d'laborer un document simple mais complet pour calculer des btiments courants en construction mtallique. Ce document est entirement bas sur l'Eurocode 3 et chaque paragraphe est totalement conforme VEurocode 3. Il n'a t pris en compte que les formules ncessaires au calcul de btiments contrevents et rigides. Les btiments trs lancs (gratte-ciel) et les halls industriels n'y sont pas traits. Les bureaux d'tudes et constructeurs mtalliques devront tre capables de calculer et d'riger un btiment courant en acier avec ce manuel de dimensionnement. Les cas de charges le plus importants issus de l'Eurocode 1 seront galement inclus dans ce document.
Le groupe de travail du projet de recherche tait constitu de 10 bureaux d'tudes europens. En premire partie ce groupe de travail a effectu diffrents exemples de calculs de btiments contrevents et rigides conformment l'Eurocode 3 Partie 1.1: vrification de structures en acier dj existantes et dimensionnement de nouveaux btiments en acier. Grce ces exemples concrets de calcul, les formules de l'Eurocode 3 utiles au dimensionnement ont t mises en vidence et une procdure gnrale de dimensionnement a t dtermine. Le manuel de dimensionnement "Version simplifie de l'Eurocode 3" se base sur cette exprience.
La jonction entre le groupe de travail et le groupe de rdaction de l'Eurocode 3 a t faite par le professeur Sedlacek de l'Universit d'Aix-La-Chapelle.
Une collaboration a t assure 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 btiments souples ( nuds dplaables)" (CSM, Italie)
VEREINFACHTE VERSION DES EUROCODE 3 FR BLICHE GEBUDE. EGKS Zulassung7210-SA/513
Zusammenfassung
Dieses EGKS Forschungsprojekt hat zum Ziel, ein einfaches aber vollstndiges Dokument fr allgemeine (bliche) Stahlbaubemessung auszuarbeiten. Dieses Dokument ist vllig auf Eurocode 3 basiert und jeder Paragraph pat genau zu Eurocode 3. Nur die Bemessungsformeln, die notwendig sind fr ausgesteifte oder unverschiebliche Tragwerke , werden bercksichtigt. Hochhuser (Wolkenkratzen) oder Hallen werden nicht behandelt. Die Ingenieurbros und Stahlkonstrukteuren haben die Mglichkeit mit diesem Design-Handbuch einen einfachen Stahlbau zu berechnen und zu bauen. Dafr sind die wichtigsten Lastflle von Eurocode 1 in diesem Dokument beinhaltet.
Die Arbeitsgruppe des Forschungssprojekt bestand aus 10 europischen Ingenieurbros. Die Arbeitsgruppe hat, im ersten Teil dieses Forschungsvorhabens, verschiedene Berechnungsbeispiele mit ausgesteiften oder unverschieblichen Tragwerken nach Eurocode 3 Teil 1.1 durchgefhlt : Berechnungs-Nachweis einer existierenden Stahlstruktur und Dimensionierung eines neuen Stahlbaus. Anschlieend 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 Universitt 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 11 3.1. Exercise 1 : Verification of an existing braced or non-sway structure 11
3.2. Exercise 2: Verification of a non-sway wind bracing in a building 1 2
3.3. Exercise 3: Design of a braced or non-sway structure 1 2
4. Part 2 : Design handbook 12
FIGURES (Ito 8)
APPENDICES 15 List of symbols (6 pages) 23 List of tables (3 pages) 29 List of flow-charts (1 page) 32
"Design handbook according to Eurocode 3 for braced or non-sway steel buildings" 33 (short title : "EC3 for non-sway buildings") (196 pages)
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
2
3
4
6
7
9
10
13
14
16
Engineering office
Adem
Bureau Delta
Varendonck Groep / Steelrrack
Ramboll & Hanneman
Bureau Veritas
Socotec
Sofresid
Danieli Ingegneria
Schroeder & Associs
D3BN
City
Mons
Lige
Gent
Copenhagen
Courbevoie
Saint-Quentin-Yvelines
Montreuil
Livorno
Luxembourg
Nieuwegein
Country
Belgium
Belgium
Belgium
Denmark
France
France
France
Italy
Luxemburg
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
5
12 18 19
Engineering office
Verdeyen & Moenart Associate Partner
Ingenieur gruppe Bauen Ove Arup & Partners
ECCS-TCll
City
Bruxelles
Karlsruhe London
Kiel
Country
Belgium
Germany United
Kingdom Germany
10
-some members of CTICM (France) and SIDERCAD (Italy) involved in complementary research projects about simplified approaches of Eurocode 3 (respectively, "Application software of Eurocode 3 : EC3-tools" and "Design handbook for sway buildings") :
. which participated to the meetings of the full working group,
. and with which a general flow-chart (FC1) about elastic global analysis of steel frame according to EC3 has been established.
3. Part 1 : Worked examples
In order to find the needed formulae and to familiarise the engineering offices to the Eurocodes, it has been decided to perform 3 different exercises (check and design of a steel structure),
- exercise 1: verification of an existing braced or non-sway steel structure, - exercise 2: verification of a non-sway steel wind bracing in a building, - exercise 3: design of a braced or non-sway steel structure,
Different drawings issued from the exercises of the offices are enclosed in the technical report n 4 (TR4) showing the type of the calculated buildings and some details :
- office building with bracing system (engineering offices n 2, 9 and 16), (Annex 1 of TR4); -
- car park (engineering office n 3), (Annex 2 of TR4); - residential building with bracing system (engineering office n 7), (Annex 3 of TR4); - office building with bracing system (engineering office n 10), (Annex 4 of TR4); - industrial building with catalytic reactors (engineering office n 13), (Annex 5 of TR4); - office building with concrete core (engineering office n 14), (Annex 6 of TR4); - office building with concrete core (engineering office n 4), (Annex 7 of TR4); - office building with bracing system (engineering office n 6), (Annex 8 of TR4).
3.1. Exercise 1 : Verification of an existing braced or non-sway structure
The flow-chart of figure 1 shows the procedure followed for the verification of an existing building with the Eurocodes 1 and 3. This first exercise aimed to find the needed formulae given by the Eurocodes in order to check the safety of the different limit states.
This exercise was not an iterative processes, but was only a verification procedure of an existing braced or non-sway building.
The flow-chart of figure 1 is divided into 3 subjects:
a. The "Keywords" representing the different steps of a check procedure. 1. conceptional type of structure. 2. occupancies. 3. shape. 4 structural concept. 5 action effects. 6. design and verification.
b. The "Requirements and References" of each step of the verification. The references are Eurocode 1, Eurocode 3 and the product standards EN 10025 and EN 10113.
c. The "Object" describing each step of the verification.
11
3.2. Exercise 2: Verification of a non-sway wind bracing in a building
The non-sway wind bracing consisted of a latticed steel structure. The flow-chart of figure 2 gives the procedure of the verification of this wind bracing. This exercise was also not an iterative process.
The description of the present flow-chart (figure 2) is the same than in the first example presented in the chapter 3.1 (figure 1).
3.3. Exercise 3: Design of a braced or non-sway structure
After the two first exercises, the engineering offices were familiarised with the Eurocodes 1 and 3. They were able to perform a complete design of a structure by using an iterative procedure. The aim of this exercise was to analyse the way to find a good solution.
This exercise allowed us to follow step by step the calculation of a structure in practice. The practical design handbook about the simplified version of the Eurocode 3 follows an improved way than the one defined in the initial design procedure. The figure 3 shows the different data for the design and the type of chosen optimisation. The Figure 4 gives the type of building to be designed.
4. Part 2 : Design handbook
A list of the needed formulae taken from the Eurocode 3 has been established following the initial procedure defined for the exercises (see figures 5 to 8). This initial design procedure nearly corresponds to the sequence of the chapters of Eurocode 3. It had to be adapted to common practice. The solved exercises E3 (design of a building) and the experience of each engineering office allowed to determine a more suitable design procedure which constitutes the frame of the design handbook.
About that practical design procedure reference may be made to the enclosed design handbook which is called "Design handbook according to Eurocode 3 for braced or non-sway 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 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, ; , 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 of the design handbook)
12
In general, for the design of buildings we need to :
- define the analysis model of frames (assumptions of plane frames, bracing systems, connections, members,...)
- characterise the load arrangements and load cases,
- carry out the elastic global analysis of frames in order to determine the effects of actions : . deformations (), 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 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.
All references to Eurocode 3 - Part 1.1 which appear systematically, are made in [...].
Any other text, tables or figures not quoted from Eurocode 3 are considered to satisfy the rules specified in Eurocode 3 - Part 1.1.
The lists of all symbols, tables and flow-charts included in the "Design Handbook" are enclosed to the present appendices.
13
1. conceptiqnal type of structure nonsway wind bracing in a building
(latticed structure ) . . 2. occupancies
EC 3: Classification nonsway :VSd / VCT b /1 classification
5. action effects determination of the action effects
(global and local) elastic or plastic model
SLS ULS
6. dirnehsioning and verification
EC 1: Load cases EC 3: Load combinations
EC 3: Imperfections EC 3: Modelling depending on
b / 1 classification 1 s t order analysis
SLS limits deformations
vibrations
ULS limits Frame stability Static equilibrium Resistance 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 buckling Resistance of members (stability)
- compression members : buckling - lateral torsional budding of beams - bending and axial tension - bending and axial compress ion
Connection -joints baae of columns
Legend
Keywords WB
Requirement & References C Object
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)
Floor structure (not defined) Material properties (not defined)
I 5. action effects determination of the action effects
(global and local) elastic or plastic model SLS t ULS t 6. dimensioning and verification
SLS limits deformations
vibrations
7. optimisation of the weight
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
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 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
front view
ce
I CA C
!
I I
Reference number
2 6 7 9 10 13
Engineering office Adem
Rambll, Hannemann & Hjlund Veritas Socotec Sofresid Danieli
n 1 2 3 4 5 6
X (m) 30 30 50 50 50 50
Y (m) 10 10 14 14 18 18
storeys n = 5 15 10 15 20 15
Joints Rigid Rigid
Hinged Hinged Rigid
Hinged Exercise 3 : Type of building to be designed
Figure 4
18
i . C Eurocode 3 Formulae References 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: 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 (2.17) 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
19
Eurocode 3 Formulae References 6. Verification SLS. -> Chapter 4 6.1. Global analysis. -> beams, portal f rames,structural frames Calculation for
- > bracing system vertical and horizontal
6.2. Deformations.
6.3. Vibrations.
-> Chapter 4.2.2 clause (1) vertical table 4.1, figure 4.1 clause (4) horizontal
-> 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) => Av n e t > -2- ,i 0.9 U ' Mo
(remark: ym factors should be ignored) 7.2.4. shear.
> Chapter 5.4.6 clause (1) formula (5.20) clause (2): Ayz
Avy: ECCS publication n65: 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 + (Mp1>Rd Mf>Rd) 1 VSd 'pl,Rd 1 ^ M c ,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 65: tables 5.15 and 5.16)
Figure 6
20
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)
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. bolted joints. -> Chapter 6.5 7.4.1.1. Positioning of holes.
-> Chapter 6.5.1 figures 6.5.1 to 6.5.4 (ECCSpublication n65: 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 of forces 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 n65: 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 -> 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 Welded connections.
[-> 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 J clause (1) formula (6.11) and figure 6.5.10 clause (2) formula (6.12)7 clause (1) formula (6.13)7 tables 6.5.6 and 6.5.7, figure 6.5.12 -> Chapter 6.5.67 -> Chapter 6.6 clause (3)7 clause (1) clause (4) clause (7) clause (2) clause (2) clause (1) Annex M clause (3) formula (6.14) clause (4) formula (6.15) clause (5) clause (2) formula (6.16) clause (3) clause (1)7 clause (3) formula (6.18)7 clause (2) clause (3)
7.4.4 Beam-to-column connections. -> Chapter 6.9 and Annex J 7.4.5. Column bases.
7.5. Frame stability. -> Chapter 5.2.6.1
7.6. Static equilibrium. -> Chapter 2.3.2.4
-> Chapter 6.11 and Annex L
clause (1) clause (3) clause (4)
clauses (1) to (12)
Figure 8
22
L Lb LTB Ly m max min M Mb.Rd MCT M c R d M
Mf.Rd
MN.Rd MN.VJld
MN.V.yJRd
MN.V.z.Rd
MN.y.Rd
MN.z.Rd Mpf MpRd Mp/iw.Rd Mpy.Rd MptzJRd MRd Msd Mv.Rd Mw.sd My My.Sd Mz Mz.sd rie nr n8 NAD Nbd Nb.yJld NbiJld 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 reduced design plastic resistance moment allowing for axial force and by shear force V reduced design plastic resistance moment about yy axis allowing for axial force and shear force V reduced design plastic resistance moment about zz axis allowing for axial force and shear force V reduced design plastic resistance moment about yy axis allowing for axial force reduced design plastic resistance moment about zz axis axial force 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
N R d Nsd NLRd rN tension Nu.Rd Nx.sd PlP2 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 VpRd VpiyJld VpzJld v R d 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) Wd design wind load w e wind pressure on external surface W welded sections Weff elastic section modulus of effective class 4 crosssection Weff.y elastic section modulus of effective class 4 crosssection according to yy axis Weff.z elastic section modulus of effective class 4 crosssection according to zz axis Wef elastic section modulus of class 3 crosssection Wey elastic section modulus of class 3 crosssection according to yy axis Wez elastic section modulus of class 3 crosssection according to zz axis Wpi plastic section modulus of class 1 or 2 crosssection Wpy plastic section modulus of class 1 or 2 crosssection according to yy axis WpZ plastic section modulus of class 1 or 2 crosssection according to zz axis x, xx axis along the member Xk characteristic value of the material properties y, yy principal axis of cross section (parallel to flanges, in general) z, zz principal axis of cross section (parallel to the web, in general) Ze reference height for evaluation of c e 2u Oreek symbols coefficient of frequency of the basis mode vibration coefficient of linear thermal expansion factor to determine the position of the neutral axis aa coefficient of critical amplification or coefficient of remoteness of critical state of the frame PA nondimensional coefficient for buckling M equivalent uniform moment factor for flexural buckling Ml/r equivalent uniform moment factor for lateraltorsional buckling My equivalent uniform moment factor for flexural buckling about yy axis equivalent uniform moment factor for flexural buckling about zz axis w non-dimensional coefficient for lateral-torsional buckling w correlation factor (for a fillet weld) YF partial safety factor for force or for action YG partial safety factor for permanent action YM partial safety factor for the resistance at ULS YMb partial safety factor for the resistance of bolted connections 7Ms.ser partial safety factor for the slip resistance of preloaded bolts TMW partial safety factor for the resistance of welded connections YMO partial safety factor for resistance at ULS of class 1,2 or 3 cross-sections
(plasticity or yielding) YMI partial safety factor for resistance of class 4 cross-sections
(local buckling resistance) partial safety factor for the resistance of member to buckling YM2 partial safety factor for the resistance of net section at bolt holes YQ partial safety factor for variable action relative horizontal displacement of top and bottom of a storey Ob horizontal displacement of the braced frame 5d design deflection 6dv design vertical deflection of floors, beams, . . . d design horizontal deflection of frames OHmax recommended limit of horizontal deflection in plane deflection of the bracing system due to q plus any external loads
27
List of symbols (6/6) deflection due to variable load (q) \, horizontal displacement of the unbraced frame vd design vertical deflection of floors, beams,... Vmax 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) 2 variation of the deflection of the beam due to the variable loading (Q) (state 2) displacement
J235 (with fy in N/mm2) 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 .y effective nondimensional slenderness of the member for buckling about yy axis . effective non-dimensional slenderness of the member for buckling about zz axis XLT 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 y 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 Hi 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 py reduction factor due to shear force Vy.sd pz reduction factor due to shear force Vz.sd normal stress Gq numerical values for the stabilizing forces of a bracing system GxEd,
2. List of tables in the "Design Handbook" List of tables (1/3) Pages of the 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
Table .1 Table .2 Table .3 Table .4
Table .5 Table .6 Table .7
Table .8 Table .1 Table .2 Table .3 Table .4 Table .5
Table .6 Table .7 Table .8 Table .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
SYMBOLS AND NOTATIONS Dimensions and axes of rolled steel sections INTRODUCTION Summary of design requirements Partial safety factor 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 ce as a function of height 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 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
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
29
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
List of tables (2/3) Pages of the Handbook
Table Table Table Table Table Table Table Table
vm.2 Vni.3 Vm.4 vm.5 vm.6 vm.7 Vffl.8 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
Classification of crosssection : limiting widthto thickness ratios for class 3 I crosssections submitted to different types of loading Buckling factor k
Table K.4 Table D.5 Table DC.6 Table DC.7 Table Di. 8 Table D.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 .1 Table .2 Table .3 Table .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 TRANSVERSE FORCES ON WEBS (F ; (F,N,V,M)) 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, ss Interaction formula of crippling resistance and moment resistance Effective breadth beff for web buckling resistance Compression flange buckling in plane of the web Maximum widthtothickness ratio d/tw CONNECTIONS 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 sup resistance per bolt and friction interface for 8.8 and 10. 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 DESIGN OF BRACING SYSTEM Load arrangements of the bracing system Bracing system imperfections Values for the equivalent stabilizing force Zq Bracing system imperfections (examples) APPENDK D List of references to Eurocode 3 Part 1.1 related to all check formulas at ULS
181
187 188 189 190 190 191 192 1*93 193
196 196 197 197 198 199 200 200 201 201 202 203 204 204 205 206
216 218 218 219
221
31
3. List of flow-charts in the "Design Handbook"
Chapter Elastic global analysis of steel frames according to Eurocode 3 General Details I
Comments (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 nonsway steel frames according to EC 3
General IV Details IV
Comments (4 pages) IV FC 5. l Classification of I crosssection V
(FC 5.2J Calculation of effective crosssection properties of Class 4 rv crosssection
(FC6.) (FC 6.11 Members in tension (Ntension)
( F C 6 . 2 ) Angles connected by one leg and submitted to tension
( F C 7 ) Members in compression (Ncompression)
VI
VI
vn vm (FC 8 Design of I members in uniaxial bending (Vz;My;(Vz,My)) or
(Vy;Mz;(VyJvIz); FC 12Elastic global analysis of bracing system according to
Eurocode 3 General Details
Comments (6 pages)
Pages
14 15 16 to 21
38
39
50 51 52 to 55
62
63
82
83
90 102
168 169 170 to 175
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 41 41 41 41 41 42 42 43 44 44 44 44 45 47 47
' 47
0.a O . u . l 0.a.2 0.a.3 O.a.4 0.a.5
O.b
O.c O.c.l O.c.2 0.C.3 0.C.4
O.d O.d.1 0.d.2
Foreword Generalities Objective of this design handbook Warning How to read this design handbook Acknowledgements
References
Symbols and notations Symbols Convention for member axes Dimensions and axes of rolled steel sections Notations in flow-charts
Definitions and units Definition of special terms Units
INTRODUCTION f La Basis of design ._
I.a.1 Fundamental requirements .R I.a.2 Definitions 7
I.a.2.1 Limit states ~ I.a.2.2 Actions 4 9 I.a.2.3 Material properties 4 9
I.a.3 Design requirements 50 I.a.3.1 General 50 I.a.3.2 Serviceability Limit States 50 I.a.3.3 Ultimate Limit States 50
Lb General flow-charts about elastic global analysis 53 I.b.l Flow-chart FC LElastic global analysis of steel frames according to EC 3 53
Lb. 1.1 Flow-chart FC 1: general 53 I.b.1.2 Flow-chart FC 1: details 53 I. b. 1.3 Comments on flow-chart FC 1 56
Le Content of the design handbook 61 I.c.1 Scope of the handbook 61 I.C.2 Definition of the braced frames and non-sway frames 62 I.C.3 Summary of the table of contents 64 I.C.4 Checks at Serviceability Limit States 64 I.C.5 Checks of members at Ultimate Limit States 65
35
TABLE OF CONTENTS 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 \?
n.h.3.1 Bolts 7 5 U.h.3.2 Welding consumables 76
n.h.4 Design values of material coefficients 76 m LOAD ARRANGEMENTS AND LOAD CASES 77
ULa Generalities 77 ni.b Load arrangements 80
m.b.l Permanent loads (g and G) 80 m.b.2 Variable loads (q, Q, w and s) 80
III.b.2.1 Imposed loads on floors and roof (q and Q) 80 m.b.2.2 Wind loads (we,i, Fw) 81 m.b.2.2.1 Wind pressure (we) 81 m.b.2.2.2 Wind force (Fw) 84 m.b.2.3 Snow loads (s) 84
ULc Load cases 85 m.c.l Load cases for serviceability limit states 85 m.c.2 Load cases for ultimate limit states 86
IV DESIGN OF BRACED OR NONSWAY FRAME 87 rV.a Generalities 87
IV.a.l Analysis models for frames 87 IV.a.2 Flowchart FC 4:Elastic global analysis of braced or nonsway steel frames
according to Eurocode 3 89 IV.a.2.1 Flowchart FC 4 general 89 rV.a.2.2 Howchart FC 4 details 89 rv.a.2.3 Comments on flowchart FC 4 92
rv.b Static equilibrium 96 rv.c Load arrangements and load cases 96
IV.c.l Generalities 96 IV.C.2 Frame imperfections 96
rV.d Frame stability 97 rv.e First order elastic global analysis 98
rV.e.l Methods of analysis 98 IV.e.2 Effects of deformations 98 IV.e.3 Elastic global analysis 99
rv.f Verifications at SLS 99 rv.f.l Deflections of frames 100
rv.g Verifications at ULS 1 0 rv.g.l Classification of the frame *00
rv.g. 1.1 Hypothesis for braced frame *00 rv.g. 1.2 Hypothesis for nonsway frame 100
rv.g.2 ULS checks 100
36
TABLE OF CONTENTS V CLASSIFICATION OF CROSS-SECTIONS
V.a Generalities 101 V.b Definition of the cross-sections classification 104 V.c Criteria of the cross-sections classification 106
V.c. 1 Classification of compression elements of cross-sections 106 V.C.2 Classification of cross-sections 106 V.c.3 Properties of class 4 effective cross-sections 106
V.d Procedures of cross-sections classification for different loadings 109 V.d. 1 Classification of cross-sections in compression 109 V.d.2 Classification of cross-section in bending 109 V.d. 3 Classification of cross-sections in combined (N,M) 110
VI MEMBERS IN TENSION (Ntension) 121 Vl.a Generalities 121 VLb General verifications at ULS 124
Vl.b. 1 Resistance of gross cross-section to Ntension 124 VI.b.2 Resistance of net cross-section to Ntension 125
VLc Particular verifications at ULS for angles connected by one leg 126 VI.c. 1 Connection with a single row of bolts 126 VI.C.2 Connection by welding 128
VII MEMBERS IN COMPRESSION (NCOnipression) 129 Vn.a Generalities 129 VILb Classification of cross-sections 132 VII.c General verifications at ULS J 33
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 133 Vn.c.2.2 Resistance to torsionnal buckting and to flexural-torsional buckling 137
VILd Particular verifications at ULS for class 4 monosymmetrical cross-section J38 VILd. 1 Resistance of cross-section to Ncompression ^ VII.d.2 Stability of member to Ncompression ^ 8
VILe Particular verifications at ULS for angle connected by one leg 139 VILe. 1 Connection with a single row of bolts 139
Vn.e. 1.1 Resistance of cross-section to NCOmpression ^ 9 Vn.e. 1.2 Stability of member to Ncompression 139
VII.e.2 Connection by welding 139 Vn.e.2.1 Resistance of cross-section to Ncompression 139 Vn.e.2.2 Stability of member to NCOmpression 139
VIII MEMBERS IN BENDING (V ; M ; (V, M)) 140 VHLa Generalities 140 VHLb Verifications at SLS 145
Vm.b.l Deflections 145 Vin.b.2 Dynamic effects - vibrations 147
VIII.c Classification of cross-section 147 VIILd Verifications at ULS to shear force Vsd 148
Vin.d. 1 Resistance of cross-section to Vsd 148 VIII.d.2 Stability of web to Vz.sd 150
Vin.e Verifications at ULS to bending moment Msd 152 Vin.e. 1 Resistance of cross-section to Msd 152 Vm.e.2 Stability of member to My.sd I53
Vin.f Verifications at ULS to biaxial bending moment (My.sd> Mz.sd) 156 Vin.f. 1 Resistance of cross-section to (My.sd, Mz.sd) 156 Vm.f.2 Stability of member to (My.sd, Mz.sd) 157
37
161
TABLE OF CONTENTS Vm.g Verifications at ULS to combined (Vsd, Msd) 157
Vrn.g.1 Resistance of cross-section to (Vsd. Msd) 157 Vin.g. 1.1 Shear force Vsd and uniaxial bending Msd 157 Vin.g. 1.2 Shear force Vsd and biaxial bending moment Msd 158
Vm.g.2 Stability of web to (Vz.Sd,My.Sd) 159 LX MEMBERS WITH COMBINED AXIAL FORCE AND
BENDING MOMENT ((N, M) ; (N, V; M)) Di.a Generalities 161 K.b Verifications at SLS 167
LX.b.l Deflections 167 LX.b.2 Vibrations 167
DC.c Classification of cross-section 167 DCd Verifications at ULS to (N,M) 167
LX.d. 1 Resistance of cross-section to (Nsd, Msd) 1 ^ 7 LX.d. 1.1 Uniaxial bending of class 1 or 2 cross-sections 167 LX.d. 1.2 Biaxial bending of class 1 or 2 cross-sections 170 LX.d. 1.3 Bending of class 3 cross-sections 170 LX.d. 1.4 Bending of class 4 cross-sections 171
LX.d.2 Stability of member to (Nsd,Msd) 171 K.d.2.1 Stability of member to (Ntension My.sd) 171 LX.d.2.2 Stability of member to (Ncompression* Msd) 172
DC.e Verifications at ULS for (N$d ,Vsd) 1 7 6 LX.e.l Resistance of cross-section to (Nsd.Vsd) I 7 7
JX.f Verifications at ULS to (Nsd ,Vsd,Msd) 1 7 7 LX.f.l Resistance of cross-section to (Nsd>Vsd>Msd) ^7^
LX.f. 1.1 Uniaxial bending of class 1 or 2 cross-section 178 LX.f. 1.2 Biaxial bending of class 1 or 2 cross-section 180 LX.f. 1.3 Bending of class 3 cross-section 180 LX.f. 1.4 Bending of class 4 cross-section 181
LX.f.2 Stability of web to (Nx.Sd, Vz.Sd, My.Sd) 182 X TRANSVERSE FORCES ON WEBS (F ; (F, N, V, M)) 184 X.a Generalities 184 X.b Classification of cross-section 185 X.c Resistance of webs to (F,N,V,M) I85
X.C.1 Yield criterion to (F,N,V,M) 185 X.c.2 Crushing resistance to F 187
X.d Stability of webs to (F ; (F, M)) 188 X.d.l Crippling resistance to (F;(F, M)) 188
X.d. 1.1 Crippling resistance to F 188 X.d. 1.2 Crippling resistance to (F,M) 188
X.d.2 Buckling resistance to F 189 X.e Stability of webs to compression flange buckling 190
XI CONNECTIONS 191 XLa Generalities 191 XI.b Bolted connections 191
XLb. 1 Positioning of holes 191 XI.b.2 Distribution of forces between bolts 191 XI.b.3 Prying forces 193 XI.b.4 Categories of bolted connections 193 XI.b.5 Design ULS resistance of bolts 194
XI.b.5.1 Bearing resistance 194 XI.b.5.2 Shear resistance 196
XI.b.5.2.1 General case 196
38
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
XII DESIGN OF BRACING SYSTEM XILa Generalities
XILa. 1 Flow-chart FC 12:Elastic global analysis of bracing system according to 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 A : List of symbols
EC 3
APPENDIX APPENDIX C APPENDIX D
List of tables List of flow-charts List of references to Eurocode 3 Part 1.1 related to all check formulas at ULS
196 197 197 197 198 198 198 198 198 199 199 199 200 200 201 201 202 202 202 202 203 203 203 203 203 206 212 212 212 213 216 216 216 216 216 216 216
217 223 226 227
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 : | Ref. EC 3 for non-sway buildings - VI Members in tension Page 68
\ f left column short title for references of the handbook
t concerned chapter
t number of the page
References k
Main text with a following example about layout of chapters: (...) STRUCTURAL CONCEPT OF THE BUILDING (...) ILh (...) n.h.3 (...) II.h.3.2
Material properties
Connecting devices
(...) 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), Rambll, Hannemann & Hjlund (Denmark), Bureau Veritas (France), Socotec (France), Sofresid (France), CPU Ingenieurbro (Germany), IGB-Ingenieurgrappe Bauen (Germany), Danieli Ingegneria (Italy), Schroeder & Associs (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
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) (EC1)
HI Eurocode 3, ENV 1993-1-1, Design of steel structures Part 1.1 General rules and rules for Buildings (EC3)
131 Eurocode 8, draft version, Design of structures for earthquake resistance (EC8) 141 ECCS technical publication n65, 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 n71, Examples to Eurocode 3,1993, First Edition 161 "Design handbook for sway buildings", from Sidercad (Italy) I 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 mtallique, n 1-1991.
43
O.c Symbols and notations
O.e.! Symbols
[1.6] (1) See Appendix A for a list of symbols used in this design handbook. Those symbols are conform to Eurocode 3.
Q.C.2 Convention for member axes
[1.6.7] (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 My 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" ( [ , 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 ) Flowchart number (x)
Title ,___L__, [ Assumption j
Action: determination, calculation,
<
I ^ Z 7 o ^ o , y ^ otherflowchax,number(y)
yes 1 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
1 =tf +
I
" ? '
y 7
*
7e
y
t t f y
Htw
46
O.d Definitions and units
iLdJ Definition of special terms [14.2 (i)] (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 three-dimensional 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 - effects). Second order global analysis: Global analysis taking into account the deformation of the structure which influences the effects of actions (- 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 cross-section is based on its plastic resistance (see chapter V about classification of cross-sections). 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 ilniiS
[1.5 (2)] (1) For calculations the following units are recommended in accordance with ISO 1000:
Forces and loads kN, kN/m , kN/m2
Unit mass : kg/m3
Unit weight : kN/m3
Stresses and strengths : N/mm2 (=MN/m2 or MPa) Moments (bending....) 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
.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.
(5) The design (factored) values Fd of an action (for instance Gd, Qad,...) 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^):
[form. (2.3)] R d=R(X ka k , . ) / 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 Design requirements r.a.3.1 General
[2.3.1 (l)] (1) It shall be verified that no relevant limit state is exceeded [2.3.1 (2)] (2) All relevant design situations and load cases shall be considered. [2.3.1 (3)] (3) Possible deviations from the assumed directions or positions of actions shall be considered. [2.3.1 (4)] (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)]
where Ed^Cd or E d < R d 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:
(gVd>SHd) ^ (5vma*>SHmax) f d ^ f min
where vd
Hd
fd
is the design vertical deflection of floors (recommended limits oVmax = L/250 ) is the design horizontal deflection of frames (recommended limits ,^ = h/300 ) is the design natural frequency of floors (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: [form. (2.7)] Sd^Rd
where 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:
(NSd ,VSd ,MSd)
[form. (2.1)]
Table LI Summary of design requirements 11 frame submitted to SLS and ULS combinations of design actions Fd (Gd, Qd, wd, sd,...):
|Fd=YFFk
[2.3.4(1)]
where F^ is the characteristic value of actions YF is the partial safety factor for the considered action
(see chapter )
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):
Sd (=(Nsd, Vsd, MSd) )
3) verification conditions at limit states: for SLS checks (see chapter I.b.4):
. in general: where
[2.3.2.1 (2)]
[form. (2.3)]
E H < C
Cd is the nominal value related to the design effect of considered actions (design capacity).
for instance:
where
(Vd>5Hd) < (vmax'aHmax f d ^ f min
OVd Hd fd Vmax
is the design vertical deflection of floors is the design horizontal deflection of frames is the design natural frequency of floors
.8Hmaxfmin are recommended limits (for instance: L/250, h/300, 3 Hz>
for ULS checks (see chapter I.b.5): . in general: Sd < R
where Rd is the design resistance (=(NRd, VRd , MRd)):
Rd = Rk/YM where Rk
YM is the characteristic value of the used material is the partial safety factor for the resistance (see table 1.2)
for instance: (N S d ,V S d > M s d )
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; - resistance of class 1,2 or 3 cross-section*) :
(plasticity or yielding)
- resistance of class 4 cross-section*) : (local buckling)
- resistance of members to buckling : (global and local buckling)
- resistance of net section at bolt holes :
- resistance of bolted connections :
- resistance of welded connections :
- at Serviceability Limit States: - slip resistance of preloaded bolts :
Note 1 : The different JM factors are explicitly introduced in 1
Note 2: The yui factors are provided according to the official Those "boxed" values are only indicative. The value practice are fixed by the national authorities in each the relevant National Application Document (NAD)
= M
YMI = W
=
YM2 = 1 .25
Mb=1.25
YMW = 1'25
Ms.ser ~~*>*
he design formulas.
version of Eurocode 3. s of YM to be used in country and published in
*) 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 non-sway 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 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 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 .
(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 FC 1) : Elastic global analysis of steel frames according to Eurocode 3 (General)
Actions row:
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
ULS checks of members submitted to internal forces and moments (N, V, M)
14
16
I I
19
ULS checks of local effects ULS checks of connections
20
54
Flowchart ( FC l) : Elastic global analysis o Steel frames according to Eurocode 3 (Details) Determination of load arrangements (EC1 and EC 8)
1 Load cases for ULS [2.3.3.]
Load cases for SLS [2.3.4.]
C~ Predesign of members^beams & columns => Sections^ ~^ l not fulfilled ^ with pinned and/or rigid connections JT
row:
ULS checks [Chap. 5]
SLS checks [Chap. 4]
notfulfilled
Frame with bracing system / Classification of the frame
Design of the bracing system
Frame without bracing system
, Braced framed yes \no
6b0 ,2 5u [5.2.5.3. (2)] 1
Global imperfections of the frame
[5.2.4.3.] Non-sway frame yes /Nonsway frame [5.2.5.2. m Sway frame
Vsd 0 ,1 1 no
yes / 0,1 < ^ . < 0,25 \nov Ver [5.2.6.2. (4)]
> 0,5 [A.fy / NSd]05 V T v [5.2.4.2.(4)]
S.
. , :
FIRST 'ORDER ANALYSIS SECOND ORDER ANALYSIS' Nonsway mode buckling
length approach [5.2.6.2(1) a)][5.2.6.2. (7)]: with sway moments amplified by factor
l/(l-VSd/Vcr) [5.2.6.2.(3)]
Sway mode buckling length approach
[5.2.6.2(1) b)][5.2.6.2. (8)1: with sway moments
amplified by factor 1,2 in beams & connections
Mjembers imperfectiojis l eo,d [5.2.4.5.] i
152.62.(2)]
eo,d where necessary [5.2.4.5.(3)]
eo,d in all members [5.2.4.5.(2)]
- --0 f- -:
Nonsway mode iL b
/members \_ \ with eo.d /
yes
I Sway mode L b ) Nonsway mode L b a, n Checks of connections [Chap. 6 and Annex J]
55
I.b.l .3 Comments on flow-chart FC 1
comments (1/6) on flow-chart FC 1:
[5.2.1.2(1)]
[5.2.1.2 (2)]
* 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:
. 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,
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 the vertical loads
types of frames
the horizontal loads
the global imperfections of
the frame (row 7)
the member imperfections
(row 12) 1) braced frames &)
(path) X(b)
2) non-sway frames (path ) X X
3) sway frames (c) (paths and ) X X
[5.2.5.3 (3)]
[5.2.5.3 (5)]
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) on flow-chart FC 1:
[5.2.1.2(3)]
[5.24.5(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
(path )
(path )
The second order elastic global analysis of the frame should take into account
the vertical loads
X
X
X
the horizontal loads
X
X
X
the global imperfections of the
frame (row 7)
X
X
X
the member imperfections
(row 12)
X(a)
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 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)] 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.
[5.2.5.3 (2)] * row 6: braced frame unbraced frame
[5.2.4.3]
5b: horizontal displacement of the frame with the bracing system
u: 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 \ is always fulfilled.
* row 7: global imperfections of the frame initial sway imperfections of the frame
F2
equivalent horizontal forces F2
JMii could be applied
in the form of Fi
(Fi + F2) (Fi + F2) 2 2
58
[5.2.5.2]
comments (4/6) on flow-chart FC 1: * row 8: 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)]
or, [5.2.5.2(4)]
Sd _ cr
< 0,1 cr
, condition which is equivalent to aCT > 10
where Vsd: design value of the total vertical load VCT: 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; Vcr of a column does not correspond necessarily to Vcr of the frame including that column) aCT : 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:
._.(1-2) h . ^ H h.(H1 +H2) < 0,1
where H, V: total horizontal and vertical reactions at the bo
