Knjiga Composite Steel Concrete Buildings

EUROPEAN CONVENTION FOR CONSTRUCTIONAL STEELWORK CONVENTION EUROPEENNE DE LA CONSTRUCTION METALLIQUE CECM

E K S

rrzowLFAEl3EI3 Recherches

STEEL RESEARCH

Design Handbook for Braced Composite Steel-Concrete Buildings According to Eurocode 4

i FIRST EDITION

2000 No 96

All rights reserved. No parts of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the Copyright owner :

ECCS General Secretariat CECM Avenue des Ombrages, 32/36 bte 20 EKS B - 1200 BRUSSELS (Belgium)

Tel: 32-217620429 Fax : 32 - 2 I762 09 35 E mail : [email protected]

ECCS assumes no liability with respect to the use for any application of the material and information contained in this publication.

ISBN : 92 - 9147 - 000 - 23

Authors:

Name Company

SCHLEICH Jean Baptiste, Ingenieur Principal

Language

MATHLEU Jules, Ingknieur Chef de Departement

Prof. Dr.-Ing. J. Fake

Ing. M. Bands

Prof. Dr.-Ing. F. Millanes Mat0

CONAN Yves, Ingenieur Techcien

Universitat-GH- Siegen German Siegen

SIDERCAD S.p.a. Italian Genova

I D E M / Uni. Pol. Madrid Madrid

Spanish

Service Recherche et Promotion technique Structures ProfilARBED Recherches 66, rue de Luxembourg

LUXEMBOURG L - 4221 ESCH / ALZETTE

I

Ir. H.M.G.M. Steenbergen "NO-BOUW Delft

Dutch

Ph. Beguin C.T.I.C.M. Saint-Remy-les-Chevreuse

French

3

Table of contents 1

TABLE OF CONTENTS page

0 PRELIMINARIES 9

0.1 Foreword 0.1.1 Generalities 0.1.2 0.1.3 Warning 0.1.4 0.1.5 Acknowledgements

Objective of this design handbook

How to read this design handbook

0.2 Units and notations 0.2.1 units 0.2.2 Convention for member axes 0.2.3 Notations in flow-charts

11 11 11 11 12 12

13 13 13 13

0.3 Terminology 14

0.4 References 16

0.5 List of Symbols 0.5.1 Latin symbols 0.5.2 Greek symbols

17 17 21

0.6 List of Tables 24

0.7 List of Figures 27

I INTRODUCTION 31

I. 1 Benefits of composite structures 33

1.2 Basis of design

I 1.2.2 Definitions I. 2.1 Fundamental requirements

1.2.2.1 Limit states 1.2.2.2 Actions 1.2.2.3 Material properties

1.2.3.1 General 1.2.3.2 Serviceability Limit States

1.2.3 Design requirements

I 1.2.3.3 Ultimate Limit States

1.3 Design of composite braced frame

1.3.1.1 Analysis models for frames 1.3.1.2

1.3.1 Generalities

Design procedure for composite b r a d frame 1.3.2 Static equilibrium 1.3.3

1.3.3.1 Generalities 1.3.3.2 Frame imperfections

I Load arrangements and load cases

1.3.4 First order elastic global analysis

37 37 37 37 38 39 39 39 40 40

42 42 42 44 46 46 46 47 48

Previous page is blank

5

Table of contents

1.3.4.1 Methods of analysis 1.3.4.2 Effects of deformations 1.3.4.3 Elastic global analysis

1.3.5.1 Deflections of frames

1.3.6.1 1.3.6.2 ULS checks

1.3.5 Verifications at SLS

1.3.6 Vedkations at UL.S Definition of braced frames and non-sway frames

1.4 Content of the design handbook 1.4.1 Scope of the handbaok 1.4.2 1.4.3 1.4.4

Summary of the table of contents Checks at Serviceability Limit States Checks of members at Ultimate Limit States

11 STRUCTURAL CONCEPT OF THE BUILDING

II.1 Structuralmodel

II.2 Non structural elements

II.3 Loadbearingstructure II.3.1 Types of columns II.3.2 Types of beams II.3.3 Types of slabs II.3.4 Types of shear connector II.3.5 Types of joints

II.4 Recommendations for composite design

II.5 Material properties II.5.1 Concrete II.5.2 Structuralsteel 11.5.3 Reinforcing steel II.5.4 II.5.5 Connecting devices

Profiled steel decking for composite slabs

II.6 Partial safety factors for resistances and material properties at ULS

III LOAD ARRANGEMENTS AND LOAD CASES

m.1 Generalities

III.2 Loadarrangements III.2.1 III.2.2

Permanent loads (g and G) Variable loads (4, Q, w and s)

III.2.2.1 Imposed loads on floors and roof (q and Q) III.2.2.2 Wind loads (We,i , Fw)

III.2.2.2.1 Wind press~re (We$ III.2.2.2.2 Wind force (Fw)

III.2.2.3 Snow loads (s)

m.3 Loadcases

6

48 49 49 50 50 50 50 52

52 52 54 54 54

57

59

59

59 59 60 61 62 62

64

68 68 70 72 72 73

73

75

77

80 81 81 82 84 85 89 89

90

I Table of contents I III.3.1 III.3.2

Load cases for serviceability limit states Load cases for ultimate limit states

IV MEMBERS IN COMPRESSION (N)

IV.l Generalities IV. 1.1 IV. 1.2 N. 1.3 IV. 1.4

Limits of applicability of the simplified design method Local buckling of steel members Influence of longitudinal shear Regions of load introduction

IV.2 Resistance of cross-section to axial compressive force Nx.Sd

N . 3 Stability of member to axial compressive force Nx.Sd

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

V.l Generalities

V.2 Checks at Ultimate Limit States V.2.1 V.2.2

Properties of cross-sections of composite beams Classification of cross-sections of composite cross-sections

V.2.2.1 Generalities V.2.2.2 Definition of cross-sections classification V.2.2.3 V.2.2.4 Classification of steel webs

Classification of steel flanges in compression

V.2.2.4.1 V.2.2.4.2

Classification of steel webs where the compression flange is in Class 1 or 2 Classification of steel webs where the compression flange is in Class 3 or 4

V.2.3 V.2.4

Distribution of internal forces and moments in continuous beams Verification at ULS to vertical shear VZ.Sd

V.2.4.1 V.2.4.2 V.2.4.3

V.2.5.1 V.2.5.2

Resistance of cross-section to vertical shear V Z . ~ Stability of web to vertical shear VZ.Sd for composite beams Stability of steel web to crippling

Resistance of cross-section to My.Sd Stability of member to My.Sd

V.2.5 Verifications at ULS to bending moment My.Sd

V.2.5.2.1 Generalities V.2.5.2.2 V.2.5.2.3 Buckling resistance moment

Check of lateral-torsional buckling without direct calculation

V.2.6 Verification at ULS to combined (Vz.Sd, My.Sd) V.2.6.1 V.2.6.2

Resistance of cross-section to ( V z . ~ , My.sd) Stability of web to (VZ.Sd, My.sd)

V.2.7 Verification of shear connectors at ULS to longitudinal shear V.2.7.1 V.2.7.2

V.2.7.2.1 V.2.7.2.2

V.2.7.3.1 V.2.7.3.2

V.2.7.3

V.2.7.4 V.2.7.5 V.2.7.5.1

Generalities Design longitudinal shear force

Full shear connection Partial shear connection with ductile connectors

Headed studs in solid slabs Headed studs in composite slabs with profiled steel sheeting

Design shear resistance of headed studs

Spacing and detailing of headed studs Design shear resistance of concrete slab Longitudinal shear in the slab vsd

91 91

93

95 97 98 99

100

102

105

113

115

119 119 122 122 123 126 128 128 129 138 139 139 141 143 144 144 148 148 148 150 152 152 153 155 155 155 156 159 162 162 163 165 168 169

7

Table of contents

V.2.7.5.2 V.2.7.5.3 V.2.7.5.4 Minimum transverse reinforcement

Design resistance to longitudinal shear q d Contribution of profiled steel sheeting as transverse reinforcement, v~

V.3 Vedications at Serviceability Limit States SLS V.3.1 Generalities about SLS V.3.2 Deflections V.3.3 Cracking of concrete V.3.4 Vibrations

VI MEMBERS WITH COMBINED AXIAL COMPRESSIVE FORCE AND BENDING MOMENT ( (N 9 M) ; (N 9 V 9 M) )

VI.1 Generalities VI. 1.1 VI. 1.2

Second order effects on bending moments Specific remarks for N-M calculations

170 171 172

172 172 173 177 180

181

183 186 187

VI.2 Resistance of cross-sections to combined compression and uniaxial bending (Nx.Sd ; My.sd) or (Nx.Sd ; MZ.Sd) 190

vI.3

VI.4

VI.5

VI.6

VII

W. 1

W . 2

Stability of members to combined compression and uniaxial bending (Nx.Sd;My.Sd) or (Nx.Sd;Mz.Sd) 198

Resistance of cross-sections to combined compression and biaxial bending (Nx.Sd, My.Sd and Mz.Sd) 200

Stability of members to combined compression and biaxial bending (Nx.Sd, My.Sd and MZ.sd)

Influence of transverse shear forces

COMPOSITE SLABS OR CONCRETE SLABS

Generalities

Initial slab design VII.2.1 Proportions of composite slab W.2.2 Construction condition VII.2.3 Composite action W.2.4 Deflections

W . 3 Influence of decking on the design of composite beams W.3.1 W.3.2

Ribs transverse to the beam Ribs parallel to the beam

W . 4 Minimum transverse reinforcement

200

202

205

207

209 209 209 209 210

210 21 1 21 1

212

8

1 Preliminaries I

PRELIMINARIES

9

I I Foreword 1

0 PRELIMINARIES

0.1 Foreword

0.1.1 Generalities

(1) The Eurocodes are being prepared to harmonize design procedures between countries which are members of CEN (European Committee for Standardization).

(2) E u r d e 4 - Part 1.1 “Design of Composite Steel and Concrete 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) : ENV 1994-1-1: 1992.

(3) The national authorities of the members states have issued National Application Documents (NAD) to make Eurocode 4 - Part 1.1 operative whilst it has ENV-status.

0.1.2 Objective of this design handbook

(1) The present publication is intended to be a design aid in supplement to the complete document E u r d e 4 - Part 1.1 (always with references to it) in order to provide simplified guidance and to facilitate the use of Eurocode 4 for the design of such composite steelconcrete structures which are usual in common practice : braced composite steelconcrete structures. As this handbook is less formal and more user-friendly than Eurocode 4 additional information have been introduced to offer explanations on design principles or application rules and, about usual design results.

(2) Therefore, the “Design handbook according to Eurocode 4 for braced composite steel-concrete buildings” presents the main design formulas and rules extracted from Eurocode 4 - Part 1.1, which are needed to deal with :

- elastic nlobal analwis of buildings and similar structures,

- checks of structural members at limit states,

- in case of braced structures,

- according to the European standard Eurocode 4 -Part 1.1 (ENV 1994-1-1:1992).

0.1.3 Warning

(1) Although the present design handbook has been carefully established and intends to be self- standing it does not substitute in any case for the complete document Euroc.de 4 - Part 1.1, which should be consulted, in case of doubt or need for clarification, in conjunction with the National Application Document (NAD) specific to the country where the building project is situated.

(2) All references to Eurocode 4 - Part 1.1 are made in [...I and given in appropriate left column called “Ref.”.

References to Eurocodes 1,2,3 and 4 are called respectively either Ref. 1, Ref. 2, Ref. 3 and Ref. 4 or EC1, EC2, EC3 and EC4 (see the list of references in chapter 0.4).

(3) Any other text, tables or figures not quoted from Eurocode 4 are considered to satisfy the rules specified in Eurocode 4 - Part 1.1.


11

Foreword J 0.1.4 How to read this design handbook

(1) Example of numbering of chapters and paragraphs : V.2.7.2.2

(2) Layout of pages :

IRef. Chapter V - Members in bending I left column for references

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

Checks at Ultimate Limit States

Verifications of shear connectors at ULS to longitudinal shear . . .)

. . .)

. . .)

.2.7.2 Design longitudinal shear force

.2.7.2.2 Partial shear connection with ductile connectors

(3) In the left column of each page : - references to Eurocode 4 are also given in the text between brackets [...I - other references are designated by (Ref. i) and are listed in chapter 0.4.

0.1.5 Acknowledgements

(1) Particular thanks for fiuitful collaboration are addressed to members of the project working group:

- 15 engineering offices: Adem (Belgium), Bureau Delta (Belgium), Varendonck Groep/Steeltrak (Belgium), VM Associate Partner (Belgium), h b s l l , Hannemann & Hsjlund (Denmark), Bureau Veri- (France), Socotec (France), Sofiesid (France), CPU hgenieurburo (Germany), IGB-Ingenieurgruppe Bauen (Germany), Danieli hgegneria (Italy), Schroeder & Associes (Luxemburg), D3BN (the Netherlands), Ove Amp & Partners (United Kingdom), ECCS / TC 11 (Germany),

- RWTH: Steel Construction Department from Aachen University with Professor SEDLACEK G. and G R O W D.,

- SIDERCAD (Italy) with MM. BANDINI M. and CATTANEO F.,

CTICM (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 no P2724 (contract no 7210 - SA/516),

- the F6 executive committee which has followed and advised the working group of the research,

- anyone who has contributed to the work MM. CHANTRAIN Ph., MAUER Th., GERARDY J.C and WARSZTA F.

12

I Units and notations I 0.2 Units and notations

0.2.1 Units EC4 p . 5 (211 For calculations the following units are recommended in accordance with IS0 1000:

- Forcesandloads EN, Wlm, kNlm2

- unitmass Wm3

- Unitweight kN/m3

- Stre~~e~andstrengths N/-2 ( = MNIm2 or Mpa)

- Moments kN.m

0.2.2 ' Convention for member axes

(1) For steel members, the conventions used for cross-section axes are: - xx: along the member

- generally:

YY: zz:

EC4 [ 1.6.7

cross-section axis parallel to the flanges

cross-section axis perpendicular to the flanges or parallel to the web

(2) The convention used for subscripts which indicate axes for moments is :

"Use the axis about which the moment acts."

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.

0.2.3 Notations in flow-charts

All 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 4 are given in [...I, "n.$" means that the checks are notjk@ZZed and that stronger sections or joints have to be selected.

Title

Assumption 7, - convention for flow-charts :

+ Action : determination, calculation, ...

ir Criterion to check,

condition or comparison

the dotted (-) means that path has to be followed through the box

Results 13

0.3 Terminology

EC4 [I .4.2 (1)] (1) The following terms are used in Part 1.1 of Eurocode 4 (Ref. 4) with the following meanings:

- Frame: A structure or portion of a structure, comprising an assembly of directly connected structural elements, designed to act together to resist load. It covers both plane W e s and threedimensional frames.

- Sub-fiame: A frame which forms part of a larger frame, but is treated as an isolated W e in a structural analysis.

- Tyue of flaming: Terms used to distinguish between frames which are either:

I

. Continuous, in which only both equilibrium and the structural properties of the members need explicit consideration in the global analysis,

. Semi-continuous, in which also the structural properties of the connections need explicit consideration in the global analysis,

. Simule, in which only equilibrium needs to be considered in the global analysis. - Global analvsis: 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, and are based on the properties of the materials.

- First order alobal analvsis: Global analysis using the initial geometry of the structure and neglecting the deformation of the structure which influences the effects of actions (no P-A effects).

- Second order nlobal analysis: Global analysis taking into account the deformation of the structure which influences the effects of actions (P-A effects).

- Elastic nlobal analvsis: 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.

- Composite frame: A composite frame is a framed structure for a building or similar construction works, in which some or all of the beams and columns are composite members and most of the remaining members are structural steel members. The use of reinforced or prestressed concrete or masonry members in bracing systems is not excluded.

ComDosite member: A structural member with components of concrete and of structural or cold-formed steel, interconnected by shear connection so as to limit the longitudinal slip between concrete and steel and the separation of one component from the other.

-

- Prouued structure or member: A structure or member the steel elements of which are supported until the concrete elements are able to resist stresses.

- Unurouued structure or member: A structure or member in which the weight of concrete elements is applied to steel elements.

- Shear connection: An interconnection between the concrete and steel components of a composite member that has sufficient strength and stifhess to enable the two components to be designed as parts of a single structural member. For composite beams shear connection means generally mechanical shear connection that does not rely on bond or adhesion at interfaces between steel and concrete.

- Full and vartial shear connection are defined in chapter V.2.7

14

Terminology 1

- Headed stud connector : A particular form of shear connector comprising a steel bar and flat head that is welded automatically to the beam.

- Comuosite connection : A connection between a composite member and any other member in which reinforcement is intended to contribute to the resistance of the connection.

- Riaid comuosite connection : A composite connection such that its deformation has no significant influence on the distribution of internal forces and moments in the structure, nor on its overall deformation.

- Comuosite column : A composite member subjected mainly to compression and bending. Only columns with cross-sections of the types defined in chapter IV are treated in this handbook.

- Comuosite beam : A composite member subjected mainly to bending. Only those in which the structural steel section is symmetrical about its minor axis are treated (see chapter V).

- Continuous comuosite beam : A beam with three or more supports, in which the steel section is either continuous over internal supports or is jointed by full-strength and rigid connections, with connections between the beam and each support such that it can be assumed that the support does not transfer significant bending moment to the beam. At the internal supports the beam may have either effective reinforcement or only nominal reinforcement.

- H m * n g moment : Negative moment causing compression in the bottom flange of the beam.

- Saapinn moment : Positive moment causing tension in the bottom flange of the beam.

- Comuosite slab : A bi-dimensional horizontal composite member subjected mainly to bending, in which profiled steel sheets (see chapter VII) :

are used as permanent shuttering capable of supporting wet concrete, reinforcement and site loads, and

subsequently combine structurally with the hardened concrete and act as part or all of the tensile reinforcement in the finished slab.

- DecknR : Profiled steel sheeting which may be embossed or specially formed to ensure composite action with the concrete slab.

- Transverse reinforcement : Reinforcement placed in the slab transversely (across) the steel beam.

- Svstem 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.

- Desimer : Appropriately qualified and experienced person responsible for the structural design.

.

.

15

References

0.4

Ref. 1

Ref. 2

Ref. 3

Ref. 4

Ref. 5

Ref. 6

Ref. 7

Ref. 8

Ref. 9

Ref. 10

Ref. 11

Ref. 12

Ref. 13

Ref. 14

References

(= EC1) ENV 1991-1-1, Eurocode 1 (draft version) : Basis of Design and Actions on Structures (Parts 1,2.2,2.4,2.5,2.7, 10).

(= EC2) ENV 1992-1-1, Eurocode 2 : Design of concrete structures, Part 1.1 : General rules and rules for Buildings.

(= EC3) ENV 1993-1-1, Eurocode 3 : Design of steel structures, Part 1.1 : General rules and rules for Buildings.

(= EC4) ENV 1994-1-1, Eurocode 4 : Design of composite steel and concrete structures, Part 1.1 : General rules and rules for Buildings.

(= EC8) Eurocode 8, draft version, Design of structures for earthquake resistance.

ECCS technical publication n”65, “Essentials of Eurocode 3 - Design Manual for Steel Structures in Building”, 199 1, First Edition.

ECCS technical publication n”72, ‘Composite Beams and Columns to Eurocode 4”, 1993, First Edition.

SCI publication 121, “Composite Beam Design to Eurocode 4”, 1994.

SCI publication 142, “Composite Column Design to Eurocode 4”, 1994.

R.P.Johnson and D. Anderson, “Designers’ Handbook to Eurocode 4, Part 1.1 : Design of composite steel and concrete structures”, 1993, Thomas Telford.

Albitar A. - “Application de 1’Eurocode 4. Classification des sections transversales de poutres mixtes”. pages 71 to 90. Revue Construction Metallique, no 4-1994.

Bergmann R., “Composite columns”, pages 39 to 68, IABSE Short Course about Composite steel-concrete Construction and Eurocode 4, Brussels 1990.

Bode H. and Sauerborn N., “Composites Beams”, pages 89 to 115, IABSE Short Course about composite steel-concrete construction and Eurocode 4, Brussels 1990.

ARBED S.A., “Composite construction system AF with integrated fire resistance - Code of good practice”.

16

List of symbols I List of Symbols

Latin symbols

designation of a buckling curve; throat thickness of fillet weld; position of reinforcing bars measured from the bottom of concrete flange in composite beam. geometrical data of the effects of actions geometrical data for the resistance design throat thickness for submerged arc welding accidental action; area of building loaded by external pressure of wind; area of gross cross-section cross-sectional area of the structural steel concrete area effective area of class 4 cross-section reference area for cf (wind force) effective area of the steel sheet in tension Effective section of rib of composite slab Effective section of rib of composite slab cross-sectional area of the steel reinforcement shear area of the structural steel member effective shear area for resistance to block shear shear area of structural steel cross-section according to yy axis shear area of structural steel cross-section according to zz axis designation of a buckling curve; flange width; building width effective width effective width of the slab for concentrated load effective width of the concentrated load, perpendicular to the span of the slab width of the concentrated load, perpendicular to the span of the slab width of the haunch for headed studs designation of a buckling curve; outstand distance; effective perimeter altitude factor for reference wind velocity dynamic fiator for wind force direction factor for reference wind velocity exposure coefficient for wind pressure and wind force wind force coefficient external pressure coefficient for wind pressure roughness coefficient for determination of ce topography coefficient for determination of ce temporary (seasonal) fictor for reference wind velocity nominal value related to the design effect of actions thickness of concrete cover in concrete encased section designation of a buckling curve; web depth bolt diameter, headed stud diameter distance from the top of the slab to the centroid of the effective area of the sheet hole diameter distance of the plastic neutral axis of the effective area of the sheeting to its underside equivalent initial bow imperfection design value of equivalent initial bow imperfection effect of actions at SLS

17

List of symbols

Ea ECCS ECSC EC 1 EC 2 EC 3 EC 4 EC 8 Ecm EC Ed Ek E.N.A. Es fck fct fcte 6 G fmin fsk fu

fY fyb = fyp fyw Fa,Fal,Fa;! FC

modulus of elasticity or Young Modulus of structural steel European Convention for Constructional Steelwork European Community of Steel and Coal Eurocode 1 (Ref. 1) Eurocode 2 (Ref. 2) Eurocode 3 (Ref. 3) Eurocode 4 (Ref. 4) Eurocode 8 (Ref. 8) secant modulus of elasticity of the concrete "effective" modulus of concrete design value of the effect of action characteristic value of effects of actions at SLS elastic neutral axis modulus of longitudinal deformation of reinforcing steel characteristic cylinder compressive strength charactenstic cylinder tensile strength effective tensile strength of concrete design natural frequency natural frequency recommended limit of natural frequency characteristic yield strength of reinforcing steel ultimate tensile strength yield strength nominal value of yield strength for profiled steel sheeting (EC4) yield strength of the web forces in structural steel section to resist to plastic bending moment compressive force in the concrete flange necessary to resist the design sagging bending moment longitudinal shear force design value of action characteristic value of action design longitudinal force caused by composite action in the slab force in the reinforcing bars to resist to plastic bending moment characteristic value of transverse force design transverse force caused by composite action in the slab design tensile force per stud resultant wind force, force in the web of structural steel section to resist to plastic bending moment distributed permanent action; dead load permanent action shear modulus design permanent action characteristic value of permanent action overall depth of cross-section; storey height; building height depth of structural steel section thickness of the slab above the ribs of the profiled sheeting height of deckings ribs total depth of the slab

18

List of symbols I

kLT kt

ko kT K* e ~ L T

e0 L Lb LTB m

min M Mb.Rd Mcr

Me1

max

&.Rd

&l.Rd Mf.Rd

Mapl.Rd

Mpl.Rd Mpl. w.Rd Mp1.y.Rd Mpl.z.Rd

MRd

MPl

I

I Mp.Rd

MSd MV.Rd

I Mw.Sd

MY My.Sd

overall height of structure total horizontal load radius of gyration about relevant axis using the properties of gross steel cross-section moment of inertia torsional constant

moment of inertia about yy and zz axes subscript meaning characteristic (unfhctored) value coefficient for the minimum reinforcement effective length factor reduction factor for the shear resistance of headed studs in composite slab with ribs parallel to the beam factor for lateral-torsional buckling with N-M interaction reduction factor for the shear resistance of headed studs in composite slab with ribs perpendicular to the beam buckling factor for outstand flanges buckling factor for shear roughness factor of the terrain portion of a member effective length for out-of-plane bending equivalent length system length; span length; weld length buckling length of member lateral-torsional buckling mass per unit length maximum minimum bending moment design resistance moment for lateral-torsional buckling elastic critical moment for lateral-torsional buckling design resistance moment of the cross-section elastic moment capacity design elastic resistance to bending of beam design plastic resistance moment of the cross-section consisting of the flanges only, with effective section design plastic resistance moment of the structural steel alone plastic moment capacity design plastic resistance moment of the structural cross-section design plastic resistance moment of the web design plastic resistance moment of the structural cross-section about yy axis design plastic resistance moment of the structural cross-section about zz axis sagging bending resistance of a composite slab 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

warping constant

19

List of symbols 1 Mz MZ.Sd n n, nr 11s N NAD Nb.Rd Nb.y.Rd Nb.z.Rd ~Comp. Ncr

NG.Sd Nc.Rd

Npl.Rd NRd NSd Nxsd P.N.A. P PRd PRk 9 9k qref Q Qd Qk Qk.max r R Qd Rd Rk S

sd Sk

SS

S s d sk SLS t tf tP t W

ULS Vref

20

bending moment about zz axis design bending moment about zz axis applied to the member nominal modular ratio number of columns in plane number of members to be restrained by the bracing system number of storeys n o d force; axial load National Application Document design buckling resistance of the member design buckling resistance of the member accordmg to yy axis design buckling resistance of the member according to zz axis compressive n o d force elastic critical axial force design compression resistance of the cross-section part of the design axial load that is permanent design plastic resistance of the gross cross-section design resistance for member in compression design value of compressive force design internal axial force applied to member according to xx axis plastic neutral axis point load design resistance of shear connector characteristic resistance of shear connector 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 resistance of the member subject to internal forces or moment characteristic value of & snow load 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 a plate welded to an unstiffened flange web thickness ultimate Limit states 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 total design longitudinal shear 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 (I 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 design wind load wind pressure on external surface design crack width welded sections elastic section modulus of effective class 4 cross-section elastic section modulus of class 3 cross-section elastic section modulus of class 3 cross-section according to yy axis elastic section modulus of class 3 cross-section according to zz axis plastic section modulus of class 1 or 2 cross-section plastic section modulus of class 1 or 2 cross-section according to yy axis plastic section modulus of class 1 or 2 cross-section according to zz axis axis along the member characteristic value of the material properties principal axis of cross section (parallel to flanges, in general) principal axis of cross section (parallel to the web, in general) position of plastic neutral axis measured from the top of concrete flange in composite beam position of plastic neutral axis measured from the bottom of concrete flange in composite beam reference height for evaluation of Ce

vertical distance

Greek symbols

coefficient of linear thermal expansion factor to determine the position of the neutral axis coefficient of critical amplification or coefficient of remoteness of critical state of the fhme coefficient of nominal linear thermal expansion nondimensional coefficient for buckling equivalent uniform moment factor for flexural buckling equivalent uniform moment fictor for lateral-torsional buckling equivalent uniform moment factor for flexural buckling about yy axis equivalent uniform moment factor for flexural buckling about zz axis nondimensional coefficient for lateral-torsional buckling

21

I

List of symbols

reduction factor for the relevant buckling mode ratio of compression for the resistance of members reduction factor for lateral-torsional buckling

ratio of compression for the resistance of members reduction Eactor for the relevant buckling mode about yy axis reduction factor for the relevant buckling mode about zz axis relative horizontal displacement of top and bottom of a storey horizontal displacement of the braced frame design deflection design vertical deflection of floors, beams, . . . design horizontal deflection of frames recommended limit of horizontal deflection in plane deflection of the bracing system due to q plus any external loads deflection due to variable load (9) horizontal displacement of the unbraced fi-ame design vertical deflection of floors, beams, ... recommended limit of vertical deflection

minimum of xy a d

pre-camber (hogging) of the beam in the unloaded state (state 0) variation of the deflection of the beam due to permanent loads (G) immediately after loading (state 1) variation of the deflection of the beam due to the variable loading (Q) (state 2) displacement

coefficient = E (with fy in N/mm2)

ultimate strain of structural steel total long-term free shrinkage strain ultimate strain of reinforcing steel partial safety factor for structural steel partial safety factor for profiled steel decking partial safety factor for concrete partial safety factor for force or for action partial safety factor for permanent action partial safety factor for the resistance at ULS partial safety factor for the resistance of bolted connections partial safety factor for the slip resistance of preloaded bolts partial safety factor for the resistance of welded connections partial safety factor for resistance at ULS of class 1,2 or 3 cross-sections (plasticity or yielding) partial safety k t o r for resistance of class 4 cross-sections (Id buckling resistance); partial safety factor for the resistance of member to buckling partial safety factor for variable action partial safety factor for reinforcing steel partial safety factor for shear connector Eactor for lightweight concrete slenderness of the member for the relevant buckling mode

List of symbols I Euler slenderness for buckling non-dimensional slenderness ratio of the member for buckling nondimensional slenderness ratio of the member for lateral-torsional buckling web slenderness non dimensional slenderness ratio of the member for buckling about zz and yy axes friction coefficient; ratio of moment for the resistance of members; opening ratio factor for N-M interaction snow load shape coefficient factor for N-M interaction factor for N-M interaction factor for N-M interaction Poisson's ratio for structural steel rotation unit mass for structural steel reduction factor due to shear force VSd reduction factor due to shear force Vy.Sd

reduction factor due to shear force Vz.Sd

normal stress maximum stress in the reinforcement shear stress simple postcritical shear strength elastic critical shear strength initial sway imperfection of the frame

23

List of tables ~

0.6 List of Tables page

I INTRODUCTION

Table I. 1 Table 1.3 Modelling of connections Table 1.2 Table 1.4 Table 1.5 Table 1.6 Table 1.7 Table 1.8 Table 1.9 Table I. 10

Table I. 1 1

Summary of design requirements

Modelling of frame for analysis Global imperfections of the frame Values for the initial sway imperfections 4 Recommended limits for horizontal deflections Definition of fr-aming for horizontal loads Checks at Serviceability Limit States Member submitted to internal forces and bending moments Planes within internal forces and bending moments (Nsd, Vsd, Msd) are acting Internal forces and bending moments to be checked at ULS for different types of loading

I1 STRUCTURAL CONCEPT OF THE BUILDING

Table II. 1 Table II.2

Table II.3

Table II.4 Table II.5

Table II.6 Table II.7 Table II.8 Table II.9

Table II. 10

Concrete classes and characteristic values for compression and tension Nominal values of shnnkage strain ECS

Values of nominal modular ratios n =

Design values of mterial coefficient for concrete Nominal values of yield strength fy for structural steels accordmg to EN 10025 and EN 101 13 Comparison table of different steel grades designation Design values of material coefficients for steel Yield strength fsk for reinforcing steel Yield strength of basic material fyb for steel sheeting

Partial safety factors ' y ~ for resistances and material properties at Ultimate Limit State

?XI

I11 LOAD ARRANGEMENTS AND LOAD CASES

Table III. 1 Table III.2 Categories of building areas, traflic areas in buildings and roofs Table III.3 Table III.4 Table m.5 Table III.6 Table III.7 Table III.8

Load arrangements Fk for composite building design according to Eurocodes 1 & 4

Imposed load (qk, Qk) on floors in buildings depending on categories of loaded areas Exposure coefficient as a function of height z above ground

External pressure cpe for verticals walls of rectangular plan buildings Combinations of actions for serviceability limit states Combinations of actions for ultimate limit state Examples for the application of the combinations rules in Table III.7. All actions Cg, q, P, s, w) are considered to originate from different sources

31

41 42 43 47 48 50 51 54 55 55 56

57

68 69

69

70

~

,

71 71 71 72 72 74

75

80 83 84 87 I 88 91 91 I

92

I

24

I List oftables I


Table IV. 1 Table IV.2 Table IV.3

Table IV.4 Table N.5 Table IV.6

List of checks to be performed at ULS for the composite member in compression Limiting width-to-thickness ratios to avoid local buckling Design shear resistance stresses (due to bond and friction) at the interface between steel and concrete Values of q 10 and q20 in function of h Design plastic resistance to compression Npl.Rd Cross-sectional areas of the structural steel (&), the reinforcement (As) and the concrete (Ac)

Table IV.7 Imperfection factors a Table IV.8 a) Moments of inertia of totally and partially concreteacased steel profile Table IV.8 b) Moments of inertia of concrete-filled rectangular hollow section Table IV.8 c) Moments of inertia of concrete-filled circular hollow section Table IV.9 Limiting values of h for long-term loading Table IV. 10 Buckling length of column, Lb

Table IV. 1 1 Buckling reduction factors x = f (x ) for composite cross-sections

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

Table V. 1 Critical sections for the design calculation and related action effects to be checked TableV.2 List of checks to be performed at ULS for the member in bending according to the

applied internal forces andor moments (V ; M ; (V , M)) TableV.2 List of checks to be performed at ULS for the member in bending according to the

applied internal forces and/or moments (V ; M ; (V , M)) Table V.3 Definition of the classification of cross-section Table V.4 Classification of composite cross-sections : limiting width-over-thickness ratio (c / tf)

for steel outstandflanges in compression Table V.5 Classification of composite cross-section : limiting width-to-thickness ratios for steel

internal flange elements in cornpression Table V.6 Classification of composite cross-sections : limiting width-over-thickness ratios (d / tw)

for steel webs Table V.7 a) Classification of flange and web subjected to particular loading for standard hot-rolled

WE, IPE A and IPE 0 steel profiles Table V.7 b) Classification of flange and web subjected to particular loading for standard hot-rolled

HE AA and HE A steel profiles Table V.7 c) Classification of flange and web subjected to particular loading for standard hot-rolled

HE B and HE M steel profiles Table V.7 d) Classification of flange and web subjected to particular loading for standard hot-rolled

UB steel profiles Table V.7 e) Classification of flange and web subjected to particular loading for standard hot-rolled

UC steel profiles TableV.8 Limits to redistribution of hogging moments at supports (in terms of the maximum

I

I percentage of the initial bending moment to be reduced)

I Table V.9 Shear area AV for cross-sections

93

96 99

100 103 103

104

105 107 108 109 110 111

112

113

116

117

118 124

130

131

132

133

134

135

136

137

138 140

25

List of tables

Table V. 10 Limiting width-to-thickness ratio related to the shear buckling in web Table V. 11 Simple post-cntical shear strength rba

Table V. 12 Buckling factor for shear kr Table V. 13 a) Plastic stress distributions, positions of plastic neutral axis and plastic bending moment

resistance Mpley.U for sagging bending moment

Table V. 13 b) Plastic stress distributions, positions of plastic neutral axis and plastic bending moment resistance Mpl.y.Rd for hogging bending moment

Table V. 14 Maximum depth ha in [mm] of the steel member to avoid lateral-torsional buckling in the hogging moment region

Table V.15 Interaction of shear buckling resistance and moment resistance with the simple postcritical method

Table V. 16 Design resistance PRd w] of headed studs with h / d > 4

141 142

142

146

147

150

153 163

Table V. 17 Basic shear strength rRd m/mm2] 170

Table V. 18 Recommended limiting values for vertical deflections 174 Table V. 19 Vertical deflections to be considered 174 Table V.20 178 Table V.21

180

Minimum percentage of reinforcement bars for propped and unpropped constructions Maximum bar diameters for high bond bars for different maximum reinforcement stresses and crack widths at SLS

VI MEMBERS WITH COMBINED AXIAL COMPRESSIVE FORCE AND BENDING MOMENT ( (N , M) ; (N ,V , M) ) 181

Table VI.2 Factors p for the determination of moments according to second-order theory 187 Table VI.3 a) Neutral axes and plastic section moduli for totally and partially concreteencased steel

profile bent about major axis @) 195 Table VI.3 b) Neutral axes and plastic section moduli for totally and partially concreteencased steel

profile bent about minor axis (U) 196 Table VI.3 c) Neutral axes and plastic section moduli for concrete-filled circular and rectangular

hollow sections 197 Table VI.4 Typical values of Xn 198

Table VIS 203 Reduced steel thickness tred allowing for transverse shear force

VI1 COMPOSITE SLABS OR CONCRETE SLABS 205

Table W. 1 Maximum span to depth ratios of composite slabs (L / hslab) 210

26

0.7 List of Figures page

I INTRODUCTION

Figure I. 1

Figure 1.2

Figure 1.3

Figure 1.4

Figure 1.5

I1

Advantage of composite column

Advantage of composite beam Ratio of moment resistances for composite section to steel section

Ratio of moments of inertia for composite Section to steel section

Design procedure for composite braced frame

STRUCTURAL CONCEPT OF THE BUILDING

Figure II.1

Figure II.2

Figure II.3

Figure II.4

Figure II.5

Figure II.6

Figure II.7

Figure II.8

Types of composite columns

Types of composite beams

Types of composite slabs and concrete slabs

Minimum dimensions of headed stud shear connector

Examples of joints in composite frames

Modelling of joints

Effects of propped and unpropped construction

Framing plans for medium and long span beams


Figure III. 1 Flow-chart for load arrangements and load cases for general global analysis of the structure

Figure III.2 Flow-chart for load arrangements and load cases for first order elastic global analysis of the structure

Figure III.3 Construction loads on profiled steel decking

Figure III.4 Values of dynam.~c factor cd for composite buildings

Figure III.5 Pressures on surfaces

Figure III.6 Reference height z, depending on h and b

Figure III.7 Internal pressure coefficient q,i for buildings with openings in the wall

29

33

34

35

36

44

55

59

60 I 61

62

63

64

65

67

73

78

79

82

85

85

87

88

27

I List of finures I

I IV MEMBERS IN COMPRESSION (N) 91

Figure IV. 1 Type of cross-sections of composite columns 95

Figure IV.2 Introduction length for the shear force 100

Figure IV.3 Mechanical shear connection 10 1

Figure IV.4 Shear resistance of headed stud connectors used to create direct load transfer into the concrete 102

V MEMBERS IN BENDING (V ; M ; (V , M) ) 111

Figure V. 1 Effective width beff and equivalent spans &, of concrete flange

Figure V.2 Elastic analysis of composite beam under sagging and hogging moment

120

121

Figure V.3 Flowchart for classification of a composite beam cross-section (with references to pC4] and to (design ~ d b o w ) 126

Figure V.4 Spacing requirements of shear connectors for the Class 1 steel flange in compression 127

Figure V.5 Requirements for encased web 128

Figure V.6 Improved classification of steel webs with compression flange in class 1 or 2 and with specific conditions129

Figure V.7 Definition of "uncracked" and "cracked" sections for elastic global analysis 139

Figure V.8 Load introduction and length of Mbearing, s, 143

Figure V.9 Inverted U-frame action 149

Figure V. 10 Normal stress distribution for M-V interaction with hogging bending moment 152

Figure V. 11 Resistance in bending and vertical shear in absence of shear buckling 153

Figure V. 12 Calculation of the longitudinal shear force Vf! in simply supported beams 157

Figure V. 13 Calculation of the longitudinal shear force Vf! in continuous beams 158

Figure V. 14 Minimum degree of shear connection allowing ductile behaviour of headed studs 160

Figure V. 15 Relation between F, and MSd for partial shear connection 16 1

Figure V. 16 M R ~ , reduced bending moment resistance of composite cross-section because of partial shear connection 162

Figure V. 17 Composite beam with solid slab 162

Figure V. 18 Beams with steel decking ribs parallel to the beam 163

164

Figure V.20 Detailing of shear connectors in solid slab 165

166

168

169

178

Figure V. 19 Beams with steel decking ribs transverse to the beam

Figure V.2 1 Types of composite beams with composite slabs

Figure V.22 Detailing of shear COM&O~S in composite slabs with steel decks including central stiffener

Figure V.23 Typical potential surfaces of shear failure in slabs

Figure V.24 Reinforcement length at supports for a composite beam

28

List of figures I

VI MEMBERS WITH COMBINED AXIAL COMPRESSIVE FORCE AND BENDING MOMENT ((N 9 M) ; (N 9v 9 M) 1 179

Figure VI. 1

Figure VI.2

Figure VI.3

Figure VI.4

Figure VI.5

Figure VI.6

Figure VI.8

Internal forces and bending moments applied to composite member

Type of cross-sections of composite columns

183

183

190

Cross-section interaction curve (with polygonal approximation) for compression and uniaxial bending 19 1

Stresses distributions corresponding to the interaction curve (Figure VI.4) 192

199

Reduction of normal stresses of steel profile within shear area in the presence of transverse shear stress 202

Cross-section interaction curve for compression and uniaxial bending

Design procedure for compression and uniaxial bending interaction

VI1 COMPOSITE SLABS OR CONCRETE SLABS

Figure W. 1 Typical composite slabs

Figure W . 2 Orientation of profiled steel decking

203

208

211

29

I INTRODUCTION

is blank

31

1 Ref. Chapter I - introduction 1

Ref. 4

I INTRODUCTION

1.1 Benefits of composite structures

Following figures illustrate the main advantages of composite structures that may be reached in comparison with other forms of construdion:

- for columns: the load currvine cuuacitv of the composite profile may reach twice that of the steel profile acting alone. For an applied axial load Nx.Sd, a composite column may allow to reduce the section size and always delivers better fire resistance than for steel section alone; this fire resistance increases with the amount of reinforcing bars protected by concrete (see Figure I. 1).

Comparison of different columns. with a buckling length of 4 meters and

HE 240 B

s 355 C25

COMPOSITE COLUMN

bearing the same ultimate load : Nx.Sd = 3 000 kN

c 400 mm

4 4 2 0 00 h( {I J 280mmJ 4 4 12

HE 280 B

s 355 C40 / S 500

PURE STEEL REINFORCED CONCRETE COLUMN COLUMN

Figure 1.1 Advantage of composite column

- forbeams:

the bearinn capacitv of composite beams relative to steel sections alone may be increased in the range of 1,5 to 2,5 for typical slab depth and for all P E and HE steel section (up to 600 mm deep) as shown in Figure 1.3. This figure provides the ratio of

moment resistances for composite sections to steel sections, (Mpl.Rd)-Posite , for

certain assumptions regarding the slab depth & + hp = 130 mm; hp = 50 mm), the slab width 5 & + hp + ha)), the concrete strength (C25/30), both steel grades S 235 & S 355 and P E and HE sections (see Table V.13 for notations and formulas). For an applied bending moment (My.sd), composite beams with naked steel section and with partiallyencased steel section (calculated with Annex G of Eurocode 4), may allow to reduce the section size, as shown in Figure 1.2; composite beams with partially-encased section also provide better fire resistance in comparison with naked steel section.

(Map1.M )steel


33

I Ref. Chapter I - Introduction I

I

I

! I I - I

I

I I

Ratio of Moment Resistance : MPleRd / MapleRd

0 0 W

0 0 m

0 0 d

0 0 m

0 0 c\1

0 2

0

Figure 1.3 Ratio of moment resistances for composite section to steel section

35

I Ref. Chapter I - Introduction

I

- 1

6

E! I I

- 1

W E4,

I 0- s- 3 z- :- d

Ratio of Moment of Inertia : Ic / Ia

0 0 W

0 0 M

0 0 d

0 0 rc)

0 0 c\1

0 E:

0

Figure 1.4 Ratio of moments of inertia for composite section to steel section

36


1.2 Basis of design

The table I. 1 summarises this chapter 1.2 providing the practical principles of design requirements. Details and explanations are given in the following subchapters 1.2.1 to 1.2.3.

1.2.1 Fundamental requirements

(1) A structure shall be designed and constructed in such a way that: - with acceptable probability, it will rernain 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 other influences likely

to occur during execution (i.e. the construction stage) and use (i.e. the composite stage) and have adequate durability in relation to maintenance costs.

(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 on@ cause.

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

1.2.2 Definitions

12.2.1 Limit states

[2.2.1.1(1)] (1) Eurocode 4 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) 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: EC4 [2.2.1.1 (611 a) for SLS, problems which may limit the serviceability because of

- deformations or deflections which adversely affect the appearance or 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 discodort to people, damage to the building or its contents, or which limits its functional effectiveness,

- cracking of the concrete which is likely to af€ect appearance, durability or water- tightness adversely,

- damage to concrete because of excessive compression, which is likely to lead to loss of durability,

- slip at the steelconcrete intehce when it becomes large enough to invalidate design checks for other serviceability limit states in which the effects of slip are neglected.

37


EC4 [2.2.1.1 (411 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 shear connection, supports and foundations.

12.2.2 Actions

(1) Details about actions are provided in Eurocode 1 (Ref. 1). EC4 p.2.2.1 (I)] (2) An action (F) is:

- a force (load) applied to the structure (direct action), or

- an imposed deformation (indirect action); e.g. temperatures effects, settlement or shnnkage.

p2.2.1 (211 (3) Actions (F) are classified as: EC4

a) by their variation in time : - 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.

b) by their spatial variation :

- fixed actions, e.g. self-weight, - free actions, which result in different arrangements of actions, e.g. movable imposed

loads, wind loads, snow loads. EC4 p.2.2.2 (111 (4) Characteristic values Fk 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.

EC4 [2.2.2.4 (l)] (5) The design (hctored) values Fd of an action (for instance Gd, Qd, wd, sd) iS expressed in gened

terms as:

[form. (2.111 IFd 'YF Fkl

where Fk is the characteristic (unfactored) value of action.

YF is the partial safety factor for the action considered - taking into account of, for example, the possibility of unfavourable deviations of the actions, the possibility of inaccurate modelling of the actions, uncertainties in the assessment of effects of actions and uncertainties in the assessment of the limit state considered (the values of yF are given in Eurocode 4 (Ref. 4: 2.3.3.1) and present chapter III.3: yG (permanent actions), yQ (variable actions), . . .).

38

I Ref. Chapter I - Introduction I (6) The combinations of actions respectively for ULS and for SLS are given in chapter TII.

EC4 [2.2.2.5] (7) Design values of the effects of actions :

The e f f i of actions (E) are responses (for example, internal forces and moments (Nu V s MSd), stresses, strains, deflections, rotations) of the structure to the actions. Design values of the effects of actions (Ed are determined fiom the design values of the actions, geometrical data (ad) and material properties when relevant:

[form. (2.211 IEd =E(Fd,ad, ...)I 12.2.3 Material properties

EC4 [2.2.3.1(1)] (1) Characteristic values of material properties:

- A material property is represented by a characteristic value Xk which in general *

corresponds to a hctile in the assumed statistical distribution of the particular property of the material specified in relevant standard or according to tests results (e.g. concrete, steel reinforcing bars). Certain properties of some components (e.g. resistance of a shear connector PRk) are treated as material properties,

- Structural steel parts (e.g. steel beam, profiled steel decking) of composite structures are generally represented by nominal values used as characteristic values (dbctored) 0,

- For other materials properties the characteristics values are for some verifications substituted or supplemented by mean or nominal values which correspond to the most likely values throughout the structure for which a minimum characteristic value has been specified (case for concrete properties and for physical coefficients).

EC4 [2.2.3.1 (2)]

EC4 I2.2.3.1 (311

EC4 [2.2.3.2 (211 (2) Design values of material properties:

For composite structures, the design values of the material strengths (a) and geometrical data (ad), when relevant, shall be used to determined the design resistances of members or cross- sections, according to the individual chapters, as :

EC4 [2.3.4 (611 in most cases where ' y ~ is the partial safety factor for the resistance. The different ' y ~ factors are

explicitly given in the design formulas and their values are provided in table 11.10 for ULS checks. ' y ~ factors shall be taken as 1,0 for SLS checks, except where stated otherwise in particular clauses. Where the resistance is influenced by the buckling of the structural steel, other formulations are used, including a specific safety factor YRd (see chapter II.6).

1.2.3 Design requirements

12.3.1 General

EC4

[2.3.1 (111

[2.3.1(2)]

[2.3.1(3)]

(1) It shall be verified that no relevant limit state is exceeded.

(2) All relevant design situations and load cases shall be considered.

(3) Possible deviations fiom the assumed directions or positions of actions shall be considered.

39

I Ref. Chapter I - Introduction I [2.3.1 (411 (4) Calculations shall be performed using appropriate design models (supplemented, ifnecessary, by

tests) involving all relevant variables. The models shall be sufficiently precise to predict the structural behaviour, commensurate with the standard of worlananship likely to be achieved, and with the reliability of the information on which the design is based.

12.3.2 Serviceability Limit States

EC4

r2.3.4 (111 (1) It shall be verified that:

[form. (2.1311

where Ed

c d

is the design effect of actions, determined on the basis of one of the combinations defined in chapter III, is a nominal value or a function of certain design properties of materials related to the design effect of actions considered.

(2) Practical checks of SLS in floors and frames for instance (see chapter 1.4):

where 6vd is the design vertical deflection of floors

(recommended limits 6v- = L/250, . . .), is the design horizontal deflection of frames (limits 8~max = h/300, ...),

is the design natural frequency of floors (recommended limits ffin = 3 Hz, ..A

6Hd

fd

L2.3.3 Ultimate Limit States

EC4

[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. (2.711 Isd Rd I where sd

Rd

is the design value of an internal force or moment (or of a respective vector of several internal forces or moments),

is the correspondmg design resistance, associating all structural properties with the respective design values.

(2) Practical checks of ULS in members for instance (see chapter 1.4):

condition concerning separate internal forces or moments or, interaction between them

where (NM, VM, MM) are design internal forces and moments applied to the members,

(NRd, VRd, M R ~ ) are design resistance of the members.

( 0 7 7 M)7 ( N 7 M), ... )

40

pf. Chapter I - Introduction 1

EC4 [2.2.2.4 (l)]

EC4 [2.3.4 (111

EC4 [2.3.2.1 (211

EC4 [form. (2.311

Table 1.1 Summary of design requirements

.) frame submitted to SLS and ULS combinations of design actions Fd (Gd, Qd, wd, sd, ...) :

where Fk is the characteristic value of actions,

YF is the partial safety factor for the considered action (see chapter III.3)

!) after global analysis of the frame :

- design effects of actions (e.g. deflections, frequencies) (for SLS):

Ed ( = ( & L f d ) ) - design values of internal forces and moments (for ULS):

s d ( = (NSd, vSd7 MSd) ) I) verification conditions at limit states :

for SLS checks

- ingeneral:

- for instance:

for mschecks

- ingeneral:

where Cd is the nominal value related to the design effect of considered actions (design capacity).

where 8vd is the design vertical deflection of floors,

6Hd is the design horizontal deflection of frames,

fd is the design natural frequency of floors,

Gv-, G-, ffin are recommended litnits (for instance: L/250, h/300, 3 Hz).

where & is the design resistance (= (NRd, VRd, M R ~ ) :

where & is the characteristic value of the used material,

' y ~ is the partial safety factor for the resistance (see table 11.10)

- for instance:

condition concerning separate internal forces or moments or, interaction between them ((V, M), (N, w,...)

41


Type of connection

1.3 Design of composite braced frame EO? [4.9]

Symbols in the analysis Designed for Design or detail criteria

1.3.1 Generalities

tension, compression or shear only

pinned connection

(1) Frames shall be checked : - at Serviceability Limit States :

ECQ [5.2.1 (311 - for horizontal deflections (see chapter 1.4.3),

- atUltimateLimitStates: EC4 [4.1.1 (3)] - for static equilibrium (see chapter I.3.2),

EC3 p1.2 (211

- for resistance of cross-sections, members and connections (see chapter 1.4.4).

(2) When checking the resistance of composite cross-sections and members of a frame, each member may be treated as isolated from the frame, with forces and moments applied to each end as determined from the frame analysis. The conditions of restraint at each end should be determined by considering the member as part of the frame and should be consistent with the type of analysis and mode of failure.

L3.1.1 Analysis models for frames

Small restraint to sufficient rotations : example in Figure II.5 a) @

Ref. 6 [Table 5.21

Rigid connection

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

Small rotations, sufficient elastic moment and shear strength : example in Figure II.5 a) @

I For semi-rigid connections no application rules are given in Eurocode 4

42

I k f . Chanter I - introduction 1

0 0

/ 0

0 /

0 0 r

/ 0 ' 0 0

0 0 ,

43


13.1.2

(1) The Figure 1.5 presents a sequence given by Eurocode 4 to follow in order to verify the design of

Design procedure for composite braced frame EC4 [4.9.1(7)]

a composite braced frame.

Define the imperfections of the frame (EC4 : 4.9.3) and represent them by equivalent horizontal forces at nodes (see chapter 1.3.3.2) Ensure that no steel connection is “semi-rigid”, using 4.10.5 of EC4 and clause 6.9.6 of EC3. For members of reinforced or prestressed concrete, ensure the ductility requirements of clause 2.5.3 of EC2 are met. Check that the frame is braced (EC4 : 4.9.4.3) (see clause 1.3.1.2 (2)). Check that the bracing substructure is non-sway (EC4 : 4.9.4) (see clause 1.3.1.2 (3)). Decide whether the requirements for rigid-plastic global analysis (EC4 : 4.9.7) are satisfied if relevant. Carry out global analyses (EC4 : 4.9.5 to 4.9.7) for relevant load combinations and arrangements and hence find design internal forces and moments at each end of each member (see chapter III. 1). Verify the composite beams (EC4 : 4.2 to 4.4) (see chapter V), columns (EC4 : 4.8) (see chapters IV and VI), and connections (EC4 : 4.10). Verify beams, columns, and connections of structural steel (to EC3) and of concrete (to EC2). Reference is made to the effective length (buckling length) of reinforced concrete and steel columns in EC4,4.8.3.6(4). For reinforced concrete columns, clause 4.3.5.5.3 and 4.3.5.6 of EC2 (“isolated columns”) are applicable.

Figure 1.5 EC3 p2.5.3 (211 (2) Classification of braced or unbraced frame :

Design procedure for composite braced frame

braced frame unbraced frame

6 b

I I 0

- - - - - - I I ‘\ ,/ I

I 0

l-r- I

I I I 0

. I Theframe is braced if: 18b I 0,26 “1

where 6b

6u is the horizontal displacement of the frame with the bracing system

is the horizontal displacement of the unbraced frame,

according to first order elastic global analysis of the fiame submitted to hypothetic horizontal loads.

44

I Ref. Chapter I - Introduction I ~~~

Note: In the case of simple frames with all beamcolumn nodes nominally pinned, the frame without bracing would be hypostatic, hence 6, is infinite and thus the condition 6b I 0,2 & is always fulfilled.

EC3[5.2.5.2] (3) Classification ofswav or non-swqv fiame : A frame may be classified as non-sway if accordmg to first order elastic global analysis of the frame for each ULS load case, one of the following criteria is satisfied :

a) in general : EC3

[5.2.5.2 (3)]

EC3 [5.2.5.2 (4)]

I 0,l , condition which is equivalent to IF=& 1 where V u

vcr

is the design value of the total vertical load,

is the elastic critical value of the total vertical load for failure in a sway mode ( = x2 E I / L2 with L, buckling length for a column in a sway mode; V, of a column does not correspond necessarily to V, of the frame including that column),

a, is the coefficient of critical amplification or coefficient of remoteness of critical state of the frame.

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

I I I

where H, V are the total horizontal and vertical reactions at the bottom of the storey,

is the relative horizontal displacement of top and bottom of the storey,

is the height of the storey,

are deduced from a first order analysis of the frame submitted to both horizontal and vertical design loads and to the global imperfections of the frame applied in the form of equivalent horizontal forces (see Table 1.4).

6

h

Y V , S

Notes: - A same frame could be classified as sway according to a load case (Vu1 for instance) and

as non-sway according to another load case ( V w for instance).

- The simplified method b) may provide non conservative results if the geometry of the structure and/or the applied loading are non symmetrical.

45

1 Ref. Chapter I - Introduction I - For multi-storeys buildings the relevant condition is

Vcr

condition which is equivalent to a, = minimum (%), where (2) - or- are related

to the storey I.

1.3.2 Static equilibrium

EC3 [2.3.2.4] (1) For the verification of static equilibrium, destabilising (unfavourable) actions shall be represented

by upper design values and stabilising (favourable) actions by lower design values.

(2) For stabilising effects, only those actions which can reliably be assumed to be present in the situation considered shall be included in the relevant combination.

(3) Variable actions should be applied where they increase the destabilising effects but omitted where they would increase the stabilising effects (YQ = 0, in Table 111.7).

(4) Account should be taken of the possibility that non-structural elements might be omitted or removed.

(5 ) For building structures, the normal partial safety factor given in Table III.7 apply to permanent actions (YG = 1,O if favourable actions).

(6) Where uncertainty of the value of a geometrical dimension significantly affects the verification of static equilibrium, this dimension shall be represented in this verification by the most unfavourable value that it is reasonably possible for it to reach.

1.3.3 Load arrangements and load cases

13.3.1 Generalities

(1) Load arrangements which may be applied to buildings are provided in chapter III.2.

(2) Load cases (see chapter III.3) may be established according to two procedures to study structures submitted to actions :

- a general procedure presented in Figure In. 1 or,

- a particular procedure presented in Figure III.2 which is applicable for braced buildings because such structure may be studied by first order elastic global analysis.

(3) Two types of load cases shall be considered : - load cases for Serviceability Limit States and,

- load cases for Ultimate Limit States,

where differences are related to combination rules: - see Table III.6 for SLS combinations of actions

- see Table III.7 for ULS combinations of actions

46


Initial sway imperfections + of the frame

F2

L3.3.2 Frame imperfections EC4

[4.9.3 (311 (1) In case of braced frame the effects of global frame imperfections shall be taken into account in the global analysis of the bracinn svstem.

EC3 [5.2.4.1(1)] (2) Appropriate allowances shall be incorporated to a v e r the effects of practical imperfections,

including residual stresses and geometrical imperfections such as lack of vertically, lack of straightness due to weldmg or lack of fit and the unavoidable minor eccentricities present in practical connections.

EC3 p.2.4.3 (111 (3) The effects of imperfections shall be allowed for frame analysis by means of:

- an equivalent geometric imperfection in the form of an initial sway imperfection + or,

- equivalent horizontal forces according to Table 1.4, either method is permissible.

(4) As shown in Table 1.4 the initial sway imperfections of a frame are directly proportionate to the relevant applied vertical loads of each load case. Therefore global imperfections of a frame should be calculated for each load case.

Table 1.4 Global imperfections of the frame

equivalent horizontal forces

F2

Ref. 6 (table 5.5)

I I

I I Fi I - [,"

0 (Fi + F2) Q (Fi + F2)

2 2

EC3 p.2.4.3 (411 (5) The initial sway imperfections 4 apply in all horizontal directions, but only need to be considered

in one direction at a time. The Table 1.5 gives the numerical values for 4 : EC3

[form. (5.211 14 = kc ks 001

1 where +o =- 200

1 kc =40.5+- "C I 1,0, and ks =

where is the number of columns per plane,

% is the number of storeys.

47

~ I Ref. Chapter I - Introduction I EC3 p.2.4.3 (211 (6) Only those columns which cany a vertical load NSd of at least 50% of mean value of the vertical

load per column in the considered plane, shall be included in R. EC3 p.2.4.3 (3)] (7) Only those columns which extend through all the storeys included in ns shall be included in .

Only those floor or roof levels which are connected to all the columns included in n, shall be included when determining ns.

Table 1.5

I

Values for the initial sway imperfections + number

* = 2 Q = 3 Q = 4 n , = 5

m in plane

\F! number of storeys rn

1 I230

1 I 275

1 1315

1 1345

1 1280 1 I240

1 1285

1 1325

1 1355

1 I 3 3 5

11515

1 1385

1 1535

1 I420

1 I630

1.3.4 First order elastic global analysis

L3.4.1 Methods of analysis EC4 p.9.5 (I)] (1) The internal forces and moments in a statically determinate structure shall be obtained using

statics. EC4 [4.5.9(2)] (2) The internal forces and moments in a statically indeterminate structure may generally be

determined using either :

- elastic global analysis

- plastic global analysis

(3) Elastic global analysis may be used in all cases.

48

I Ref. Chapter I - Introduction 1 13.4.2 Effects of deformations

EC4 [4.9.2.5]

(1) The internal forces and bending moments may generally be determined using either : - first order theory, using initial geometry of the structure, or,

- second order theory, taking into accoul?f the influence of the deformation of the structure.

(2) First order theory may be used for the global analysis of braced frames, in general. Alternatively second order theory may be used for the global analysis.

L3.4.3 Elastic global analysis EC4 [4.9.6]

EC4 [4.9.6.1 (I)] (1)

EC4 [4.9.6.1 (411 (2)

EC4 [4.9.6.1 (2)] (3)

EC4 I4.9.6.1 (3)] (4)

EC4 [4.9.6.2] (5) EC4 [4.9.6.2 (2)]

I EC4

I [4.9.6.2 (411

EC4 [4.9.6.2 (111

(7)

Elastic global analysis shall be based on the assumption that the stress-strain behaviour of the material is linear, whatever the stress level. Concrete in tension shall be included or neglected. When it is included, reinforcement in tension may be neglected. Reinforcement in compression may normally be neglected. This assumption may be maintained even where the resistance of a cross-section is based on its plastic resistance. Concrete in tension may be included or neglected. When it is included, reinforcement in tension may be neglected.

In order to determine the internal forces and moments (N, V, M) in braced composite frames, first order elastic global analysis may be used only where all connections are either rigid or nominally pinned (see chapter 1.3.1.1 (2)).

The effects of slip and uplift may be neglected at interfaces between steel and concrete at which shear connection is provided in accordance with chapter V.2.7.

The principles about sequence of construction (Ref. 4 : 4.5.3.2) and shnnkage of concrete (Ref. 4 : 4.5.3.3) are applicable.

FlexuraI stifjhess :

For composite beams in braced frames both methods of elastic global analysis are allowed (see chapter V.2.3) :

- with uncracked section (Ea Il),

- or, with cracked section (Ea 11 and Ea I2), where flexural stifhesses Ea I1 and Ea I2 are evaluated according to clause V.2.1 (5).

In first order analysis of braced frames the elastic flexural stifhess of composite columns should be taken as Ea 11 , where I1 is the "uncracked" second moment of area, as defined in Eurocode 4 (Ref. 4 : 4.2.3) and with the help of Table IV.8.

Creep effects shall be considered if they are likely to reduce the structural stability significantly. But creel effects in composite columns may be ignored if conditions of Eurocode 4 are satisfied (Ref. 4 : 4.9.6.2 (3)).

Redistribution of bending moments are allowed in Eurocode 4 within certain conditions (Ref. 4 : 4.9.6.3).

In case of first order elastic global analysis the principle of superposition is applicable because the effects of actions (E, S) are linear functions of the applied actions (F = G, Q, ...) (no P-A effects and used material with an elastic linear behaviour).

49

1 Ref. Chapter I - Introduction

Ref. 6 [Table 4.31

The principle of superposition allows to consider a particular procedure to study structure submitted to actions. This procedure illustrated in Figure III.2 could be more practical because it should simpllfy the decision of which load case gives the worst effect.

Table 1.6 Recommended limits for horizontal deflections

Multi-storey frame

160 I ho / 500

1.3.5 Verifications at SLS

Single storey frame

s H

- Portal frame without

gantry cranes 6 S h / 1 5 0

- Other buildings 6 I h / 3 0 0

The limiting values for vertical deflections of beams, cracking of concrete and vibrations of floors are given respectively in chapters V3.2, V.3.3 and V.3.4.

13.5.1 Deflections of frames

EC4 [5.2.1 (3)] EC3 [4.2.2 (411 The limiting values for horizontal deflections of frames given in Table 1.6 are illustrated by

reference to the multi-storey and single-storey frame.

1.3.6 Verifications at ULS

L3.6.1 Definition of braced frames and non-sway frames

EC3 [5.2.5.1(1)] (1) All structures shall have sufficient stiffhess to resist to the horizontal forces and to limit lateral

sway. This may be supplied by:

a) the sway stif35ess of the bracing svstems, which may be :

- triangulated frames,

- rigid-jointed fiames, - shear walls, cores and the like.

b) the sway stifhess of theframes, which may be supplied by one or more of the following :

- triangulation,

- stiffhess of the connections,

- cantilever columns.

50


(2) Framing for resistance to the horizontal loads and to sway. Two examples are given in Table 1.7 :

a) typical example of a frame with “bracing system”, which could be sufficiently stiff: EC3 p 2 . 5 . 3 (111 - for the frame to be classified as a “braced fiame”,

- and, to assume that all in-plane horizontal loads are resisted by the bracing system. EC3 15.2.5.3 (211

EC3 p2.5.2 (I)]

The criterion of classification as braced or unbraced frames is explained in chapter 1.3.1.2.

b) example of a bracing system which could be sufficiently stiff: - to be classified as a “non-swav flame”,

- and, to neglect any additional internal forces or moments arising from in-plane horizontal displacements of its nodes.

EC3 [5.2.5.2 (3), (411 The criteria of classification as sway or non-sway frames are detailed in chapter 1.3.1.2.

Table 1.7 Definition of framing for horizontal loads

1) With bracing svstem :

11111111 11111

Braced Frame 2) Non-swav frames :

Frame fully supported laterally

+

+ Bracing System

(3) According to Eurocode 4 application rules, composite frames should be braced and the bracing system (composite or not) should be checked to be according to Eurocode 3 rules (Ref. 3 : 5.2.5) (see chapter 1.3.1 .2)7 sway or non-sway for each load case.

EC3 15.2.5.3 (311 (4) A braced composite frame may be treated as a non-sway frame fdly supported laterally.

51

I Ref. Chapter I - Introduction I (5) As the criterion of braced or unbraced frame classification is related to the sti&ess of the frame

and on hypothetic horizontal loads, the frame should be classified as braced or not independently of load cases.

L3.6.2 ULS checks

EC4 The frames shall be checked at ultimate limit states for the resistances of cross-sections, members and ~ ~ e c t i o n ~ . For those ULS checks reference may be made to the following chapters :

- Members in compression : chapter lV - Membersinbending: - Members with combined axial force and bendhg moments

chapter V chapter VI

- COMeCtiOnS: see Eurocode 4 (Ref. 4) [4.10]

1.4 Content of the design handbook

1.4.1 Scope of the handbook

(1) In summary, the document covers the following aspects in detail: - Composite beams with composite or solid slabs,

- Bracedframes, - Continuous beams (or with connections equivalent to the moment resistance of the beam),

- Welded headed stud shear connectors,

- Full or partial shear connection,

- Class 1 or 2 sections (class 3 webs are permitted for continuous beams),

- Composite columns (encased I sections or concrete filled sections) under axial load,

- Composite columns with moments using simplified interaction method,

- Partially encased sections, - Elastic global analysis of composite frames.

(2) The document makes only general reference (and does not include detailed information) on: - Simply supported (simple connections),

- Design of connections,

- Behaviour of composite slabs,

- Cmlanginconcrete, - Other forms of shear connector,

- Use of precast concrete slabs,

- Lightweight concrete,

- Lateral-torsional buckling,

- Fire resistance aspects, - General analysis of composite columns,

- Class 3 or 4 sections for composite beams.

52

I Ref. Chapter I - Introduction 1

(3) Following topics are exchded: - Non-uniform cross-sections,

- Swayframes,

- Partial strength co~ections.

EC4 p.1.2 (6)] (4) E u r d e 4 Part 1.1 (Ref. 4) does not cover:

- resistance to fire (see Eurocode 4, Part 1.2: Fire resistance) nor, more generally, resistance at nonclimatic temperatures;

- resistance to highly repeated actions liable to result in fatigue;

- resistance to dynamic actions that are not quasi-static;

- particular aspects of special types of civil engineering works (such as bridges, crane girders, masts, towers, offshore platforms, nuclear containment vessels); for bridges, see Eurocode 4, Part 2;

- particular aspects of special types of buildings (such as industrial buildings as fkr as htigue would need to be considered);

- prestressed structures; - members the structural steel component of which has cross-sections with no axis of

symmetry parallel to the plane of its web;

- members the structural concrete or of concrete including heavy aggregate, or has less reinforcement than the minimum values given in clause [5.4] of Eurocode (Ref. 2), or contains expanding or non-shrinkage admixtures;

- composite plates consisting of a flat steel plate connected with a concrete slab;

- swayframes; - some types of shear connectors (see chapter 11.3.4);

- semicontinuous frames such that rigid-plastic global analysis cannot be used (see [1.4.2(1)] in Eurocode 4 (Ref. 4), and in Eurocode 3 (Ref. 3) clause [5.2.2.4] and [Table 5.2.11);

- base plates beneath composite columns;

- particular aspects of composite piles for foundations;

- particular aspects of members with haunched or tapered steel components (non uniform cross-section);

- particular aspects of box girders;

- particular aspects of totally or partially encased beams (see however [4.3.3.1], Annex B and Annex G);

- and more generally particular aspects mentioned as not covered in the following chapters (relating for example to the form of cross-sections);

- thermal or sound insulation (see [ 1.1.1(2)] of Eurocode 4 (Ref. 4));

- partial strength connections; - beams with fullyencased steel sections (see [4.1.1( l)] of Eurocode 4 (Ref. 4)).

53

1 Ref. Chapter I - Introduction

Type of checks

1.4.2 Summary of the table of contents

- chapter I: 0 benefits of composite structures; 0 limit states (SLS, ULS), design requirements; 0 design procedure for global analysis of braced composite frames according to

0 scope, definitions; - chapter 11: 0 Complete set of data of the structure (types of elements, material properties);

0 recommendations for composite design; - chapter 111: 0 determination of load arrangements and load cases for Ultimate Limit States

- chapter IV to VI:

EC4;

and, Serviceability Limit States;

0 SLS checks for beams (see chapter 1.4.3); 0 ULS checks of members (beams and columns, ...) submitted to internal forces

and bending moments (N, V, M) considering the resistance of cross-sections, the overall buckling of members (buckling, lateral-torsional buckling) and local effects (shear buckling of webs 0): see chapter 1.4.4;

- chapter VII: 0 generalities about design of composite slabs

Vertical Horizontal cracking of Vibration of

beams beams deflections of deflections of concrete floors

1.4.3

(1) The Table 1.8 presents the different checks which shall be fulfilled by beams and frames at

Checks at serviceability Limit States

Serviceabilitv Limit States with references to the design handbook :

Table 1.8 Checks at Serviceability Limit States

1 BCXUllS Chapter V.3.2 - Chapter V.3.3 Chapter V.3.4

Frames Chapter V .3.2 Chapter 1.3 Chapter V.3.3 Chapter V.3.4

1.4.4 Checks of members at Ultimate Limit States

For building structures, the requirements of clause 2.3.4 of EC3 concerning static equilibrium shall be satisfied.

No consideration of temperature effects in verifications for ultimate limit states is normally necessary for composite structures for buildings.

The effects of shrinkage of concrete may be neglected in verifications for ULS for composite structures for buildings, except in global analyses with members having cross-sections in Class 4 (4.3 and 4.5.3.3).

The effects of creep of concrete on both global and local analyses may be allowed for in composite members and frames in building structures by the use of modular ratios. For slender columns, 4.8.3.6(2) is relevant.

54


Nx. sd

axis x

[4.1.1 (9)] (5 ) For composite members in building structures, a fatigue check is not normally required, except for:

- members supporting lifting appliances or rolling loads

- members supporting vibrating machinery - members subject to wind-induced oscillations

- memben subject to crowd-induced oscillations.

(6) The following tables define the different checks which shall be fulfilled at Ultimate Limit States by all the members of frames submitted to internal forces and moments (N, V, M).

Table 1.9 Member submitted to internal forces and bending moments

vy . Sd VzSd My. Sd Mz. Sd

Xy xz xz Xy

- Table I. 10: 0 Definition of the planes of cross-sections within internal forces and bending moments (Nsd, VSd, MSd) are acting.

- Table I. 1 1: For different types of loading on the members (tension, compression, bending, combined (N, M)) the table I. 1 1 provides the internal forces, bending moments ((Ncompression), V (Vy, Vz), M (My, MA), and i n t e r x t h ~ between them ((V, M), (N, M), (N, V), (N, V, M) ,...) to be checked at Ultimate Limit States.

(7) In respective following chapters tables present lists of the checks to be performed at Ultimate Limit States for members or webs submitted to different loading:

- in chapter IV, Table IV. 1 for member in compression,

- in chapter V, Table V.2 for members in bending,

- in chapter VI, Table VI. 1 for members with combined axial force and bending moment.

Planes within internal forces and bending moments (NM, VM, Msd) are acting Table 1.10

, A

55


Table 1.11 Internal forces and bending moments to be checked at ULS for Merent types of

Type of loading on the members

Internal forces and bending moment an& i n t e d o n s betweenthem

Members in compression (columns, ...) : chapter IV

Members in bending

chapter V (beams, ...) :

Members with combined (N , M)

chapter VI (beamscolumns,. . .) :

Ncompression

I sagging hogging ' M y S d M y.Sd Vz.Sd

Z I

.- X

2'

.- X 1. v z.Sd

! M y.Sd

56

Chapter I1 - Structural concept of the building I

I1 STRUCTURAL CONCEPT OF THE BUILDING

57

I Ref. Chapter II - Structural concept of the building I

I1 STRUCTURAL CONCEPT OF THE BUILDING This chapter intends to list the characteristics of composite buildings concerning the types of structure, members and joints, the geometry and the material properties. Recommendations for composite design are also provided. The load arrangements applied to the building are defined in chapter III.

11.1 Structural model

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

(2) The geometry of the building should be defined : the height, width and length of the structure, the number of storeys, the dimensions of a rch imra l elements,. . .

11.2 Non structural elements

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

11.3 Load bearing structure

All the elements which bear the loads should be defined : frames, beams, columns, bracing system, concrete core, slabs, shear connectors, joints, props, . . .

11.3.1 Types of columns

There are two main type of composite columns ; - concrete-encased columns : totally (Figure 11.1 a)) or partially (Figure II. 1 b) and c)),

- and, concrete-filled columns (Figure II.1 d) to 0). This design handbook only deals with the types a), b), d) and e) of composite columns from Figure II. 1.

Figure 11.1 Types of composite columns


59

I Ref. Chapter 11 - Structural concept of the building 1 11.3.2 Types of beams

Ref. 7 [4.1.2] Composite beams may be of form shown in Figure II.2. Beams are usually of hot-rolled sections @E, HE, UB or UC section). Partial encasement of the steel section provides increased fire resistance and resistance to buckling.

Shear cokectors (see chapter II.3.4) between the slab and beam provide the necessary longitudinal shear transfer for composite action. The shear connection of the steel beam to a concrete slab can either be by full or partial shear connection. These different types of shear connection are considered in chapter V.2.7.

Partially encased steel section

A ComDosite slab

/ Steel beam

transverse reinforcement

)I - + rolled steel section

headed studs

Figure 11.2 Types of composite beams

60

I Ref. Chapter I1 - Structural concept of the building 1 11.3.3 Types of slabs

Ref. 7 j4.1.31 Slabs are either ( see Figure II.3) :

- concrete slabs : prefibricated, or cast in situ, or - comDosite slabs : profiled steel decking and concrete (see chapter W).

Slabs are generally continuous but are often designed as a serie of simply supported elements spanning between the beams.

\ profiled steel decking / -

/ prefabricated slab

Figure 11.3 Types of composite slabs and concrete slabs

61

1 Ref. Chapter II - Structural concept of the building 1 I

d 7' /'

1 weld collar

meanw20,2d \

min w 20,15 d ,\ I

11.3.4 Types of shear connector

\ I

Ref.7 [4.1.4] In principal, any type of shear connector is permitted provided it has sufficient resistance and ductility and prevents uplift. Headed stud shear connectors (see Figure II.4) are in common use and are the only ones considered in this hanbook for some other types of ~ ~ e c t o r ~ in solid slabs, refer to Eurocode 4 (Ref. 4 : chapter 6) : fiiction grip bolts, block connectors (bar connector, T-connector, [connector, Horseshoe), anchors and hoops, block C O M ~ C ~ O ~ S with anchors or hoops, angle connectors. Shear connectors comprising steel angles fixed by shot-fired pins are also in common use, but no application rules are given in Eurocode 4.

l

t20 .4d

EC4

[3.5.2 (711

[6.4.2 (111

[6.1.2 (111

[6.3.2.1]

[6.4.2 (411

\\ I/////////\/ I

h 1 3 d! generally ""I I h 1 4 d for ductile behaviour

Figure 11.4 Minimum dimensions of headed stud shear connector

11.3.5 Types of joints

Ref.7 [4.1.6] (1) There are many types ofjoints. Some examples are given in Figure II.5 for beam-tocolumn and beam-to-beam connections. In design to Eurocode 4, the two forms of joints generally envisaged are nominally pinned or rigid and full strength (see Figure II.5 a and b). No application rules are given for partial strength connections, in Eurocode 4.

(2) In Figures II.5 b and c, the joints may be considered to be rigid, but may or may not develop the full strength of the composite section. In the case of Figure 4.6 c the joint is pinned in the construction stage, but is made moment resisting by the slab reinforcement and fitting pieces which transfer the necessary tension and compression forces.

(3) This design handbook only assumes the use of pinned or ripid joints. Semi-rigid joints are not considered. In the case of semi-rigid joints whose behaviour is between pinned and rigid joints, the designer should take into account the moment-rotation characteristics of the joints (moment resistance, rotational stifiess and rotation capacity) at each step of the design @redesign, global analysis, SLS and ULS checks) when Eurocode 4 will provide application rules.

(4) The Figure II.6 presents the modding of joints. The joints may be modelled by nodes offset from the member centrelines to reflect the actual locations of the connections.

EC4 [4.10.5]

62

I Ref. Chapter I1 - Structural concept of the building I

I lr-- 1 anti-crack reinforcement - n - I-

I I I

secondary beam

reinforcement ‘-I

I II

secondary beam I sections J

a) Examples of “nominally pinned” joints both in the construction and composite stages

I - - - - .. - tensile reinforcement

b) Examples of “rigid” and full strength joint

c) Examples of joint “pinned” in the construction stage and “semi-rigid” (partial strength) in the composite stage

Figure 11.5 Examples of joints in composite fiames

63

~ I Ref. Chapter II - Structural concept of the building I Type of joint

RIGID joint (see Figure II.5 : example b)

SEMI-RIGID joint (see Figure II.5 : example c)

PINNED joint (see Figure 11.5 : example a)

Modelling

I I

----

I I

----1----- I I

I

!

----1-----

Behaviour

t M

t M

M

Figure 11.6 Modelling of joints

11.4 Recommendations for composite design Ref. 7 [2]

(1) ComDosite beams comprise I or H section steel beams attached to a “solid” or “composite” floor slab by use of shear connectors (see Figure 11.2). Comuosite slabs comprise profiled steel decking which supports the self weight of the wet concrete during construction and acts as “reinforcement” to the slab during in-service conditions (see Figure 11.3).

(2) Simply-supported composite beams behave as a series of T beams in which the concrete is in compression when subjeded to sagging moment and the steel is mainly in tension. The beams may be designed as simplv-sutmorted, or as continuous over a number of supports. The relative economy of “simple” or “cOntinuous” construction depends on the benefits of reduced section size and depth in relation to the increased complexity of the design and the connections in continuous construction.

64

I Ref. Chapter I1 - Structural concept of the building 1 (3) Construction methods :

Ref. 7 [4.1.5] Steel beams andor profiled steel deckings may be eitherpromed or unuropped during concreting of the slab in the construction stage of composite building. The most economic method of construction (speed of construction, ...) is generally to avoid the use of temporary propping (unpropped construction method). But propping may be needed where the steel beam and/or the profiled steel decking are not able to support the weight of a thick concrete slab during construction, or where deflections of those steel elements would otherwise be unacceptable. The number of tempomy supports need not be high. These props are usually left in place until the concrete slab has developed an adequate strength.

Figure II.7 shows the effects of the different construction methods - propped or unpropped - in principle, and this in comparison with a bare steel beam without any composite action. The drawing represents bending moments at midspan 0 over midspan deflections (6). MG denotes the bending due to the dead weigth of the structure.

Under service conditions, the different construction methods lead to different deflections, force distributions and stress states. But when the composite beams of same cross section are loaded up to failure, they fail at the same bending moment (Mpl.~d). Their strength is independent of the method of construction, and this bending strength can be calculated easily on the basis of on rectangular stress block, as demonstrated in chapter V.2.5.1. There is another reason for different strain and stress distributions and deflections under service conditions : the longterm behaviour of concrete. Both, creep and shnnkage of the concrete part yields larger strains and stresses in the steel section under service conditions. At the ultimate limit state, however, strains due to loadings are much larger than the strains due to creep and shnnkage, and the latter can be neglected.

Ref. 13

I $l.Rd - - - - r r * cumnq .:.:.:.:.:.:.:.:.. . ...... ......... :.:.:.: ...... '.:.:.:.,.:.:.:.:. ........ .... ..... . " WPropped

I

.:.:.:.:.:.:.:.:.. '.:.:.:.,.:.:.:.:. . . . . . . ........ ........................ cumnq f l 7 #q"J . ...... ......... :.:.:.: ...... ........ .... ..... . - I EJJfiaq

Figure 11.7

(4) The following recommendations are made for initial sizing of composite beams. It is important to recognize the difference between secondav beams which directly support the decking and composite slab and primuv beams which support the secondary beams as point loads. Primary beams usually receive greater loads than smndary beams and therefore are usually designed to span a shorter distance for the same beam size. Alternatively, long span primary beams, such as composite trusses, can be designed efficiently with short span secondary beams. These cases are illustrated in Figure II.8.

Effects of propped and unpropped construction

Ref. 7 [2]

65

I Ref. Chapter II - Structural concept of the building I ( 5 ) General features for comDosite slab

- Slabdepth: typically 120 mm to 180 mm depending on fire resistance, structural and other requirements.

- slabspan: . 2,5 m to 3,5 m, ifunpropped steel decking,

. 3,5 m to 5,5 m, if propped steel declung,

. with maximum slab span to slab depth ratio (L / (hp + b) of 32 for a simply-supported slab (see chapter VI1 for further guidance).

(6) General features for composite beams :

- Gridsizes: primary and secondary beams can be designed for approximately the same depth when grid dimensions are in proportion of 1 / 1,5 respectively.

- Beamdesign:

The following beam proportions should give acceptable deflections when the section size is determined for moment resistance. The ratios (span to depth ratio) can be expressed as (L / (ha + hp + b)) where L is the distance between adjacent supports and (ha + hp + b) is the total beam and slab depth.

a) Simply supported beam :

. Secondary beam :

. Primary beam :

b) Continuous beam :

. Secondary beam :

. Primary beam :

span to depth ratio of 18 to 20,

span to depth ratio of 15 to 18.

span : depth ratio of 22 to 25 (end bays),

span : depth ratio of 18 to 22.

- Steelgrade: higher grade steel (S 355) usually leads to smaller beam sizes than lower grade steel (S 235 or S 275).

- Concretegrade: C 25/30 for composite beams.

- Shear connectors : 19 mm diameter welded stud connectors are placed typically at about 150 mm spacing. These headed studs can be welded through the profiled steel decking up to 1,25 mm thick;

66

I Ref. Chapter II - Structural concept of the building I

&6- 12m Secondary beam

-I

m

Secondary beam

Span of slab s

-

73 - 1

Column 7 .

Primary beam 6

I Primarybeam

-T 2,5 - 4 m

t :'I I -4 8 - 12m-

Primary beam Column .

span of

+ slab

\ I I J

6-8m

\ I I I I

/ / 12 - 18 m]

Figure 11.8 Framing plans for medium and long span beams

67

I Ref. Chapter II - Structural concept of the building

Strength class of concrete

c20125

c25130

c30137

11.5 Material properties

V I The material properties given in this chapter II.5 are those required for design purposes.

Partial safety factors for resistance and material properties are also provided.

fck Etm fctk 0,05 fctk 0,95 Ecm N I m 2 N l m 2 NImm2 Nlmm2 kNlmm2

20 292 1,5 299 29,O

25 2,6 198 333 30,5

30 2,9 290 398 32,O

11.5.1 Concrete

c35145

c40150

c45155

C50160

EC4 [3.1.2 (211 (1) Normal-weight and lightweight concretes may be used. Table II.1 aves properties of normal-

weinht concrete. The classification of concrete, e.g. C20125, refers to cylinder strength (20) and cube strength (25) of concrete.

EC4 [3.1.2(3)] (2) For Zinhtweinht concretes, tensile strengths (b; fctk 0,05; f& 0,95) can be obtained by

multiplying the values provided in Table 11.1 by the factor :

35 392 2 2 492 333

40 395 235 476 35,O

45 3,8 297 4,9 36,O

50 491 299 5,3 37,O

-(24pOojl, q = 0,30 +0,70 - where p is the oven-dry unit mass in kg/m3

c35145

c40150

c45155

C50160

EC4 [3.1.4.1 (311 In the same way, the secant moduli Ecm for light-weight concretes can be obtained by multiplying

the values given in Table II. 1 by the factor : - /o21- EC4 [3.1.1(2)] (3) Concrete classes higher than (30160 should not be used unless their use is appropriately justified.

No Application Rules are given in Eurocode 4 for this case.

Table 11.1 Concrete classes and characteristic values for compression and tension

35 392 2 2 492 333

40 395 235 476 35,O

45 3,8 297 4,9 36,O

50 4-1 2 3 5 33 37,O

68

& 0,05

f& o,g5

is the lower value of the characteristic tensile strength (fractile 5%),

is the upper value of the characteristic tensile strength (hcti le 95%),

Notations : fck is the characteristic compressive cylinder strength measured at age 28 days,

I w. Chapter 11 - Structural concept of the building I

Conditions

EC4 13.1.31 (4) For shrinkane of concrete, the total long-term free shnnkage strain from setting of the concrete may be taken as nominal values of Table II.2.

Nominal values of shnnkage strain Table 11.2

for normal-weight for lightweight concrete concrete

C25130

Dry environments (filled members excluded)

C30137 C35145

325.104

C45155

11,7

598

17,5

I 500.104

C50160

11,4

597 17,O

Other environments and filled members 200.104 I 300.104

EC4 [3.1.4.2] (5) Modular ratios :

For the design of braced composite buildings, it is accurate enough to take accounf of creel> by replacing in analyses concrete areas & by effective equivalent steel areas equal to AJn, where n is the nominal modular ratio (see Table 11.3) defined by :

where Ea

E::

is the elastic modulus of structural steel (see Table II.7),

is an “effective” modulus of concrete defined as follows : EC4 [3.1.4.2 (4)] a) in most structures for composite buildings, for both short-term and

long-term effects : IE, = E,, 121 ,

b) in buildings mainly intended for storage,

- for short-term effects: -1, - where Em is the mean secant modulus for short-term

loading, depending on the strength class of concrete (see Table II. 1).

for long-term effects: IE’, = E cm / 3 I ,

Table 11.3 Values of nominal modular ratios n = (Ea/, ’I Strength Class C

of concrete

of buildings ComDosite buildings in general : for short-term and long-term effects ComDosite buildings for storage : for short-term effects

for long-term effects

C20125

14,5

21,7 =

20,7 19,7 18,8

C40150

18,O

69


(6) The material coefficient (pc, C~T, vc) to be adopted in calculations for concrete shall be taken as given in Table 11.4.

Table 11.4 Design values of material coefficient for concrete

EC4 [3.1.6]

EC4 [3.1.4.3]

density for normal-weight concrete coefficient of linear thermal expansion

pc = 2400 kdm3

- for normal-weight concrete : CtT = 10 lod 1/'c

- for lightweight concrete CXT = 7 lod 1/'c Poisson's ratio :

- ingeneral,forelasticstrains : vc = 0,2

assumed to be cracked v c = o - for concrete in tension

11.5.2 Structural steel EC4 [3.3]

(1) The nominal values of the yield strength fy for hot-rolled steel are given in Table II.5 for steel grades S 235, S 275 and S 355 in accordance with EN 10025 and for steel grades S 275, S 355, S 420 and S 460in accordance with EN 101 13. Those nominal values may be adopted as characteristic (unfactored) values in design calculations.

(2) The european standard EN 10025 specifies the requirements for long and flat products of hot rolled weldable non-alloy structural steels (steel grades: S 235, S 275, S 355).

The european standard EN 10 1 13 specifies the requirements for long and flat products of hot- rolled weldable fine grain structural steels (steel grades: S 275, S 355, S 420, S 460).

(3) Similar values as defined in Table II.5 may be adopted for hot finished structural hollow sections.

(4) For a larger range of thichesses the values specified in EN 10025 and EN 101 13 may be used.

( 5 ) For high strength steels (S 420 and S 460) specific application rules given in the normative Annex H of Eurocode 4.

70

[ F2ef. Chapter II - Structural concept of the building I

EN 10027-1 Designation

Table 11.5 Nominal values of yield strength fy for structural steels according to EN 10025 andEN 10113

Nominal thickness t (mm)*)

> 16 > 40 > 80 > 100 1 I 4 0 1 5 6 3 1 2:; 1 I 1 0 0 1 I 1 5 0

EN 10025 Standard 5 1 6

Nominalsteelgrade I Nominal values of fy (N/ mm2)

S 235 S 275 s 355

EN 10113

S 275 s 355 S 420 S 460

Standard

235 225 215 215 215 195 275 265 255 245 235 225 355 345 335 325 3 15 295

275 265 255 245 235 225 355 345 335 325 3 15 295 420 400 390 370 360 340 460 440 430 410 400 -

S 235 S 275 s 355

S 275 s 355 S 420 S 460

Notes:

EN 10027-1

S235 S275 s355

EN EN NFA35-504/ NFA35-501 DIN DIN BS ASTh4 17102 17100 4360 NF A 36-201 10113 10025

S235 S235 E 24 St37 40 S275 S275 E 28 StE285 St44 43 2335.5 s355 E 355 E 36 StE355 St52 50 gr.50

5

*) t is the nominal thickness ofthe element : - of the flange of rolled sections (t = tf) - of the particular elements of the welded sections

(6) The Table II.6 compares the symbolic designations of steel grades according to various standards even if some of them have been replaced. The design handbook always uses the single designation of structural steels defined by the european standard EN 10027-1: "S" followed by the value of yield strength expressed in N/mm2 (= MPa).

Table 11.6 Comparison table of different steel grades designation

EC4

[3.3.3] , (7) The material coefficients (Ea, Ga, CLT, Pa, Va) to be adopted in calculations for the structural steels covered by Eurocode 4 shall be taken as given in Table II.7.

Table 11.7 Design values of material coefficients for steel ~~

. modulus of elasticity (E = Ea = E,) E = 210000 N/ltUll2

. shear modulus ( G = 2 ( 1 ~ , , J ( ~ = ~ a = ~ s ) : G = 80700 N/ItlIll2

. coefficient of linear thermal expansion aT' 10.106 1PC

. density (P = Pa = PSI p = 7850 kg/m3

. Poisson's ratio (V=Va=vS) : v = 0,3

71


S 500 Reinforcing steel grades s 220 S 420

fsk [N/mm21 220 420 500 I

11.5.3 Reinforcing steel EC4 [3.2]

Standard

EN 10 147

(1) In reference to EN 10 080 specification, different types of reinforcing steels are covered by E u r d e 4, with differences :

- according to ductility characteristics : high ductility (class H) or n o d

- according to surface characteristics : plain smooth bars or ribbed bars or wires

~

class (class N),

(including welded mesh).

fyb (= fyp) [N/mm21

Grade

FeE 220 G 220 FeE 250 G 250 FeE 280 G 280 FeE 320 G 320 FeE 350 G 350

[Ref. 121 (2) Euroc.de 2 (Ref. 2) gives 3 different classes for reinforcing steel (see Table II.8).

Table 11.8 Yield strength f& for reinforcing steel

(3) The material coefficients (Es, Gs, aT, ps, vs) to be adopted in calculations for reinforcing steels are presented in Table 11.7.

11.5.4 Profiled steel decking for composite slabs EC4 [3.4]

Ref. 7 [4.2.4](1) Composite slabs are dealt in this handbook only as far as they affect the design of composite beams. Reference should be made to Eurocode 4 (Ref. 4 : chapter 3.4 and 7) for fbrther information on the design of composite slabs, with EN 10 147 as the product standard for steel sheeting.

EC4 [3.4.2 (2)J (2) The nominal values of fyb provided in Table II.9 may be adopted as characteristic values fyp in

calculations.

Table 11.9 Yield strength of basic material fyb for steel sheeting

EC4 p a l e 3.41

72

I Ref. Chapter Il - Structural concept of the building 1

a) for column length with relative slenderness lh10,2] or I 0,l

11.5.5 Connecting devices EC4 [3.5]

:

EC4 [3.5.1(2>]

I

(1) For connecting devices (bolts, rivets, pins, welds) other than shear connectors chapter 3.3 of Eurocode 3 (Ref. 3) is applicable.

EC4 (3.5.21 (2) Shear connectors :

As explained in chapter II.3.4 this design handbook only provides application rules for headed studs with minimum dimensions detailed in Figure II.4.

The specified ultimate tensile strength of headed studs is commonly

If, = 450 N/-'I.

11.6 Partial safety factors for resistances and material properties at ULS

(1) In general resistance is determined by using design values of strength of the different materials and components, &, that takes into account uncertainties at ULS with partial safety factors ' y ~ .

The different ' y ~ Eactors are explicitly introduced in design formulas of this handbook.

EC4 [4.8.3.2] (2) The design of composite columns according to the simplified method is presented in chapter N

(Members in compression) and in chapter VI (Members with combined axial force and bending moment). In that case, the partial safety factor for structural steel is written as ' y ~ a and, in general, may have one of the 2 following values :

lYMa = Y a l ,

where Nx.Sd is the applied design axial load,

andNa are dehed in clause N.3 (4) and, if relevant, by additional comments in clauses VI. 1.2 (1) and (2),

b) otherwise, columns are influenced by buckling :

73

I Ref. ChaDter II - Structural ConceDt of the building I

(3) Recommended values of partial safety factors for fundamental load combinations are given in Table II.10. Improved values of y~ factors may be obtained in case of accidental load combinations : refer to Eurocode 4 (Ref4 : 2.3.3.2).

(4) The ’ y ~ factors shown in Table II.10 are provided according to the present official version of Eurocode 4 (Ref. 4). Those “boxed” values are only indicative. The values of y~ factors to be used in practice are fixed by ~ t i ~ d authorities in each country and are published in the relevant National Application Document OVAD) to EUroc.de 4.

(5 ) Values of y~ fixtors for bolts, rivets, pins, welds and slip resistance of bolted connections are given in Eurocode 3 (Ref. 3 : 6.1.1 (2)).

Table 11.10 Partial safety factors y~ for resistances and material properties at Ultimate Limit State

- Resistance of structural steel :

. ya is equivalent to ’ y ~ o of Euroc.de 3

. y&j is equivalent to ’ y ~ 1 of Eurocode 3 (if buckling of structural steel)

= ‘ya or ’yRd (see clause II.6 (2)) 4

.

- Resistance of concrete

- Resistance of reinforcement steel

- Resistance of profiled steel decking

- Resistance of shear connectors and longitudinal shear in slabs : (yv=1,251

74

ChaDter III - h a d arrangements and load cases I

I11 LOAD ARRANGEMENTS LOAD CASES

AND

75

I Ref. Chapter 111 - Load arrangements and load cases I


111.1 Generalities

(1) A loud urrunpement identifies the position, magnitude and direction of a free action (see chapter III.2).

(2) A loud cuse identifies compatible load arrangements, set of deformations and imperfections considered for a particular verification (see chapter 111.3).

EC4 [2.2.5 (111

[2.2.5(2)]

(3) For the definitions of actions (load arrangements: F= G, Q, ...) and effects of actions (E, S) and for the design requirements it should be referred to chapter 1.2 (Basis of design).

(4) Figure III. 1 presents the general procedure to study structures submitted to actions : - all load cases are defined by relevant combinations (with partial safety factors, E) of

characteristic (unfactored) values of load arrangements (Fk),

- for each load case the global analysis of the structure determines the design values for the effects of actions (Ed = &, 6h, f, (T ,... ; Sd = N, V, M ,...) which shall be checked at Serviceability Limit States (Cd limits) and at ultimate Limit States (Rd resistances).

This genral procedure is used in the procedure for elastic global analysis of composite braced frame presented in chapter 1.3.

(5 ) For braced buildings it is explained in chapter 1.3 that the elastic global analysis of the structure could be based o n j r s t order theory. In that case of first order elastic global analysis the princiule of superposition is applicable because the effects of actions (E, S) are linear functions of the applied actions (F = G, Q, ...) (no P-A effects and used material with an elastic linear behaviour). The principle of superposition allows to consider a particular procedure to study structures submitted to actions. This procedure illustrated in Figure 111.2 could be more practical because it should simplify the decision of which load case gives the worst effect. For each single characteristic (unfactored) value of load arrangement (Fk) the global analysis of the structure determines characteristic (unfactored) values for the effects of actions :

- Ek = <&, 6h, f, O,...)k

- sk = (N, v, M, ...)k. All load cases are defined by relevant combinations (with partial safety factors, 'yF) of the characteristic (unfactored) values for the effects of actions (Ek;Sk). All these load cases directly fkrnish the design values for the effects of actions (Ed = &, 6h, f, (T ,,... ; sd = N, V, M ,...) which shall be checked at Serviceability Limit States (cd limits) and at Ultimate Limit States (Rd resistance).

EC4 [2.2.1.2(2)] (6) For composite structures attention is drawn to the necessity of identifymg and considering, when

relevant, several transient design situations corresponding to the successive phases of the building

steel profiles have first to support the selfweight of fresh concrete slab and other construction loads before the concrete has gained adequate strength for composite action.

I I , process. The sequence of construction has to be considered especially for composite beams where

, Previous page

is blank 77

I Ref. Chapter III - Load arrangements and load cases

Two main stages may be considered with different load arrangements :

a) the construction stage and, b) the composite stage - .

But more specific transient design situations may be taken into acount : for example, at construction stage, it may be necessary not only to consider the situation of the steel beam supporting the fresh concrete, but even to distinguish several situations corresponding to successive phases of pouring the concrete.

w

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

i f

i > Determine al l SLS load cases with relevant

SLS combinations of load arrangements (Fk) \ J

2 ' Determine all ULS load cases with relevant

ULS combinations of load arrangements (Fk) (with partial safety factors y~ = 'yet 'yp, ...)

I I + All ULS load cases

0 analysed ? analysed ?

braced frame

' Global analysis of the structure submitted ' to the considered load case in order to

determine the design values for the ULS effects of L J

actions: Sd = N, V, M, ... 4

Determine ULS resistances (Rd)

I "O I /

SLS checks P ' Global analysis of the structure submitted ' to the considered load case in order to determine

the design values for the SLS effects of actions: Ed = Sh, &, f, 0, ...

4 Determine SLS limits (cd)

no I \ I

1-4 Select stronger section(s) or joint(s)

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

&& for the definition of Flt (Gk, Qk), yF ('p, ')Q, Sd, Rd, Ed, Cd : see chapter 1.2 (Basis of design).

Figure 111.1 Flow-chart for load arrangements and load cases for general global analysis of the structure

78

I Ref. Chapter III - Load arrangements and load cases 1

I

Global analysis of the structure submitted to the considered single load arrangement (Fk) in order to determine characteristic (unfactored) values for the effects of actions :

- for ULS Checks: Sk = (N, V, M ...) k - for SLS checks: Ek = (8h, &, f, 0, ...) k

Tows. Tows:

5

1 Determine all load arrangements with characteristic (unfactored) values of actions Fk (Gk, Qk, ...) 1

/

Determine all ULS load cases with relevant ULS combinations of effects of actions (Sli)

(with partial safety factors y ~ = F. YQ. ... )

Yes (All load arrangements analysed ?

\ I

no f \

ULS checks SL Design values for the effects of actions:

Sd = N, V, M, ...

7

8

9

10

11

1 2

t All ULS load cases

analysed? no

Classification of frame: braced frame

1 Determine ULS resistances (Rd) t

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

Design values for the effects of actions: Ed = 8h, 8v, f, 0, ...

analysed?

T (5 Determine SLS limits (Cd)

Sd 5 Rd? Adopt the structure if both

ULS and SLS checks are fulfilled

-4- Select stronger section(s) or joint(s) I

for the defmition of Fk (Gk, Qk), yF (s, 'jQ), Sd, Rd, Ed, c d : see chapter 1.2 (Basis of design)

2

3

4

5

6

7

8

9

.o

I1

12

FigureIII.2 Flow-chart for load arrangements and load cases for first order elastic global analysis of the structure

79

1 Fkf. Chapter III - Load arrangements and load cases

111.2 Load arrangements

(1) The following load arrangements are characteristic (unfactored) values of actions (Fk) to be applied to the structure. The characteristic values of load arrangements given hereafter are issued fromEurocode 1 (Ref. 1).

(2) The table III. 1 provides a list of

- all the load arrangements (Fk) to be taken into account in composite building design, either

- the references to the chapters of the handbook where details are given about those load

at construction stage, or at composite stage, and,

arrangements.

Table 111.1 Load arrangements Fk for composite building design according to Eurocodes 1 & 4

Load arrangements (Fk) at construction stage or at composite stage Reference to the I handbook

III.2.1 1) Permanent loads: distributed, g concentrated, G

2) Variable loads: - Imposed loads on floors and roof

-Wind loads: wind pressure, we,i

- Snow loads: distributed, s

distributed, q concentrated, Q

wind force, Fw

III.2.2.1 III.2.2.1 III.2.2.2 111.2.2.2 III.2.2.3

EC4 [2.2.5(5)] (3) For continuous beams and slabs in buildings without cantilevers subjected to dominantly

a) alternate spans Carrying the design variable and permanent loads (YQ Q + YG &, other

uniformly loads, it will generally be sufficient to consider only the following load arrangements:

spans carrying only the design permanent load 'YG gk :

EEiIEa W k yQqk

A B C D E

-> This load arrangement produces higher sagging bending moments and deflections in spans AB and CD.

80

I Ref. Chapter I11 - Load arrangements and load cases I

ECl-I [1.5.3.3]

ECl-I [ 1 53.41

b) any two adjacent spans carrying the design variable and permanent loads (YQ a + YG &, all other spans canying only the design permanent load YG gk :

c y Q k

+ + + i + + + i i t + + + i + i + + + + i + t + Y ~ g k

A B C D E

-> This load arrangement finishes higher hogging bending moment at support B.

111.2.1 Permanent loads (g and G)

(1) In general permanent loads are actions which are likely to act throughout a given design situation and for which the variation in magnitude with time is negligible in relation to the mean value (e.g. dead weight), or for which the variation is always in the same direction until the action attains a certain limit value.

(2) At construction stage, permanent loads should be limited to dead weight of steel profiles, whereas at comDosite stuge, they could include dead weight of steel profiles, concrete and steel decking, additional dead weight due to “ponding” of the concrete and service permanent loads.

111.2.2 Variable loads (9, Q, w and s)

(1) Variable loads are actions which are unlikely to act throughout a given design situation or for which the variation in magnitude with time is not negligible in relation to the mean value nor monotonic.

81


IIL2.2.1 Imposed loads on floors and roof (q and Q) EC4 [7.3.2.1( I)] (1) At construction staae, variable imposed loads could be taken as :

- dead weight of cast in-situ concrete,

- additional dead weight due to the “ponding” effect (increased depth of concrete due to deflection of the beam or sheet decking),

- construction loads including local heaping of concrete during construction,

- storage(ifany).

About construction loads, Eurocode 4 gives no specific guidance regarding their magnitude for the design of steel beams, but provides values for the design of profiled steel decking. Then to remain consistent it should be convenient to consider an imposed characteristic construction load of 0,75 kN/m2 for the design of a steel beam. For the design ofprofiled steel deckinx Eurocode 4 proposes the following rules :

The construction loads represent the weight of operatives and concreting plant and take into account any impact or vibration which may occur during construction. In any area of 3 m by 3 m (or the span length, is less), in addition to the weight of the concrete, the characteristic construction load and weight of surplus concrete (due to “ponding” effect) should together be taken as 1,5 kN/m2. Over the remaining area a characteristic loading of 0,75 kN/m2 should be added to the weight of the concrete. These loads should be placed to cause the maximum bending moment and/or shear (see Figure 111.3).

EC4 [7.3.2.1(2)]

~~

Loading, :

(a) concentration of construction load : 1,5 kN/m2

(b) distributed construction load : 0,75 kN/m2

(c) dead weight ~ ~~~ -

Figure 111.3 Construction loads on profiled steel decking

82

I Ref. Chapter 111 - Load arrangements and load cases 1

EC 1-2-1 I

[6.3.1.1] I (2) At comDosite sfape, areas in residential, social, commercial and administration buildings are divided into five categories according to their specific use (see Table III.2).

Table 111.2 [Table 6.11 Categories of building areas, traffic areas in buildmgs and roofs

Categories A

B C

D

E

F

G

H

I

K

Specific use Areas for domestic and residential activities.

office areas Areas where people may congrete (with the exception of areas defined under category A, B, D and E)

Shopping areas

Areas susceptible to accumulation of goods, including access areas

Traffic and parking areas for light vehicles. (I 30kN total weight and I 8 seats not including driver) Traffic and parking areas for medium vehicles. (> 30 kN, I 160 kN total weight, on 2 axles)

Roofs not accessible except for normal maintenance, repair, painting and minor reDairs. Roofs accessible with occupancy according to categories A-G

Roofs accessible for special senices, such as helicopter landings

Example Rooms in residential buildings and houses; rooms and wards in hospitals; bedrooms in hotels and hostels; kitchens and toilets

c1:

c2:

c3:

c4:

c5:

Areas with tables, etc. e.g. areas in schools, d&, restaurants, dinning halls, reading rooms, receptions etc. Areas with fixed seats, e.g. areas in churches, theatres or cinemas, conferences rooms, lecture halls, assembly halls, waiting rooms, etc. Areas without obstacles for moving

e.g. areas in museums, exhibition rooms, etc and access areas in public and administration buildings, hotels, etc. Areas with possible physical activities e.g. danse halls, gymnastic rooms, stages, etc. Areas susceptible to overcrowding, e.g. in building for public events like concert halls, sport halls including stands,

PeQPk

terraces and access areas, etc. D1: Areas in general retail shops,

e.g. areas in warehouses, stationery and office stores, etc.

Areas for storage use including librairies. The loads defined in Table III.3 shall be taken as minimum loads unless more appropriate loads are defined for the specific case. e.g. garages; parking areas, parking halls

e.g. access routes; delivery zones; zones accessible to fire engines (I 160 kN total weight)

83


5,o

i 530

(3) At comuosite stage, the values of characteristic imposed loads on floors and roof are given in Table m.3 according to the category of areas and the loaded areas (see Table m.2).

Table 111.3

[Table 6.21

Imposed load (ay Qk) on floors in buildings depending on categories of loaded areas

Cataorv E:

Category F:

Cate~orv A: - general

- stairs

- balconies

6,O 7,o

2,o 10

Catepory B: 3YO

Categorv C: - C1 330

- c 2 4,0

- c 3 590

Category G:

Categorv H: roof slope < 20'

> 40'

- c 4

- c 5

5,o 45

0,75 1,5

oyoo* 195

CategoryD: -D1

- D2

Categorv I:

Catenorv K:

A-G A-G

Specific use Specific use

470

7YO

* For slopes between 20' and 40' the value of Q may be determined by linear interpolation

I112.2.2 Wind loads (we, Fw)

(1) The wind forces acting on a structure or a structural component may be determined in two ways: EC 1-24

[6.1(1)]

- as a summation o f Dressures acting on surfaces provided that the structure or the structural component is not sensitive to dynamic response (cd < lY2),

- or, by means of global forces.

84

1 Ref. Chapter III - Load arrangements and load cases I

EC 1-24

[9.2 (111 (2) It is proposed in this handbook to present the simple procedure which may be used for buildings less than 200 m tall provided that the value of Q is less than 1,2. For values of dynamic factor Cd

: see figure III.4. In all other cases the detailed method of Eurocode 1, (Ref. 1: Part 2-4 Annex B) may be used.

200

150

100

50 Heigth h [ml

30

20

10 Breadth b [m]

5 10 20 50 100 Values of parameters used (Vref= 28 ds; terrain roughness category I:

Figure 111.4 Values of dynamic factor cd for composite buildings

111.2.2.2.1 Wind pressure (we;)

(1) The net wind pressure across a wall or an element is the difference of the pressures on each surface taking due account of their signs (pressure, directed towards the surfhce is taken as positive, and suction, directed away from the surface as negative): see Figure III.5.

EC 1-24

[5.4 (111

Figure 111.5 Pressures on surEaces

(2) The wind Dressure acting on:

a) the external surfaces of a structure, we, shall be obtained from

EC 1-24

P.2 (111


EC 1-24

P.31

[form. 5.21

b) the internal surEaces of a structure, Wi, shall be obtained from:

[7.1(111 where

[form. (7.111

where

Vref

[form. (7.2)]

where ce(q)

[form. (8.6)]

[10.2]

[10.2.2 (1) (c)]

[10.2.9]

where cpe

where q, zi

andwhere Cpi

is the reference mean wind pressure determined from:

p is the reference wind velocity taken as follows :

is the air density (generally = 1,25 kg/m3)

Vref =cDIR C T E M CALT Vref,O

where vref,o is the basic value of the reference wind velocity at sea level given by the wind maps of the countries (Annex

C D ~ is the direction factor to be taken as 1,O unless otherwise specified in the wind maps.

~ T E M is the temporary ( s ~ ~ s o M ~ ) factor to be taken as 1,0 unless otherwise specified in the wind maps.

CALT is the altitude fktor to be taken as 1,0 unless otherwise specified in the wind maps.

6.A of EC 1-2-4).

is the exposure coefficient for z = q is defined by: I

where k,, q (z), ct (z) are given for more details in Eurocode 1 (Ref. 1: Part 2-4, section 8)

For flat terrain (i.e. upwind slope I 5% in the wind direction) , ct =1,0. For such conditions the exposure coefficient Ce is given in the Table III.4.

is the external pressure coefficient which depends on the size of the effected area A and the shape of the building (see Table III.5). is the reference height appropriate to the relevant pressure coefficient (see Figure III.6).

Buildings whose height h is greater than 2b shall be considered to be in multiple parts, comprising: a lower part extending upwards from the ground by a height equal to b for which = b; and a middle region, between the upper and lower parts, divided into as many horizontal strips as desired and for which q is the height of the top of each strip. is the internal pressure coefficient. For a homogeneous distribution of openings the value t+i = - 0,25 shall be used. Else the coefficient is given in Figure 111.7 and is a hnction of the opening ratio p, which is defined as :

’ = area of opening at the leeward and wind paraUel sides

area of opening at the windward, leeward and wind parallel sides

86

I Ref. Chapter III - Load arrangements and load cases I

EC 1-24 [Table 8.11

EC 1-24 [Fig. 8.31

EC1-24, Fig.

Table 111.4 Exposure coefficient e as a function of height z above ground

Terrain Ca-ory: I Rough open sea, lake shores with at least 5 km fetch upwind and smooth flat country

without obstacles. II Farmland with boundary hedges, occasional small fkrm structures, houses or trees.

III Suburban or industrial areas and permanent forests. IV Urban areas in which at least 15% of the surface is covered with buildings and their

average height exceeds 15 m.

loo0

200

100

10

1 0 1 2 3 4 5

.2.21

Figure 111.6 Reference height Q depending on h and b

87


Cpi 0,8

O S

0 -

- 0,25

- 0.5

Table 111.5 External pressure cpe for verticals walls of rectangular plan buildings

- 1-

-

-

- b

EC 1-2-4 [Fig. 10.2.31

EC1-24 [Table 10.2.1 [Fig. 10.2.11

EC1-24 [Fig.

Wind G -D

f

AI B I C A* I B*

E

- m: d > e = m i n ( b ; 2 h )

m: d < e = m i n ( b ; 2 h )

A, A* B, B* C D E

- 1,3 - 1,o - 0,5 + 1,o - 0,3

- 1,0 I - 0,8 - 0,5 I + 0,8 / + 0,6 I - 0,3

&: For different shapes of the buildings, the values of Eurocode 1 (Ref. 1: Part 2-4).

are given in the section 10 of

2.111

0 0,l 0.5 0,75 0,9 1

Figure 111.7 Internal pressure coefficient Cpi for buildings with openings in the wall

88

I Ref. Chapter 111 - Load arrangements and load cases I

EC 1-24

16.1 (611

[fm.(6.

111.2.2.2.2 Wind force (Fw)

(1) The global force, Fw, shall be obtained form the following expression:

IFw 'qref Ce(ze)cd Cf Arefl

where Qref is the reference mean wind pressure (see III.2.2.2. I),

ce(ze) is the exposure coefficient for z = %(see III.2.2.2.1),

ze is the reference height appropriate to the relevant pressure coefficient (see III.2.2.2. I),

is the dynamic factor (see III.2.2.2. I),

is the force coefficient derived from Eurocode 1 (Ref. 1: Part 2-4 section 10) if available,

is the reference area for cf derived from Eurocode 1 (Ref. 1: Part 2- 4 section 10).

Cd

Cf

Aref

IIL2.2.3 Snow loads (s)

(1) The snow loads on a roof are given by: EC 1-2-3

where pi is the snow load shape coefficient

sk

Ce

c t

is the characteristic value of the snow load on the ground (kN/m2)

is the exposure coefficient, which usually has the value 1,O

is the thermal coefficient, which usually has the value 1,O

89


111.3 Load cases

EC4 [2.3.2.2 ( 11

The following load cases are related to the general urocedure to study structures submitted to actions (see Figure III. 1 and clause III. 1 (4)): all load cases are defined by relevant combinations (with partial safety factor, 'yF) of characteristic (unfactored) values of load arrangements (Fk).

For each load case, design values for the effects of actions (Ed, Sd) shall be determined from

global analysis of the structure submitted to the design values of actions (Fd = 'yF Fk) involved by combination rules as given :

- in Table III.6, for Serviceability Limit States,

- in Table III.7 and Table III.8, for Ultimate Limit States.

In the case of the particular urocedure defined in Figure III.2 (see also clause III.1 (5)), the characteristic (unfactored) values for the effects of actions (Ek, Sk) are obtained from global analysis of the structure submitted to each single characteristic (unfactored) value of load

For each load case, design values for the effects of actions (Ed, Sd) shall be determined from combination rules (with partial safety factor, yF) defined in Tables III.6 to 111.8 where values of load arrangements (Fk = Gk, Qk, g, q, s, w, P) are replaced by the characteristic values for the effects of actions (Ek = (&, 6h, f, (3 ,... )k ; s k = (N, v, M ,... )k). For instance, in the case of the third example in Table III.8, the general load case 1. (1,35 gk + 1,50 wk) should be replaced by the following particular load case 1. considering the elements or the cross-sections with :

arrangement (Fk).

0 their worst effects of actions (for cohmns: axial force @ilk; for beams: shear force (V)k and bending moment (M)k) and,

their worst combined effects of actions (for beam-columns: (N)k + (M)k ; ...) :

- max N = 1,35 (N)k(due to gk) + 1,50 (N)k.-(due to wk),

- max V = 1,35 (V)k(due to sk) + 1,50 (V)k.-(due to Wk),

- m a ~ M = 1,35 o k ( d u e to gk) + 1,50 OM)k.-(due to Wk),

- max N + associated M,

- max M + associated N, ...

(3) In the following chapters 111.3.1 and 111.3.2, the proposed combinations of actions are simplifications adapted to building structures : for SLS, see Eurocode 4 (Ref. 4: 2.3.4 ( 5 ) ) and for ULS, see Eurocode 4 (Ref. 4: 2.3.3.1 (6)).

(4) If the limitations imposed at SLS and at ULS meet difficulties to be respected, more favourable combinations of actions could be used instead of the respective simplified proposals of Table III.6 (then refer to [2.3.4 (211 of Eurocode 4) or Tables III.7 and III.8 (then refer to [2.3.2.2(2)] of Eurocode 4).

90

1 Ref. Chapter III - Load arrangements and load cases]

Load combinations to be considered:

with on& the most unfavourable variable actions (Qk.max) :

111.3.1 Load cases for serviceability limit states

Table 111.6 Combinations of actions for serviceability limit states

Gk- permanent actions,

Qk - variable actions, e.g. e.g. selfweight

Ref. 6 Table 2.3

EC4 r2.3.4 (511

with all unfavourable variable actions (Qk):

2. C G k +O79CQk

Ref. 6 Table 2. I

EC4 [2.3.3.1(6)]

a.- - the variable action which causes the largest effect

imposed loads on I floors, snow loads, II I wind loads

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

111.3.2 Load cases for ultimate limit states

Table 111.7 Combinations of actions for ultimate limit state

Load combinations to be considered:

with on& the most unfavourable variable actions (a.&: Y k C G k + Y G Qk.max

1. 1,35* C G k +Is()** Qk.-

with all unfavourable variable actions (Qk):

Y & C G k +079YF C Q k

2. 1,35* C G k +1,35** C Q k

Ifthe dead load G counteracts the variable action 0 * (meaning a favourable effect of G) : G =1,001

wind load Q 4 7 7 7 7 7 7 7 dead load G -

Ifthe variable load Q counteracts the dominant loading (meaning a favourable effect of Q) :

**

& - permanent actions, e.g. self weight.

Qk - variable actions, e.g. imposed loads on floors, snow load, wind loads.

- the variable action which causes the largest effect.

YG - partial safety factor for permanent actions.

YQ- par t i a ld i fhc to r for variable actions

The load combination which gives the largest effect (i.e.internal forces or moment ) is decisive.

91

:f. Chapter III - Load arrangements and load cases

Table 111.8 Examples for the application of the combinations rules in Table III.7. All actions (g, q, P, s, w) are considered to originate from Werent sources

II

IP II I

load cases

1. 2. 3.

1.

2.

3.

4.

1.

2. 3.

4.

combinations of actions ~

1,35g + 150s 1,35g +1,5Os

1,35 (g + q + s)

1,35 g + 450 q

1,35g +1,50P*) 1,35g + 130s

I,35(g+q+s+P1))

1,35g+1,50 w 1,35 g + 130 q 1,35g+1,50s 1,35 ( g + q + w + s )

g - deadload *) assuming P is independent of g, q, s and w

P - point load(variab1e) s - snowload

q - imposedload

w - windload

92

Chapter IV - Members in compression I


93

I Ref. Chapter IV - Members in compression 1


IV.1 Generalities

(1) For each load cuse (see chapter In) the design value of the following internal force may be applied to members submitted to centered axial compression which shall be checked at ultimate limit states :

z I

Y NxSd .- x ---4-L--

i

(2) This chapter only deals with composite columns which are of two main types :

- totally (Figure IV. 1 a)) or partially (Figure IV. 1 b)) concrete encased steel sections and, - concrete filled steel sections (Figures IV. 1 c) and d)).

.I b = b c .I r

Y 4- ezr I I

h=hc

Figure IV.l Type of cross-sections of composite columns


95

IRef. Chapter IV - Members in compression

EC4 [4.8.3.1]

EC4 [4.8.3.1 (5)]

[4.8.3.1 (311

[4.8.2.5]

[4.8.2.4]

[4.8.2.6] to I4.8.2.81

[4.8.3.3]

14.8.3.81

The steel section and the uncracked concrete section usually have the same centroid.

This chapter IV only applies to isolated non-sway composite members in compression.

This chapter IV presents the simpl@ed method of design (EC4 [4.8.3]) for composite columns of double symmetrical (Figure IV.1) and uniform cross-section over the column length. This simplified method uses the European buckling curves for steel columns (Eurocode 3) as the basic design curves for composite columns.

Application rules for composite columns of mono-symmetrical cross-section are given in Annex D of Eurocode 4 (Ref. 4). When the limits of applicability of the simplified method are not fblfilled (see chapter IV. 1. l), the general method (EC4 : r4.8.31) has to be applied.

That general method includes composite columns with non-symmetrical or non-uniform cross- section over the column length.

Design assumptions :

Both approaches for the design of composite columns are based on the following main assumptions :

- full interaction between concrete and steel up to the point of collapse,

- allowances must be made for imperfections which are consistent with those adopted for assessing the strength of bare steel columns,

- proper account must be taken of the steel and concrete stresse-strain curves,

- plane sections remain plane.

The Table IV. 1 provides a list of checks to be performed at Ultimate Limit States for the member submitted to centered axial compression (Nx.sd). A member shall have sufficient bearing capacity if all checks are fUIfilled. AI1 the checks have both references to Eurocode 4 and to the design handbook.

Table IV.l List of checks to be performed at ULS for the composite member in compression

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

Check the limits of applicability of the simplified design method Check concrete cover and reinforcement Check for local buckling of steel members Check the load introduction and the longitudinal shear

(1) (2) (3) (4)

( 5 ) Resistance of cross-section to Nx.sd :

Nx.Sd 5 Npl.Rd

Stability of member to N x . ~ , for both buckling axes : Nx.Sd 5 minimum (Nby.M;Nbz.Rd) (design f l e d buckling

resistances of the composite member about Y and z axes)

(design plastic resistance to compression of the composite cross-section)

(6)

References to design handbook

lv.l.l IV 1.1 (4) to (6)

Iv. 1.2 IV.1.3 & IV.1.4

IV.2

IV.3

96

I Ref. Chapter N - Members in compression I

-1 ,where

IV.l.l Limits of applicability of the simplified design method

fY Aa -

Ya

pl.Rd 6 =

EC4 [4.8.3.1 (311

Tvue of cross-section :

The column is of double-symmetrical and uniform cross-section over the column length (see Figure IV. 1).

Steel ratio : The steel contribution ratio of rolled or welded members should lie between following limits :

[4.8.3.4]

Ref. 7 [8.3.6]

(3)

(4)

where Npl .u is the design plastic resistance to compression of the composite cross-section (see chapter IV.2),

is the area of the structural steel profile,

is the yield strength of the structural steel profile (see table IIS),

is the partial safety factor for structural steel (see Table II.10).

Aa

fY

Ya

If 6 is less than 0,2 , the column shall be designed according to Eurocode 2. If 6 exceeds 0,9 , column design shall be made on the basis of Eurocode 3.

Member slenderness : The nondimensional slenderness h of composite member should be limited for both axes :

and Ih,\ where iy and xz are the nondimensional relative slendernesses for flexural buc-

about major axis (yy) and minor axis (zz) respectively (see chapter lv.3).

Reinforcement fin general) :

If the longitudinal reinforcement is considered in design, extreme limits of reinforcement, which are expressed in percentage of concrete area, are imposed :

Ref. 7 [8.3.6]

EC4 [4.8.2.5 (411

EC4 [4.8.2.5 (S)]

0,3% I - I 4,0% I 2: 1 where As

Ac

is the cross-sectional area of all longitudinal reinforcement bars,

is the cross-sectional area of concrete.

For reasons of fire protection, greater percentages of reinforcement can be included but shall not be taken into account for the design without consideration of fire problems.

The transverse reinforcement in concrete encased columns (see Figure IV. 1 a) and b)) should be designed according to clause 5.4.1.2.2 of Eurocode 2 (Ref. 2).

For the spacing of the reinforcement clause 5.2 of Eurocode 2 applies.

97

IRef. ChaDter IV - Members in comDression I

- inthey-direction: 4Omm S cy I 0 , 4 b ,

(5 ) Minimum reinforcement : EC4

p.8.2.5 p)] Concrete filled steel sections (see Figure IV.1 c) and d)) may be fabricated without any reinforcement. But in general if the longitudinal reinforcement is neglected in calculations for the resistance of the column, guidance on minimum reinforcement is given for all types of cross- sections in clause 4.8.3.1 (3)(f) of Eurocode 4 ,

- in the z-direction, maximum 40 mm;- S c, I 0,3 h r I .

Greater cover can be used but should be ignored in calculation.

IV.1.2 Local buckling of steel members

EC4

14.8.2.4 (2)] (1)

EC4 14.8.2.4 (311 (3)

At ultimate limit states the effects of local buckling of steel members in composite columns may be neglected provided that the steel parts in compression have to satisfy the limits defined in Table IV.2.

In practice, all standard H or I hot-rolled profiles presented in Tables V.7 (designed by WE, WE A, P E 0, HE AA, HE A, HE B, HE M, UB and UC) fulfil1 the limit conditions of Table IV.2 (first type of cross-section : partially concrete encased steel profile) for all steel grades (S 235, S 275, S 355); therefore they can be designed without consideration of local buckling.

If the limit values given in Table IV.2 are exceeded, the effect of local buckling should be taken into account by an appropriate experimentally mnfirmed method.

98

1 Ref. Chapter IV - Members in compression I

Table IV.2 Limiting width-to-thickness ratios to avoid local buckling

Type of cross-section Ref. 7 Tab. 8.1

4 b J

B

IV.1.3 Influence of longitudinal shear EC4 [4.8.2.6 (111 (1)

EC4 [4.8.2.7 (111

EC4 [4.8.2.7 (211 (2)

Ref. 7 [8.2.4] (3)

Limiting ratio

bltf s

h / t S

d l t .s

- No verifkat member,

Limits for different steel grades

S 235

44

52

90

'n of loc

q-T buckling for steel

- In order to prevent premature spalling of the concrete, minimum concrete cover may be provided (see IV. 1.1 (6)) :

In general internal forces and moments applied from members connected to the ends of a composite column length have to be distributed between the steel and concrete components of the column, by considering the shear resistance at the interface between steel and concrete.

The shear resistance between the steel section and the concrete may be developed by : - chemical bond and friction at the interface steel-concrete, or

- mechanical shear connection, such that no significant slip occurs.

As the natural bond between steel profile and concrete is uncertain, the design shear resistance due to bond and friction may be limited to the values given in Table IV.3.

An exact determination of bond stresses between structural steel and concrete requires extensive calculation. Stresses may be determined in a simplified way either according to elastic theory or from the plastic resistance of the cross-section. The variation of stresses in the concrete member between two critical sections can be used for the determination of bond stresses.

For axially loaded columns, it is usually found that this intehce shear is sufficient to develop the combined strengths of both materials at the critical cross-section (mid-column height). For columns with significant end moments, a horizontal shear force is needed, which requires the development of longitudinal shear forces between the concrete and steel.

99

~~

IRef. Chapter IV - Members in compression I

Table IV.3 Design shear resistance stresses (due to bond and friction) at the interface between steel and concrete

0,6 N / m 2

0,2 N / m 2

0,O Nlmm2

0,4 N / m 2

IV.1.4 Regions of load introduction

(1) Where a load is applied to a composite column, it must be ensured that within a specified introduction length, the individual components of the composite cross-section are loaded according to their resistances so that no significant ship occurs between these parts. For this purpose, a division of the loads between the steel and the concrete must be made in a manner similar to that described in section IV. 1.3.

In order to estimate the distribution of the applied load, the stress distributions at the beginning and the end of the region of introduction must be known. From the differences in these stresses, the loads which are transferred to the cross-section components may be determined.

The following requirement on the introduction length l i of the region of load introduction should be satisfied :

Ref. 9

14.81

lei I 2 d l EC4 [4.8.2.6 (3)]

where d is the smaller of the two cross-section dimensions h or b (see Figure IV.2) or the cross-section dimension normal to the bending axis (h for My.% orb for MZ.sd).

N x.Sd -- b I I

N x.Sd -*

Figure IV.2 Introduction length Pi for the shear force

100

I Ref. Chauter N - Members in comuression I

(2) A simple method of distributing the loads to be introduced can be made by help of the plastic resistance of the different cross-section components, the steel section, the concrete and the reinforcing steel, as follows :

where Na.M is the resistance to compression of the steel cross-section

Np1.M is the resistance to compression of the composite cross-section (see chapter lV.2),

Ma.M is the moment resistance of the steel cross-section [wfy), -

Mpl . Rd is the plastic moment resistance of the composite cross-section (see chapter VI.2),

Ncs. Sd is the design axial load applied to the concrete and the reinforcement,

Mcs. Sd is the design bending moment applied to the concrete and the reinforcement .

If the loads are applied through a connection to the steel section, the elements of the load introduction, e.g. the headed studs, must be designed to transmit the concrete components of the loading, Ncs.Sd and Mcs.+j. In the case of load introduction from the concrete into the steel section, e.g. through brackets, the respective steel forces and moments, Na.Sd and Ma.Sd , must be allowed for in the design.

~4.8.2.6 (411 (3) In an I-section with concrete only between the flanges, the concrete should be gripped by stirrups and a clear defined load transmission path between concrete and steel web should be identified (see Figure lV.3).

EC4

Stirrups welded stirrups passed Shear connectors to web through web on web

Figure IV.3 Mechanical shear connection

(4) For single-storeys columns, head plates are generally used as the elements for load introduction. In those cases no other connecting devices are needed. Special detailing is necessary for continuous columns; for these cases, headed studs have proved to be economic when used with open cross-sections as shown in Figure IV.4 . The forces on the outward stud connectors are transmitted to the flanges and the friction force developed, R, may be evaluated as follows :

101

I Ref. Chapter N - Members in compression

EC4 [4.8.2.8 (2)] lR+!q

where pRd is the design resistance of one headed stud connector (see chapter V.2.7), is the coefficient of friction (= 0,5). EC4 [6.5.2.1 (l)]

EC4 [Fig. 4.1 11 P

Figure IV.4 Shear resistance of headed stud connectors used to create direct load transfer into the concrete

IV.2

4.8.3.3 (1) (1) For members in axial compression, the design value for the compressive force Nx.Sd at each composite cross-section shall satisfjr:

Resistance of cross-section to axial compressive force Nn.Sd

fY fck

fsk

mal Yc, Ys

is the design plastic resistance to cornpression of the composite cross-section (see Table NS), are the cross-sectional areas of the structural steel, the concrete and the reinforcement (see Table IV.6),

is the yield strength of the structural steel (see Table IIS),

is the compression strength of the concrete (see Table II. l),

is the yield strength of the reinforcement (see Table II.8),

are partial safety factors at ultimate limit states for the structural steel, concrete and reinforcement steel (see Table II. lO),

l

- A

qlo = 4,9 - 183 h+ 17 XL, and qlo 2 0 (see Table IV.4),

q20 = 0,25 (3+2%), and 1120 I 1,O (see Table N.4), - A is the non-dimensional relative slenderness of composite member

(see chapter IV.3),

102

[Ref. Chapter IV - Members in compression I

EC4 [Table 4.51

Table IV.4 Values of ~ 1 0 and q20 in function of 2 - h 0 07 1 072 093 074 2 0,5

r\ 10 4,90 3,22 1,88 0788 0,22 0,OO

r120 0,75 0780 0,85 0,90 0,95 1 ,oo ~ ~ ~ _ _ _ _ ___ ~ _ _ _ ___ ~~

Table IV.5 Design plastic resistance to compression N p l . u

Types of cross-sections and stress distributions for Np1.M

f Y hMa 0.85 G

4+

.Rd ..

Np1.M =

Aa- fY +Ac( 078;cfck) +As - fsk YMa Ys

A, * + A C ( ; ; ) t A , y , fck sk YMa

Notation : "+" means stresses in compression ; for calculation of Aa, As and & , see Table IV.6

103

IRef. Chapter IV - Members in compression

EC4 [4.8.3.3

(3)to(6)] (2) For concrete-filled circular hollow section (the 4th type of cross-section in Table N.5) the strength is increased because of confhement - of the steel tube and triaxial containment of concrete and, if relative slenderness of the member : h I 0,5.

Table IV.6 Cross-sectional areas of the structural steel (Aa), the reinforcement (As) and the concrete (&)

Types of cross-sections

h

d

Cross-sectional area

Aa = 2 t (h+ b - 4 r) + x (r2 - r&)

& = (b - 2 t) (h - 2 t) - (4 - x ) rint 2 - As

n(d2 - d k t )

4 A, =

104

I Ref. Chapter IV - Members in compression 1

Nx.Sd 5 Nby.Rd

Nx.Sd Nbz.Rd

IV.3 Stability of member to axial compressive force NE^

= Xy Npl.Rd

= Xz Npl.Rd

(1) The compression members shall be checked to flexural buckling mode (buckling by plane bending) according to both principal axes of the section (major axis: yy; minor axis: zz) with the appropriate buckling lengths (Lb.Y Lb.z).

EC4

[4.8.3.8] (2) For members submitted to axial compression the design value of the compressive force Nx.Sd shall satisfl:

where Nby.Rd and Nby.Rd are the design flexural buckling resistances of the member for

X y xz are the buckling reduction factors for the buckling mode about yy and zz axes,

Npl.Rd is the design plastic resistance to compression of the composite cross-section (see chapter IV.2 and Table N.3).

buckling mode about yy and zz axes,

(3) For constant axial compression in members of constant cross-section, the value of the buckling reduction coeficient x (xY, xZ ) is related to the appropriate non-dimensional relative slenderness - - - 1 (Icy ,A,>:

EC3, [5.5.1.2 ( I ) ]

1 - , but p] X = f(A) =

$+ j p [form. (5.4611

where $=02 [ l + a (x -o72)+2] ,

a is an imperfection factor (see Table N.7), depending on the appropriate buckling curve.

Table IV.7 Imperfection factors a

11 Buckling curve I a I b I C I I

11 Imperfection factor a I 0,21 I 0,34 I 0,49 11

The buckling reduction factor x is given in function of each type of cross-sections in Table IV. 1 1. When failure mode (then, x = 1,O).

and the appropriate buckling curve for I 0,2 flexural buckling is not a potential

105

IM. Chapter IV - Members in compression 1

(4) The nondimensional relative slenderness % has to be considered for the relevant plane of b e n u : zy and xz, respectively for buckling about major yy and minor zz axes :

where N p l . ~ is equal to Npl .u as defined in Table IV.5 (see chapter IV.2) with ma = yc = f i = I , O ,

is the elastic critical load of the member abut yy

axis,

1Ncr.z = II 2 (E Iz)e /LieZI is the elastic critical load of the member about zz I I

axis,

(E I)e is the effective elastic flexural stifiess of the composite cross- section, about major (yy) and minor (zz) axes :

are the moduli of elasticity of the structural steel and the reinforcement steel (see Table 11.7),

is the effective elastic modulus of the concrete according to the following clause IV.3 (9,

are the moments of inertia for bending about y axis of the structural steel, the concrete (assumed to be uncracked) and the reinforcement, respectively (see Table IV.8),

are the moments of inertia for bending about z axis of the structural steel, the concrete (assumed to be uncracked) and the reinforcement, respectwely (see Table IV.8),

are the buckling lengths of the member about y and z axes according to clause IV.3 (6).

106

1 Ref. Chapter IV - Members in compression I

Table IV.8 a) Moments of inertia of totally and partially concreteencased steel profile ~ ~~

Ia, Is, are the moments of inertia for structural steel, reinforcement and concrete (assumed to be uncracked) for bending about y and z axes

Y 4-

CZ

31

1 I,, = E[ bh3 - (b - t )(h - 2t f ) + 0,03r4 + 0,2146r2 (h - 2tf - 0,4468r)2

I,, - Is, b& I,, =--

I 12

3 1 2 t fb 3 +(h-2tf)tw +0,03r4 +0,2146r2(tw +0,4468r)*

12

n I/ i= 1

Notations : see table IV.8 c)

107

I Ref. ChaDter IV - Members in compression

Table IV.8 b) Moments of inertia of concrete-filled rectangular hollow section

Ia, Is, E are the moments of inertia for structural steel, reinforcement and concrete (assumed to be uncracked) for bending about y and z axes

(b - 2r)h3 2r(h - 2r)3 2 + 5 (1 - 3) + x r 2 [: - r (1 - $11 +

12 12 4 1a.y =

2 (b - 2t - 2qnt)(h - 2t)3 - 2rht (h - 2t - 2rmt)3 12 12 4

(h - 2r)b3 2r(b - 2r)3 4 2 1a.z = 12 + 12 + ~ ( l - ~ ) + x r ’ [ ~ - r ( l - ~ ) ] 4

I Notations : see table IV.8 c)

108

I F2ef. Chapter IV - Members in compression I

Table IV.8 c) Moments of inertia of concrete-filled circular hollow section

Ia, Is, E are the moments of inertia for structural steel, reinforcement and concrete (assumed to be uncracked) for bending about y and z axes

d t dint

4

64 1S.Z dint

1) Notations : n is the number of reinforcement bars,

is the own moment of inertia of re-bar i ( = 4 , with cp = re- 64 bar diameter),

(P4

Asi 4 is the area of re-bar i (= x - , with cp = re-bar diameter),

is the distance of the re-bar i of area Asi to the relevant eyi or ezi middle line (z axis or y axis).

109

IRef. Chapter IV - Members in compression I EC4 [4.8.3.5] (5) The effective elastic modulus of the concrete varies ifthe effects of short-term or long-term

loadmg are taken into account for the composite columns. For slender columns (with % greater than limits given in Table IV.9), the long-term behaviour of the concrete (creep and shnnkage of concrete) reduces the resistance. This influence can be considered by a simple modification of the effective elastic modulus of the concrete :

EC4 [4.8.3.5 (I)] - for short-term loading : El I r c I

where E m is the secant modulus of elasticity of the concrete according to Table II. 11,

EC2 [A.3.1] [A.3.4] yc = 1,35 according to Eurocode 2 (Ref. 2). -

E C ~ [4.8.3.5 (211 - for long-term loading and slender h is greater than limits

given in Table IV.9)

where Ecm and yc are defined for short-term loading,

N X . sd

NG.Sd

is the applied design axial force,

is the part of the applied design axial force (Nx.sd) that is permanently acting on the column,

is the nondimensional relative slenderness for flexural buckling about relevant axis ( i y , i z ) ( s e e clause IV.3 (4)).

- h

Table IV.9 Limiting values of for long-term loading

Types of cross-section For braced non-sway frames, influence of long-term behaviour of concrete should be

considered :

if h 2 -

0,8 l ( 1 - 6)

Notation : 6 is the steel contribution ratio (see chapter IV. 1.1 , clause (2))

110

[Ref. Chapter IV - Members in compression 1

EC4 r4.8.3.6

(1) and (2)] (6) The buckhp Zength Lb (Lb.y, Lb.z) of an isolated non-sway compression member with both ends effectively held in position laterally may conservatively be taken as equal to its system length L; or alternatively, the buckling length may be determined using informative Annex E of Eurocode 3 (Ref. 3) and specific rules given in Eurocode 4 (Ref. 4 : [4.8.3.6]).

Buckling lengths of columns in a non-sway mode may be provided in Table IV. 10 for different boundary conditions to be demonstrated according to Eurocode 4.

Table IV.10 Buckling length of column,

System

A

Buckling length Lb

2 L

L

0,7 L

0,5 L

111

IRef. Chapter IV - Members in compression 1

EC3 [table 5.5.21

Table IV.ll Buckling reduction factors x = f (x ) for composite cross-sections

x

relative lendemess

Reduction buckling factors x

x

Buckling axis : any

curve a

1,0000

1,0000

0,9775

0,9528

0,9243

0,8900

0,8477

0,7957

0,7339

0,6656

0,5960

0,5300

0,4703

0,4 179

0,3724

0,3332

0,2994

0,2702

0,2449

0,2229

Major buckhg axis : yy

curve b

1,0000

1,0000

0,964 1

0,926 1

0,8842

0,8371

0,7837

0,7245

0,66 12

0,5970

0,5352

0,478 1

0,4269

0,3817

0,3422

0,3079

0,278 1

0,252 1

0,2294

0,2095

x z

Minor buckling axis : zz

curve c

1,0000

1,0000

0,949 1

0,8973

0,8430

0,7854

0,7247

0,6622

0,5998

0,5399

0,4842

0,4338

0,3888

0,3492

0,3 145

0,2842

0,2577

0,2345

0,2141

0,1962

112

Chapter V - Members in bending 1

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

113

I Ref. Chapter V - Members in bending 1

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

v.l Generalities

( 1 ) For each load case (see chapter III) the design values for the following effects of actions are applied to members in bending and shall be checked at serviceability limit states (SLS) and at ultimate limit states (ULS) :

- ForSLS : . vertical deflections (&),

. craclung of concrete (4,

. vibrations ( f )

separate or combined vertical shear force and ben- moment : - ForULS :

0

EC4 [4.1.2 (I)]

EC4 [4.1.1 (l)]

EC4 [4.1.3]

(2) This chapter V only deals with composite beams which have been presented in chapter II (see Figure II.2 for m i d types of cross-sections).

Beams with concreteencased steel webs are included (see Figure II.2) but beams with fullyencased steel sections are excluded.

(3) This chapter V applies to isolated composite beams and to composite beams in composite frames.

(4) Depending on sequences of construction, steel beams loaded by wet concrete have to be checked at construction stage according to Eurocode 3 rules (Ref. 3). Those verifications are out of the scope of this design handbook.

At composite s t a s when concrete is matured, composite beams have to be checked at ultimate limit states and at serviceability limit states according to Eurocode 4 as explained in this chapter V.

(5) In composite beams the possible critical sections to be checked, are summarised in Table V. 1.


115

IRef. Chapter V - Members in bending I

Ref. 7 [Figure 6.21

EC4 [4.1.2 (3) & (411

Table V.l Critical sections for the design calculation and related action effects to be checked

D- -D

Critical cross-sections :

A-A

B-B

c-c C’-C’

Regions :

D-D

E-E and F-F

G-G

I

bending moment resistance to My. Sd (cross-section)

vertical shear resistance to VZ.Sd (cross-section, shear buckling, web crippling)

ben- moment-vertical shear interaction to Vz .u and M y . u (cross- section, shear buckling)

longitudinal shear resistance to Ve of the shear connectors

longitudinal shear resistance to Ve of the slab and transverse reinforcement

lateral-torsional buckling to My.Sd of bottom flange (for continuous beam or cantilever).

EC4 [4.1.2 (411 Critical cross-sections may be for example the sections A-A (maximum sagging moment), B-B

(support), C-C (sudden change of cross-section) and C’-C’ (internal support with maximum hogging moment) shown in Table V.l; critical cross-sections may be also sections subjected to heavy concentrated loads or reactions.

In case of simply-supported beams : no check of lateral-torsional buckling may be needed in composite stage (see chapter V.2.5.2.1) and if beam is subject to uniform load, no bending moment-vertical shear interaction has to be considered.

116

I Ref. Chapter V - Members in bending I

EC3 [5.4.6 (l)]

EC3 [5.6.1(1)]

EC3 [5.6.3 (l)]

EC3 [5.7.4 (l)]

EC4 [6.3.2.1]

EC4 [6.6.2]

EC4 [4.4.1]

EC4 [4.6.2]

EC4 14.6.31

EC4 [6.3.2.1

EC4 [6.6.2]

(6) The Table V.2 provides a list of the checks to be performed at Ultimate Limit States for the member in bending (V; M; (V, M)). A member shall have sufficient bearing capacity if all the checks are fulfilled according to the loading applied to that member. For instance, in the case of loading nr 0, all checks from 0 (1) to 0 (5 ) have to be satisfied. All the checks have both references to Eurocodes 3 or 4 and to the design handbook.

The Table V.2 proposes the following loadings applied to the member :

@ Vertical shear force : v,sd

@ Bending moment: My.Sd

@ Interaction of vertical shear force and bending moment: (v,sd and My,Sd)

Table V.2 List of checks to be performed at ULS for the member in bending according to the applied internal forces andor moments (V ; M ; (V , M))

Vertid shear force v,sd :

Resistance of cross-section to vz.sd :

VZ.M 5 Vp1.z.m

Stability of web to Vz.u, ifd / tw > 69 E :

VZ.Sd I vba.Rd

Crippling of web to Vz.sd, at internal support of a beam :

VzSd I %.Rd

Resistance of shear connectors to longitudinal shear Vg

Ve 5 m Resistance of concrete slab to longitudinal shear V p :

Ve I vu

(design plastic shear resistance of the cross- section)

(design shear buckling resistance)

(design crippling resistance)

(design shear resistance of headed studs)

(design resistance of the concrete flange)

3 Bending moment My.Sd :

(1) Resistance of cross-section to MY.sd:

My.Sd I my.^ (design bending moment resistance of the cross- section)

(2) Stability of member to hogging My.sd in continuous beam or cantilever, if initial conditions are not$lJilled : MY.M I Mb.Rd (design lateral-torsional buckling resistance

(3) Resistance of shear connectors to longitudinal shear Vp:

Ve 5 m (4) Resistance of concrete slab to longztudinal shear Vp:

ve 5 VRd

moment of the member)



References to design handbook:

V.2.4.1

Table V.8

V.2.4.2

V.2.4.3

V.2.7

V.2.7

V.2.5.1

V.2.5.2.2

V.2.5.2.3

V.2.7

V.2.7

117

)Ref. Chapter V - Members in bending

EC4 [4.4.3 (l)]

EC3 [5.4.6 (111

EC4 [4.4.1]

EC3 [5.7.4 (111

EC4 [4.6.2]

EC4 [4.6.3]

EC4 [4.4.3]

EC4 [4.4.5] EC3 [5.6.1(1)]

EC3 [5.6.7.2 (l)]

EC3 [5.6.7.2 (2)]

EC3 [5.6.7.2 (311

EC4 [6.3.2.1]

EC4 [6.6.2]

118

Table V.2 List of checks to be performed at ULS for the member in bending according to the applied internal forces andor moments (V ; M ; (V M))

~

?j) Interaction of vertical shear force and bending moment VZSd 9 : If V z . ~ I 075 Vpl.z.u then interaction (VZ.Sd , My.sd) is not considered and all checks nr 0 and nr @ of this Table V.2 shall be performed, with the following check nr @ (6).

considered and all following checks shall be carried out : ‘1) Resistance of cross-section to V z . a :

VZ.Sd I Vp1.Z.M

Ifvz.sd > 075 Vp1.z.M then i.nteraction (V2.M 7 My.sd) has to be

(design plastic shear resistance of the cross- section)

My.% I M y . u (design bending moment resistance of the cross- section)

‘3) Crippling of web to Vz.sd, at internal support of a beam : Vz.Sd 5 %.Rd (design crippling resistance)

(4) Stability of member to hogging MY.a in continuous beam or cantilever, if initial conditions are not firfilled : my.^ I M b . u (design lateral-torsional buckling resistance

(2) Resistance of cross-section to My.= :

moment of the member)

(design plastic resistance moment reduced by shear force)

(5) Resistance of cross-section to (vz.Sd, My.Sd) : My.Sd I MV.Rd

(6) Stability of web to (Vz.sd, My&, i fd / tw 69 E : One of the three following checks ((6. l), (6.2), (6.3)) shall be hlfilled :

(6.1) If My.= I M f . u (design plastic moment resistance of cross- section with the flanges only)

thenVz.sd I V h . u (design shear buckling resistance of the web)

(6.2) 1fMy.M > Mf.M and Vz.M I 075 VbaM then my.^ I M y . u (design bending moment resistance of the

cross-section)

(6.3) IfMy.Sd > Mf.Rd and VzSd > 075 Vba.Rd t h e n M y . ~ I design moment resistance reduced by s h a

buckling (interaction (VZ.Sd My.sd)) and, My.sd 5 My.Rd

and, Vz.Sd 5 vba.Rd

(7) Resistance of shear connectors to longitudinal shear Ve: vt 5 h d

(8) Resistance of concrete slab to longitudinal shear Ve: vi? 5 VRd



Reference to Lesign handbook

V.2.6.1

V.2.4.1

V.2.5.1

V.2.4.3

V.2.5.2.2

V.2.5.2.3

V.2.6.1

Table V.8

V.2.6.2 (3) A

V.2.4.2

V.2.6.2 (3) B V.2.5.1

V.2.6.2 (3) C V.2.6.2 (3) C

V.2.5.1 V.2.4.2

V.2.7

V.2.7


v.2 Checks at Ultimate Limit States

V.2.1 Properties of cross-sections of composite beams

(1) Efjpective cross-section : EC4 [4.2.1 (111 Allowance shall be made for the flexibility of a concrete flange that induces unequal ben-

n o d stress distribution over the flange width because of in-plane shear (“shear lag”). In the simple model proposed in Eurocode 4, the effective composite cross-section is composed of an effedive width beff of the concrete slab for which constant normal stress distribution replaces the true stress distribution variable along the true slab width

EC4 (2) Effective width of concrete slab : [4.2.2.1]

The effective width on each side of the steel web should be taken as eo / 8, but not greater than distances bi (see Figure V. 1):

EC4 [4.2.2.1 (311

EC4 r4.2.2.1 (4)]

be1 and be2 are evaluated independently,

bi is the half distance from the beam web to the adjacent beam web or the distance from the beam web to the free edge of concrete slab (bi = b2 and bl respectively in Figure V. l),

e0 is equal to the span length for simply supported beams,

is the approximate distance between points of zero bending moment in case of continuous composite beams ; for typical continuous beams shown in Figure V.1 values of eo at support are given above the beam and midspan values of eo are provided below the beam.

EC4 [4.2.2.1(1)] (3) For elastic gZobaZ analvsis, the effective width beff of the concrete flange may be assumed to be

constant over the whole of each span. It may be taken as the value at mid-span (for a beam supported at both ends), or as the value at the support (for cantilever beam). For continuous beams two methods are proposed (see chapter V.2.3).

EC4 [4.2.2.2] (4) For verifications of cross-sections, the effective width beE should be taken as the relevant

midspan value (for sections in sagging bending), or as the value at the relevant support (for sections in hogging bending).

119

[Ref. Chapter V - Members in bending

- Effective width. beff :

I

A 4 % $ ) ? 0 . 7 %

I

t o = 0,8 L1 ?' 1'

I r 0 , I .c L1 I L 2 , L 3 , L4

Figure V.l Effective width beff and equivalent spans eo of concrete flange EC4 [4.2.3] (5) Remral stifiess :

The elastic section properties of a composite cross-section should be expressed as those of an equivalent steel cross-section by dividing the contribution of the concrete component by a modular ratio n (see Table 11.3). The flexural stifiesses of a composite cross-section are defined as follows:

Designation Flexural cess "Uncracked" method

"Cracked" method Ea 12

where Ea

I1

is the modulus of elasticity for structural steel (see Table II.7)y is the moment of inertia of the effective equivalent steel section calculated assuming that concrete in tension is uncracked; proposed formula for sagging bending moment (see Figure V.2) :

I2 is the moment of inertia of the effective equivalent steel section calculated neglecting concrete in tension but includmg reinforcement; proposed formula for hogging bending moment if the reinforcement is placed at mid height of the slab (& / 2) above the steel sheeting (see Figure V.2) :

120

I Ref. Chapter V - Members in bendingJ

--- - E," - the modular ratio (see Table II.3), E,

- - Aa beffhc '

is the effective modulus of concrete taking into account creep effects (see clause II.5.1 (5)),

is the cross-sectional area of the steel section,

is the effective width of concrete slab (see clause V.2.1 (2)),

is the area of the concrete section,

is the cross-sectional area of reinforcement within the effective width beff of the concrete slab,

is the moment of inertia of the structural steel section (see Table W.81, is the depth of concrete flange above upper flange of the profiled steel decking,

is the depth of the profiled steel decking,

is the height of the structural steel profile.

CROSS-SECTION ELASTIC STRESSES

Figure V.2 Elastic analysis of composite beam under sagging and hogging moment

12 1

IRef. Chapter V - Members in bending

V.2.2 Classification of cross-sections of composite cross-sections EC4 [4.3]

V.2.2.1 Generalities

(1) For a designer the usual procedure is to choose a cross-section in such a way that the maximal capacity is not controlled by local buckling but is associated with the bearing load of a particular member of the structure (column, beam, beam-column). Therefore the local buckling plays an important role in the design of cross-sections including structural steel section.

The critical level over which local buckling appears in composite beams, is defined by the classification of steel sections.

(2) For the check of composite cross-sections and composite beams at Ultimate Limit States, the steel cross-sections shall be classified. The classification of cross-sections allows to evaluate beforehand their behaviour, their ultimate resistance and their deformation capacity, taking into accounf the possible limits on the resistance due to local buckling of compression elements of steel sections.

(3) The classification of cross-sections permits (see Table V.3): - to guide the selection of global analysis methods of the structure (elastic or plastic global

analysis), - to determine the criteria to be used for ULS checks of composite cross-sections and

members.

(4) Four classes of composite cross-section are defined according to (see chapters V.2.2.2 and

- the slenderness of its steel elements in compression (width-over-thickness ratios of steel web or steel flange in compression),

- the yield strength of the steel and,

- the sign of bending moment applied to the composite cross-section (sagging or hogging bending moments) :

V.2.2.3) :

sagging hogging

M y.Sd

(5 ) It is important to precise that the present classification of cross-sections is only based on the distribution of normal stresses across the steel section and is not affected by vertical shear force Vz.a . The resistance of steel webs to shear buckling (induced by Vz.sd) should be checked in chapter V.2.4.2.

Ref. 10

@. 21) EC4 p.1.2 (611

(6) The procedure of classification (and Eurocode 4 as a whole) is applicable only to composite beams where the steel section is symmhcal about an axis (zz) normal to the neutral axis (yy) of bending. Asymmetry of the concrete slab or its reinforcement is acceptable.

122

Chapter V - Members in bending 1 I Ref.

Ref. 10 (p.22)

EC4 [4.5.2.2 and4.9.q

(7) Designers of structures for buildings normally select beams with steel sections such that the composite sections are in Class 1 or 2, for the following reasons :

a) Rigid-plastic global analysis (also known as plastic hinge analysis) is available only for structures where the cross-sections at plastic hinge locations are in Class 1 and other cross- sections of beams are in Class 2. That method of plastic global analysis is out of the scope of this design hanbook.

b) Plastic theory for the bending resistances of beams is available only for cross-sections in Class 1 or Class 2. The ratio of the plastic resistance to the elastic resistance is in the range of 1,2 to 1,4 for composite sections, compared with about 1,15 for rolled steel I- section.

c) Where elastic global analysis is used, the limits to the redistribution of moments are more favourable for the lower classes (see chapter V.2.3).

d) Where floor slabs are composite, it is convenient to use partial shear connection. This is allowed only for beams where the critical cross-sections are in Class 1 or Class 2 (see chapter V.2.7).

E C ~ [4.4.1.1(2)]

EC4 [4.5.3.4]

EC4 [6.2.1]

V.2.2.2 Definition of cross-sections classification

EC4 [4.3.1 (I)] (1) Four classes of cross-sections are defined for composite beams, as follows :

. Class 1 (“plastic”) cross-sections are those which can form a plastic hinge with the rotation capacity required for plastic analysis.

Class 2 (“compact”) cross-sections are those which can develop their plastic moment resistance, but have limited rotation capacity.

Class 3 (“semicompact”) cross-sections are those in which the calculated stress in the extreme compression fibre of the steel member can reach its yield strength, but local buckling is liable to prevent development of the plastic moment resistance.

Class 4 (“slender”) cross-sections are those in which it is necessary to make explicit allowances for the effects of local buckling when determining their moment resistance or compression resistance.

(2) The Table V.3 recapitulates the characteristics of each class of cross-section in case of steel

(3) The ultimate resistance of cross-sections and of members submitted to bending depends on class of cross-sections and is based on the following properties (see Table V.3):

.

.

.

Simply-supported beam.

Class 1 or 2 L- Class 3

Class 4 c Distribution of stresses across

the section

- full plastic distribution - at the level of yield strength

- elastic distribution - with yield strength reached in

the extreme fibres

- elastic distribution across the effective section taking into account local buckling

- with yield strength reached in the extreme fibres.

Cross-section properties for ULS check formulas

plastic properties (Mpl.~d)

elastic properties (Mel.Rd)

effective properties (&ff.Rd)

ULS partial safety fixtors

Ya

Ya

YRd

123


EC4

Table V.3 Definition of the classification of cross-section

Zlass Behaviour model L M p p

1 buckling

local v buckling e

4

Design resistance

PLASTIC across full section

PLASTIC across full section

ELASTIC across full section

ELASTIC mcross effective section

Available rotation :apacity of plastic hinge

important

limited

none

none

Global analysis

of structures

plastic or7

elastic with

redistribution of moments

elastic with


elastic with


elastic with


(4) Compression steel elements of cross-section of composite beams are classified seuaratelv according to : ,

- their geometrical proportions (slenderness : width-over-thickness ratios), - the yield strength of steel material and,

[4.3.1 (2)] - the stress distribution related to the sign of applied bending moment (sagging or hogging) influencing to position of neutral axis yy.

Compression steel elements include every part of a steel section (flanges and web) which is either totally or partially in compression.

For class 1 and class 2 cross-sections the positions of the plastic neutral axes of composite sections should be calculated for the effective cross-section using design values of strengths of materials (see chapter V.2.5.1).

For class 3 and class 4 beams in buildings the position of the elastic neutral axis should be determined for the effective concrete flange, neglecting concrete in tension, and for the gross cross-section of the steel web. The modular ratio n for concrete in compression should be as used in the global analysis for long-term effects (see Table 11.3).

EC4 [4.3.1 (5 ) ]

EC4 [4.3.3.2(2)]

124


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

(6) A cross-section is normally classified by quoting the hinhest (least favourable) class of its steel comvression elements.

Alternatively the classification of a cross-section may be defined by quoting both the flange classification and the web classification. For instance, the compression flange of an I-section may be class 1 and its web may be class 3. Then this I-section is class 3.

(7) An element of a cross-section (as such a web or a flenge) which fails to satis@ the limits for class 3 should be taken as class 4.

(8) The methods of classification are described in following chapters :

EC4 ~4.3.1 (211

EC4

[4.3.2] [4.3.3]

Ref. 10 @. 23)

- chapter V.2.2.3 : classification of steel flanges in compression, - chapter V.2.2.4 : classification of steel webs.

The procedures are summarized in Figure V.3 where references to Eurocode 4 (Ref. 4) and this design handbook are given respectively on the left and right sides in boxes of the flowchart. The flowchart in Figure V.3 includes several unusual cases. The typical

situations are outlined below for members of uniform section : Ref. 10 @. 22)

a) For simulv-sumorted beams : Only the midspan region needs to be classified. The steel top flange is restrained by shear connection (see chapter V.2.2.3, Figure V.4), or by embedment in a slab , and so is in class 1. The depth of steel web in compression (if any) is so small that it is also in class 1. The other classes can occur in deep composite plate girders.

Where partial shear connection is used, the area of structural steel in compression is increased (see chapter V.2.7). Class 2 webs can then occur in the deeper beams in buildings.

b) For continuous beams and cantilevers : Midspan regions of beams are usually in class 1, as above. The other critical sections are near internal supports, where the compression flange is unrestrained. Almost all rolled sections have outstand flanges in class 1 or 2 : see Tables V.7 where all IPE, IPE A, IPE 0, HE B, HE M and UB profiles and several HE AA, HE A and UC profiles have outstand flanges in compression in class 1 or 2, for steel grades S 235, S 275 and S 355. Bottom flanges of plate girders can be so proportioned that the class is not worse than that of the web.

The class of the web is determined mainly by the area of longitudinal reinforcement in the slab that is assumed to contribute to the resistance to hogging bending. Any significant area of reinforcement will raise the neutral axis of composite cross-section and will put the web of most rolled I-sections into class 2, or even class 3 or 4 (see chapter V.2.2.4). For all standard hot-rolled I-sections (PE, IPE A, IPE 0, HE AA, HE A, HE B, HE M, UB and UC) and for steel grades S 235, S 275 and S 355, Tables V.7 present two extreme classification for webs subjected to hogging bending : the worst classification related to full webs subjected to compression and the particular classification related to webs subjected to bending (when steel profiles resist alone). The use of an effective web in accordance with Eurocode 4 (Ref. 4, clause 4.3.3.1 (3)) is intended to eliminate the anomaly caused by the sudden change from plastic to elastic section analysis at the class 213 boundary (see Fkf. 4 : Note to clause 4.3.3.1 (3)). This “hole-in-web” method is presented in chapter V.2.2.4. Partial shear connection is not allowed by Eurocode 4 in hogging moment regions. This is fortunate here, because it would be a complex matter to combine it with the “hole-in-web” method.

125


. Classify compression flange [4.3.2, Table 4.11 {Tables V.4 or V.5)'

I

/ X i e s t i e l compression flange \ llo

Flange is Flange is Flange is Class 1 Class 2 Class 3

restrained by shear connectors?

Flange is Class 4

Locate the plastic neutral axis. Allow for partial shear connection

Locate the elastic neutral axis, assuming full shear connection

Class 2 or 3 Class 4 compression classified is Class 3 (Class 3 or 4?)

(if any)

Class 1 Class 2 is Class 2

and propped construction

-*I *I e Effective section

Ref. 10 @. 23) Figure V.3 Flowchart for classification of a composite beam cross-section (with references to @X4] and to (design handbook})

V.2.2.3

(1) A steel compression flange that is restrained fiom buckling by effective attachment to a concrete flange by shear connectors in accordance with the Figure V.4 (see Ref. 4, 6.4.1.5) may be assumed to be in Class 1.

Classification of steel flanges in compression

EC4 [4.3.2 (111

EC4 I6.4.1.5 (211 (2) The classification of other steel flanges in compression in composite beams shall be in accordance

with Table V.4, for outstand flanges, and Table V.5 for internal flange elements.

126

I Ref. Chapter V - Members in bending1

EC4 [6.4.1.5 (211 [6.4.1.5 (311

Ref. 11

Figure 11

0 Case of sagging bending moment : I+lfy (stresses in steel profile)

- 3 My.Sd

0 SDacing. reauirements of shear connectors : - when solid slab :

I H eL I I I

U T! I

I I

-

I V'y 1

I I I I t f 4 I I

- when commsite slab with ribs transverse to the be am; I eL eL

U H

t I I I I tf 4 1 I

I I L

and eLS (6 (hc+hp); 800 mm)

FigureV.4 Spacing requirements of shear connectors for the Class 1 steel flange in compression

EC4 t4.3.1 (611 (3) For a web to be treated as "encased" in Table V.4 the concrete that encases it shall be reinforced,

mechanically connected to the steel section, and capable of preventing buckling of the web and of any part of the compression flange towards the web. Figure V.5 presents the requirements of Eurocode 4 for "encased" webs (see Ref. 4: 4.3.1 (7) to (9)).

127

IRef Chapter V - Members in bending 1

EC4 I4.3.1 (711 to [4.3.1 (9)]

~~

1) Concrete extended over full width of both steel flanges, 2) Concrete reinforced by longitudinal bars and stirrups, andor welded mesh, 3) Concrete between flanges fixed to the web by :

/ StirruD welded /Bars (with (p 1 6 mm) /Studs (With (p > 10 m> to the web through holes welded to the web

in the web

1 eL L eL 1 p L L eLL eLt n 1 1

Figure V.5 Requirements for encased web V.2.2.4 Classification of steel webs

Different rules are defined to evaluate the class of steel webs in function of the class of compression flange (see chapter V.2.2.3) : if compression flange is in class 1 or 2 refer to chapter V.2.2.4.1, or if compression flange is in class 3 or 4 refer then to chapter V.2.2.4.2.

V.2.2.4.1 Classification of steel webs where the compression flange is in Class 1 or 2 EC4 [4.3.3.1 (111 (1)

EC4 [4.3.3.1 (2)] (2)

EC4 [4.3.3.1 (311 (3)

The Class of the web shall be determined by Table V.6. The plastic stress distribution for the effective composite section shall be used, except if web is in class 3 (or 4) where the elastic stress distribution shall be used. The position of neutral axes of composite sections should be calculated as explained in V.2.2.2 (4).

A web in Class 3 that is encased in concrete may be represented by an effective web of the same cross-section in Class 2 (see Figure V.6). The requirements for a web to be encased in concrete> are given in clause V.2.2.3 (3) and Figure V.5.

An uncased web in Class 3 may be represented by an effective web in Class 2, by assuming that the depth of web that resists compression is limited to (20 tw E) adjacent to the compression flange, and (20 tw E) adjacent to the new plastic neutral axis (“hole-in-web” method), as shown in Figure V.6.

128

1 Ref. Chapter V - Members in bending

fy (N/mm*) 235 275

F = J m E (if t I 40 mm) 1 0,92

~ ( i f 4 0 m m C t I 1OOmm) 1 0,96

1) Encased webs in class 2 instead of class 3 (see Figure V.5 for requirements to have encased webs) :

355

0,8 1

0,84

1-1 f~ lya

f~ @a

- Compression flange : class 1 or 2

- Encased web : class 3

f~ lYa

- Compression flange : class 1 or 2

- Encased effective web : class 2

(with the same cross-section)

2) Use of an effective web in cZuss 2 for a section subjected to hogging bending moment with a web in class 3 :

Stress blocks :

7 n e w ~ ~ 4 + I ) - T initial (ad-.lOtw&))"

d d

Remark ; P.N.A = plastic neutral axis fY' ya * provided that the new P.N.A is in the web.

I - I J "1 _ _ _ 0------ -L

Figure V.6 Improved classification of steel webs with compression flange in class 1 or 2 and with specific conditions

V.2.2.4.2 Classification of steel webs where the compression flange is in Class 3 or 4 EC4 [4.3.3.2 (I)] (1) The Class of the web shall be determined by Table V.6, using the elastic stress distribution. EC4 [4.3.3.2(2)] (2) In composite beams for buildings, the position of the elastic neutral ax is of composite cross-

sections should be determined as exdained in clause V.2.2.2 (4). I

. .

129

I Ref. ChaDter V - Members in bending

II I I

Table V.4 Classification of composite cross-sections : limiting width-over-thickness ratio (c I tf) for steel outstandflanges in compression

1 TvDe of loadinn and stresses distribution in compression flange :

I

fv (N/mm2) 235 275 355

d M hogging 1 M sagging

fy r'l

in all cases - or if requirements of Figure V.4 are not fulfilled

class I Type of cross-sections

I Rolled sections I Welded sections

web encased **) 1 webencased**) I C/tf I C/tf c / tf c / tf

5 9 &

I 10&

I 2 0 € II I I 1 5 ~ I I21& I 14e

1 1 0,92 1 0,81

I 0,96 I 0,84

130

1 Ref. Chapter V - Members in bending I

“-” means stresses in compression

“+” means stresses in tension

fy W-2)

E = @ q E (if tf 40 ItUtl)

TableV.5 Classification of composite cross-section : limiting width-to-lhickness ratios for steel internal flange elements in compression

EC3 [Table 5.3.1 (sheet 211

“R” means rolled hollow sections

“0 ” means other sections

23 5 275 355

1 0,92 0,8 1

Internal flange elements (internal elements parallel to axis of ben-) :

- - -.- Axis of bending -

J

Typeofloading 1 Stresses distribution

I : ! I

M

Class 1 Class 2

internal flange

b / t f S 3 3 ~ 0 b / t f I 3 8 ~

Class 3

internal flange

(b-3tf) / tf I 4 2 E

0 b / t f I 4 2 ~

I 0,96 I 0,84

13 1

[Ref. Chapter V - Members in bending I Table V.6 Classification of composite cross-sections: limiting width-over-thichess ratios

(d / tw) for steel webs

Webs (internal elements perpendicular to axis of bending) :

d = h -2 (tf +r) d = h - 3t (t = tc = L) d = h -2 (tf + a d ) d=h-2t f

Stresses distribution on web for different classes

I) Web in COmDression (a = = 1) : 1+1 f Y

2) Web in bending (U = 0,5 and V, = -1) :

- for 1)1 f Y 1+1 f Y

1 & 2 :'=qI#-- -gss 31-#3 I-I M I--I M

3) Web subiected to combined bending and comDression : 1+1 f Y

- For class 1 and 2 :

Class 1

33 E

72 E

i f a > 0 , 5 :

396& 13a-1

if a < 0,5 :

368 a

d / t w I Class 2

38 E

83 E

class 3

42 E

124 E

i fa>0,5 : A C L c

fy W-2) 235 275 355 "-" stresses in compressioi

E = J q E (iftw I 40 mm) 1 0,92 0,81 "+" stresses in tension

I E (if40 mm<tw I100 mm) I 1 I 0,96 1 0,84 I

132

I Ref. ChaDter V - Members in bending I

Table V.7 a) Classification of flange and web subjected to particular loading for standard hot-rolled P E , IPE A and IPE 0 steel profiles

P E - P E A - P E 0 hot-rolled steel profiles

133

IM. Chapter V - Members in bending

Table V.7 b) Classification of flange and web subjected to particular loading for standard hot-rolled HE AA and HE A steel profiles

134


Table V.7 c) Classification of flange and web subjected to particular loading for standard hot-rolled HE B and HE M steel profiles

HE B - HE M hot-rolledsteelprofiles

135

JRef. Chapter V - Members in bending

UB hot-rolled steel profiles Classification of flange and web subjected to particular loading;

Designation Class of flange in compression Class of web in compression Class of web in bending

Table V.7 d) ClassitiCaton of flange and web subjected to particular loading for standard hot-rolled UB steel profiles

v

- - - - I t - - - J M,, - J

fY m with web not encased I stresses for class 1 and 2

UB 178x l02x 19 UB 203 x 102 x 23 UB 203 x 133 x25 UB 203 x 133 x 30 UB254x102x22 UB254x102x25 UB 254x 102 x 28 UB254x 146x31 UB254x 146x37 UB 254x 146x43 UB 305x 165 x40 UB 305x 165 x46 UB 305 x 165 x 54 UB356x171x45 UB 356x 171 xS1 UB 356 x 171 x 57 UB356x171x67 UB406x178xs4 UB406x178x60 UB 406 x 178 x 67 UB 406 x 178 x 74 UB457x152xS2 UB457x152x60 UB 457x 152 x 67 UB 457x 152 x 74 UB 457x 152 x 82 UB 457x 191 x 67 UB457x191x74 UB457x191x82 UB457x 191 x 89 UB 457 x 191 x 98 UB 533 x 210 x 82 UB 533 x 210x92 UB533X2lOX101 UB 533 x 210x 109 UB 533 x 210 x 122 UB 610x229~ 101 UB610x229x113 UB 610x 229x 125 UB 610x229 x 140 UB 610 x 305 x 149 UB 610x305 x 179 UB 610x 305 x238 UB686x254x125 UB686x254x140 UB686x254x152 UB 686 x 254 x 170 UB762x267x147 UB762x267x17'3 UB 762 x 267 x 197 UB 838 x292x 176 UB 838 x292x 194 UB 838 x292 x226 UB 914x 305 x201 UB 914x305 x224 UB 914x 305 x 253 UB 914x 305 x 289 UB 914x419 x343 UB 914 x 419 x 388

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 I i I : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

136


Table V.7 e) Classification of flange and web subjected to particular loading for standard hot-rolled UC steel profiles

Designation

UC 152 x 152 x23 UC 152 x 152 x 30 UC 152 x 152 x37 uc 203 x 203 x 46 UC 203 x 203 x 52 UC 203 x 203 x 60 UC 203 x 203 x 71 UC 203 x 203 x 86 uc 254 x 254 x 73 UC 254 x 254 x 89 UC 254 x 254 x 107 UC 254 x 254 x 132 UC 254 x 254 x 167 UC 305 x 305 x 97 UC 305 x305 x 118 UC 305 x305 x 137 UC 305 x 305 x 158 UC 305 x 305 x 198 UC 305 x 305 x 240 UC 305 x 305 x 283 UC 356 x 368 x 129 UC 356 x 368 x 153 UC 356 x 368 x 177 UC 356 x 368 x 202 UC 356 x406 x 235 UC 356 x406 x 287 UC 356 x 406 x 340 UC 356 x 406 x 393 UC 356 x 406 x467 UC 356 x 406 x 551 UC 356 x406 x 634

uc hot-rolled steel profiles Classification of flange and web subjected to particular loading

3-w of flange in compression

. - . - l---d fY rl

with web not encased

Steel grades

S 235 . . . . . . . .

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1

S275 I S 3 5 5

1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1

1 1

1 1

1 1

2 1 1 1 1 1

Class of web in compression

fY

Steel grades

S 235

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

S 275

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

s 355

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1

Class of web in bending

n

11 1+1 ---l--Er fY

fY

3 M Y

stresses for class 1 and 2 -~ ~~

Steel grades

S 235

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

S 275

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 =

s 355

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

137


- ~~

For “uncracked” elastic analysis 40% 30% 20% 10%

For “cracked” elastic analysis 25% 15% 10% 0% ~

V.2.3 Distribution of internal forces and moments in continuous beams EC4

I4.5.11 (1)

[4.5.3.1 (111 (2)

[4.5.3.2] (3)

[4.5.3.3] (4)

[4.5.3.4 (111 (5)

[4.5.3.1 (211

EC4 [4.5.3.4 (211 (6)

Internal forces and bending moments in composite beams at ultimate limit states may be determined by elastic or rigid-plastic global analyses, using fixtored loads. This design handbook only presents the application of elastic global analysis which may be used for all continuous beams. Elastic global analysis is based on the assumption of a linear stress-strain relationship for the materials, whatever the stress level. The tensile strength of concrete may be neglected.

When unpropped construction is used for composite beams in class 3 or class 4, appropriate global analyses shall be made to separate effects on steel members and on composite members.

No account needs to be taken of ben- moments due to shnnkage except at cross-sections in class 4.

Loss of stifhess, due to cracking of concrete in hogging moment regions, due to yielding and local buckling of structural steel, influences the distribution of bending moments in continuous composite beams.

Two methods of elastic global analysis are permitted by Eurocode 4 at the ultimate limit state to determine the bending moment dstribution (see Figure V.7):

- uncracked section elastic analysis, based on midspan effective width ignoring any longitudinal reinforcement (method 1) ; the related flexural sti&ess Ea I1 (see clause V.2.1 (5)) is assumed to be constant along the whole beam;

- cracked section elastic analysis, based on a section in the region of the internal support comprising the steel member together with the effectively anchored reinforcement located within the effective width at the support (method 2) ; the related flexural sti&ess I2 (see clause V.2.1 (5)) is taken for a length of 15% of the span on each side of each internal supports, whereas the values Ea I1 are taken elsewhere (12 < 11).

The “cracked“ method (method 2) is more suitable for computer. However, this method may be also used at the serviceability limit state to accurately determine the moments in cases of crack control in the slab.

The elastic bending moments for a continuous composite beam of uniform depth within each span may be modified :

- by reducing maximum hogging moments by amounts not exceeding the percentage of Table V.8 ;

- or, in beams with all cross-sections in classes 1 or 2 only, by increasing hogging moments amounts not exceeding 10% for “uncracked” elastic analysis, or 20% for “cracked” elastic analysis.

For each load case internal forces and bending moments after redistribution should be in equilibrium with loads. For composite cross-sections in class 3 or 4, moments applied to the steel member should not be redistributed.

Table V.8 Limits to redistribution of hogging moments at supports (in terms of the maximum percentage of the initial bending moment to be reduced)

)I Classofcross-sectioninhoggingmoment region I 1 I 2 I 3 I 4 11

138


Method 1 Method 2

pncracked sections crack@ sections

I et ails for method 2 I

/-

bl distance between steel webs : 2 b2

Figure V.7 Definition of "uncracked" and "cracked" sections for elastic global analysis

V.2.4

V.2.4.1

Verification at ULS to vertical shear vzsd

Resistance of cross-section to vertical shear V z ~ d

EC4 [4.4.2.2] The contribution of the concrete slab to the resistance to vertical shear is normally neglected. Therefore, the design value of vertical shear force VZ.Sd applied to the composite section should satis@ the rules of Eurocode 3 (see Ref. 3, 5.4.6):

where Vpl.z.M is the design plastic shear resistance of structural steel section about z axis. is the shear area of structural steel section about z axis, given in Table V.9,

is the yield strength of structural steel (see Table US),

is a partial safkty &tor (see Table II. 10).

&,z

fY

'Ya

139

pf. Chapter V - Members in bending 1

Table V.9 Shear area A, for cross-sections

EC3

[5.4.6 (2)]

~

Cross-sections AV *)

Load parallel to web Z!L* t f Ibl

A - 2btf + (tw + 2r)tf AV.2 =

Rolled Vy.Sd bltf Load

parallel to

flanges

Av.y = 2btf + (tw + r) tw

IandH sections

Load parallel to web

Av.2 = 01 - 2tf) tw

Welded Vy.Sd

L L

Load parallel

to flanges

Av.y =

Av.2 = Load

parallel to depth

A h b + h -

Rolled rectangular hollow sections

of uniform thickness

*:

A b Load

parallel to

breadth

Av.y = b + h

*: 6 Rolled circular hollow sections of uniform thickness

2 A - x:

Vote : *) A is the total cross-sectional area

140


V.2.4.2 Stability of web to vertical shear Vzsd for composite beams

EC3

I5.6.1 (I)] (1) Ifwebs are submitted to vertical shear force V z . u and if their ratio - exceeds the limits given

in Table V. 10 then they shall be checked for resistance to shear buckling

and transverse Stiffeners shall be provided at supports.

Table V.10 Limiting width-to-thickness ratio related to the shear buckling in web

1 EC3 [5.6.1(4)]

= d q

EC3 [5.6.2(1)]

EC3 [5.6.2(3)]

fy W-2) 235 275 355

E (if tw 5 40 mm) 1 0,92 0,8 1

Profiles Potential shear buckling to be checked if webs have

i) For unstiffened webs :

1) For webs with transverse stiffener : - > 3 0 ~ & d

tw

The value of kT is defined in Table V. 12

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

(3) The shear buckling resistance may be verified according to Eurocode 3 (Ref. 3) using either : - the simple postcritical method, or

- the tension field method. The first method is presented hereafter.

(4) The simple post-critical method can be used for webs of I-section girders, with or without intermediate transverse stifFmers, provided that the web has transverse stifFeners at the supports.

141

IRef. Chapter V - Members in bending 1

- - hw 5 0,8 0,8 < hw I 1,2

( 5 ) For webs with d / tw exceeding limits of Table V. 10, the design value of the shear force Vz.u shall satisfy :

> 1,2

EC3 [5.6.3(1)] [YLSd 5Vba.M = d t w 21

- fyw J? %a

fyw -- fyw 099 J? & x w -(l,5 - 0,625hw)

- (6) The web slenderness A w should be determined from :

(1, = t W

37,4 E & where E = ,/- , given in Table V. 10,

is the buckling factor for shear given in Table V. 12,

where a is the clear spacing between transverse stiffeners.

kT

Table V.12 Buckling factor for shear kT

a l d < 1 1 21 1 =m 1 1

142


V.2.4.3

(1) At internal supports of continuous composite beams designed using an effective web in class 2 (see clause V.2.2.4.1 (3) and Figure V.6 2)) transverse stiffening should be provided unless it can be shown that the unstifFened web has sufEcient resistance to web crippling (see Figure V.8). Application rules of Eurocode 3 (Ref. 3 : 5.7) are applicable to noncomposite steel flanges of composite beams and to the adjacent part of the web.

Stability of steel web to crippling EC4 [4.7.2]

(2) The design value of the transverse force applied to the unstiffened web, VZ.Sd , shall satisfy :

EC3 [5.7.4 (l)]

EC3 [Fig. 5.7.21

where &.U is the design crippling resistance of the web,

SS

fyw

is the length of stiff bearing, but ss / d I 0,2, (see Figure V.8),

is the yield strength of the web.

.J??O ,

I

I / . \ I

I - - - - - + - - - .

Figure V.8 Load introduction and length of stiff bearing, ss

143

p. Chapter V - Members in bending

Class 1 or 2 Class 3

V.2.5 Verifications at ULS to bending moment My.Sd

Class 4

V.2.5.1 Resistance of cross-section to My.Sd

EC4 [4.4.1.1(3)] (1) The elastic global analysis may be applied to cross-sections of any class in order to determine the

design values of applied bending moments My.Sd.

For members in bending and in absence of shear force, the design values of applied bending moment My.Sd shall satisfy at each section :

= Mp1.y.u I = &l.y.Rd I = &ff.y.Rd

where Mpl.y.Rd

&l.y.Rd

& f f . y . ~

is the design plastic moment resistance of the cross-section about y axis (see clause V.2.5.1(4)),

is the design elastic moment resistance of the cross-section about y axis (see clause V.2.5.1(3)),

is the design effective moment resistance of the cross-section about y axis (see clause V.2.5.1(3)).

EC4

[4.4.1.1(4)] (2) The evaluation of moment resistance of a composite cross-section is based on the following assumptions :

- the tensile strength of concrete is neglected,

- plane cross-sections of the structural steel and reinforced concrete parts of a composite member each remain plane.

EC4

[4.4.1.4]

EC4

(3)

(4)

[4.4.1.2(2)&4)]

Where the effective composite section is in class 3 or class 4 (see chapter V.2.2) reference should be made to Eurocode 4 (Ref. 4 : 4.4.1.4) to calculate the elastic resistance to bending : &l.y.u or &ff.y.Rd.

Where the effective composite section is in class 1 or class 2 (see chapter V.2.2), the design ben- resistance Mpl.y.Rd may be determined by plastic theory.

The following assumptions shall be made in the calculation of Mpl.y.Rd :

a) there is fill interaction between structural steel, reinforcement and concrete;

b) the effective area of the structural steel member is stressed to its design yield strength fy/ya in tension or compression (rectangular stress block) (see Table II.5 for fy) ;

144

I Ref. Chapter V - Members inbending I

c) the effective area of concrete in compression resists a design stress of 0,85 f&/yc constant over the whole depth of the compressed part of concrete slab (rectangular stress block) (see Table 11.1 for Eck) ;

d) the effective areas of longitudinal steel reinforcement are stressed to their design yield strengths f&/ys in tension and in compression (rectangular stress block) (see Table II.8 for fsk). Alternatively steel reinforcement in compression in concrete slab may be neglected,

e) profiled steel sheeting in compression shall be neglected;

and where ya , yc and yS are partial safety factors at ULS (see Table 11.10).

EC4 [4.4.1.3(2)] These hypothesis for calculation Mpl.y.M are defined for a composite cross-section with 111

shear interaction. When a partial shear connection is used for the composite beam, the plastic moment resistance is calculated with a reduced value of the compressive force in the concrete and two plastic neutral axes have to be considered : one axis in the slab and a second axis within the steel section (see chapter V.2.7.2.2 for details).

Typical plastic stress distributions related to different positions of plastic neutral axis and different values of Mpl.y.M are given in Table V. 13 for the two types of bending moments : sagging bending moments (e.g. in simply-supported beams) and hogging bending moment (e.g. usually on supports of continuous beams). The calculation method for Mpl.y.Rd depends on the location of the plastic neutral axis.

I

(5) Mpl.y.Mfor s a x i n 2 bending moment (see Table V. 13) :

The presence of profiled steel decking, when running transverse to the main span, reduces the area of concrete that may resist compression forces. Hence, the maximum possible depth of concrete in compression is &, which is the depth of concrete flange above upper flange of profiled steel decking of depth, hp.

Moreover, account may be taken of the concrete contained within the ribs of the profiled decking in cases where the ribs run parallel to the beams, but this benefit is usually neglected.

(6) Mpl.y.Rd for homing bending moment (see Table V.13) :

The composite cross-section consists of the steel section together with the effectively anchored reinforcement located within the effective width of the concrete flange at support. The reinforcement is located at height a, above the top flange of the steel beam.

(7) In the classification of cross-sections (see chapter V.2.2), it may result that the flange belongs to class 1 or 2 and the web to class 3. Nevertheless this cross-section may be assigned to class 2, if the effective web area is applied for hogging bending moment as explained in clause V.2.2.4.1 and in Figure V.6.

145

IW. Chapter V - Members in bending

zc = Fa 5 hc beff 07g5 fck /Y c

Table V.13 a) Plastic stress distributions, positions of plastic neutral axis and plastic bending moment resistance Mpl.y.M for sagging bending moment

If Fc > Fa then the neutral axis lies in the concrete flange :

Mpl.y.Rd = Fa($+hc+hp-%) 2

1 If Fa > Fc > Fw then the neutral axis lies in the steel flange :

-b eff-

( h + k + h p ) - ( F a -Fc)[ zc + h ') 2 2 Mpl.y.Rd = Fa

II ' I

11 If Fc < Fw then the neutral axis lies in the web :

Hence, the depth of web in compression,

zcw=--

and the neutral axis depth, Q :

and zc = hp + hc + zcw ha Fa 2 2twfy/Ya

Mpl.y.Rd =Mapl.y.Rd +Fc (%+hp

Notations : see Table V. 13 b)

146

1 Ref. Chapter V - Members in bending I

Plastic stress distributions, positions of plastic neutral axis and plastic bending moment resistance Mpl.y.u for hogging h d m g moment

Table V.13 b)

IfFa > Fs > Fw thenthe neutral axis lies in the steel flange : U

hctf- ha12

fsk/ Y .s

'?

0 - - - - - - -

J,fY I%! Y IYfY Idp

-2 p1.y .Rd

Hence, the depth of web in tension, z ~ w and the neutral axis depth, :

and zc = hp + hc + zCw h F,

zcw =a- I 2 2twfylYa

II ' I

Notations : The resistances of the different parts of the composite beam should be expressed as follows : - resistance of the structural steel section in tension or compression : - resistance of the web of the structural steel section in tension or compression :

IF,=Aafy/Yal I ~w = e a - 2 t d t w fylral

IFc = h c beff 0,85 fcklyc]

-1 [Mapl.y.Rd = WpLyfy / Y a1

are the cross-sectional areas of steel section and reinforcement (see Table IV.6),

- resistance of the concrete section in compression : - resistance of the reioforcement steel section in tension : - the plastic moment resistance of the steel section alone : where & and As

fY Gk fsk WP1.Y ya yc and ys are p a ~ W safety hctors (see Table II. 10)

is the yield strength of steel profile (see Table IIS), is the compression strength of the concrete (see Table II. l), is the yield strength of reinforcement steel (see Table II.S), is the plastic section modulus of steel section bent about yy axis (see Table VI.3a),

means compression "+" means tension z

147

Ref. Chapter V - Members in bending I V.2.5.2 Stability of member to My.Sd

EC4 [4.6]

V.2.5.2.1 Generalities EC4 [4.6.1]

(1) A steel flange that is attached to a concrete or composite slab by shear connection in accordance with chapter V.2.7 may be assumed to be laterally stable, provided that the overall width of the slab is not less than the depth of the steel member. Therefore simply-suoporfed beams with beff 2 2 ha and with adequate shear connectors do not need to be checked against lateral-torsional buckling.

(2) All other steel flanges in compression shall be checked for lateral stability. In hogging moment regions of cantilever beams and of conlinuous composite beams the lower flange is subjected to compression. The tendency of the lower flange to buckle laterally is restrained by the distorsional stifhess of the cross-section (“inverted U-frame action”: see Figure V.9).

(3) Web encasement may be assumed to contribute to resistance to lateral-torsional buckling (see Table V. 14).

(4) In checks for lateral stability of beams built unpropped, the bending moment at any cross section shall be taken as the sum of the moment applied to the composite member and the moment applied to its structural steel component.

V.2.5.2.2 Check of lateral-torsional buckling without direct calculation

(1) A continuous beam or a beam in a frame that is composite throughout its length may be designed without additional lateral bracing and without direct calculation for lateral stability when the following conditions are satisfied :

a) adjacent spans do not differ in length by more than 20 % of the shorter span or where there

EC4 [4.6.2]

is a cantilever, its length does not exceed 15 % of the adjacent span :

b) the loading on each span is uniformly distributed and the design permanent load exceeds 40 % of the total design load :

c) The top flange of the steel member is attached to a reinforced concrete or composite slab by shear connecfors in accordance with chapter V.2.7. I

148


d) The longitudinal spacing of studs or rows of studs, s, is such that for unwed beams :

) s / b I 0,02d2ha/tw3

Where d is the diameter of studs, and

are as shown in Figure V.9. b, ha and tw

I

Figure V.9 Inverted U-frame action

e) The same slab is also attached to another supporting member approximately parallel to the composite beam considered, to form an inverted-U h e of width a (see Figure V.9).

4 If the slab is composite, it spans between the two supporting members of the inverted-U frame considered.

g) For edge beams where the slab is simply-supported at the composite beam considered, fully anchored top reinforcement extends over the length AB shown in Figure V.9. The area of this reinforcement should be such that the resistance of the slab to hogging transverse bending, per unit length of beam, is not less than m/4y,b where the notation is as in d) above, fy is the yield strength of structural steel (see Table II.5) and ya is the related partial safety factor (see Table 11.10).

h) At each support of the steel member, its bottom flange is laterally restrained (e.g. bracing or transverse members) and its web is stiffened. Elsewhere, the web is W e n d .

i) The slab proportions are typical of those in general building design (see chapter W). A minimum value of flexural stifiess of the solid or composite slab may be evaluated according to Eurocode 4 (see Ref. 4 : clause 4.6.2a)).

j) The depth ha of the steel member does not exceed the limit given in Table V. 14 for IPE sections according to Euronorm 19-57 (IPE 80 to IPE 600) and for HE sections according to Euronorrn 53-62 (HE A, HE B and HE M 100 to 1000). Similar shapes or hot-rolled section to P E and HE sections given in Table V.14 may be identified with the rules of Eurocode 4 (see Ref. 4 : clause 4.5.6 (k)).

(2) If any of the conditions ( a) to j) ) presented in previous clause V.2.5.2.2(1) is not fulfilled, a check for lateral-torsional buckling according to Eurocode 4 (Ref. 4) is required and summarized in following chapter V.2.5.2.3.

149


-

Profile

P E HE

Table V.14 Maximm depth ha in [mm] of the steel member to avoid lateral-torsional buckling in the hogging moment region

Steel grades

S 235 S 275 s 355

Steel grades

S 235 S 275 s 355

Types of cross-section

XLT Mpl.y.Rd ?'a

?' Rd - -

-L

XLT Mel.y.Rd Ya

?' Rd - - = XLT &l.y.Rd

600 550 400 800 750 600 800 1 700 I 650 1 1000 1 900 I 850

V.2.5.2.3 Buckling resistance moment EC4 [4.6.3]

(1) For members with appropriate nondimensional slenderness I ~ L T I0,401 no allowance for lateral-torsional buckling is necessary. The value of XLT is defined hereafter.

(2) For laterally unrestrained members in bending, the design value for the bending moment about major axis (My.& shall satisfy :

My.Sd 5 Mb.Rd

Mb.Rd depending on classes of cross-section : I Class 1 o r2 1 Class3 I Class4 I

is the design buckling resistance moment of members in bending,

is the reduction factor for lateral-torsional buckling, XLT

Mpl.y.m

&l.y.m

is the plastic resistance moment about y axis defined in chapter V.2.5.1,

is the elastic resistance moment about y axis defined in chapter V.2.5.1 ,

are partial safety factors of steel section (see Table 11.10). Ya, YRd

150

Chapter V - Members in bending I I w.

Class 1 or 2

(3) The value of ZT for the appropriate nondimensional slenderness ~ L T may be determined from

Class 3 or 4

aLT is the imperfection factor for lateral-torsional buckling;

C~LT should be taken as :

- for rolled section ~ L T = 0,21 (buckling curve a),

- for welded section C~LT = 0,49 (buckling curve c).

(4) The non-dimentional slenderness 2 LT may be determined from :

- LT Me1.y

= JG EC4

[4.6.3(4)]

are the values of Mply.w and &l.y .u (see chapter V.2.5.1) when partial safety factors ya, yc and ys are taken as 1 ,O.

is the elastic critical moment of the gross cross-section for lateral-torsional buckling. The calculation of Mcr is detailed in Eurocode 4 (see Ref. 4 : Annex B) but if the composite beam does not comply with the conditions of that annex B, the value of Mcr could be determined from literature or numerical analysis or, conservatively, from Eurocode 3 (see Ref. 3 : Annex F).

151 I

[Ref. Chapter V - Members in bending I

V.2.6

V.2.6.1

Verification at ULS to combined (vzsd,

Resistance of crosssection to (VZSd, My.~d)

EC4 [4.4.3]

(1) Ethe design value of the vertical shear force

lvzsd 5 05 VDLZ.Rd/

Where vpl.z.Rd, is the design plastic shear resistance about minor (zz) axis (see chapter V.2.4. l),

no reduction needs to be made in the resistance moments. With this condition the design value of bending moment my.^ shall be verified according to chapter V.2.5.

(2) For the resistance of c ros s -don submitted to combined vertical shear force Vz.u and bending moment my.^ ifthe design value of vertical shear force

EC4 [4.4.3(1)]

Ivz.Sd > 075 vplz.Rd] &f$ shear) 7

then interaction between vertical shear force and bending moment shall be considered. The plastic resistance moment should thus be calculated using a reduced design yield strength f y . d for the shear area AV (see Figure V. 10). Then, if there is no shear buckling problem, the following interaction criterion (illustrated in Figure V. 1 1) should be satisfied by the design value of bending moment my.^ at each cross-section :

EC4 [4.4.3(2)] 1My.M MV.Rd1 , but IMV.Rd 5 My.RdI I - I I I

resistance moment allowing for the shear force, is the design bending moment resistance of the cross-section about y axis (see chapter V.2.5. l), is the design plastic bending resistance of a cross-section consisting of the flanges only (“flanges” meaning both structural steel flanges and reinforcement steel of concrete flange), with effective sections as used in the calculation of My.Rd,

My.Rd

Mf.Rd

m1)II. vplz.Rd

In Figure V. 10, f y . d (= fy (1 - pz)) is applied on the shear area AV.= of the profile (for values, see Table V.7).

y.Sd

I I

Figure V.10 Normal stress distribution for M-V interaction with hogging bending moment

152


EC4 pig. 4.61

" f I v-1- D A A

Figure V.11 Resistance in bending and vertical shear in absence of shear buckling

V.2.6.2 Stability of web to (Vas& MY.sd

EC4 t4.4.51

EC3 [5.6.1(1)]

EC3 [5.6.1(4)]

EC3 [Fig. 5.6.4(a):

(1) If webs are submitted to combined shear force Vz.Sd and bending moment My.Sd and if they have

ratio - exceeding the limits given in Table V. 10 then they shall be checked for resistance to

shear buckling and transverse stiffeners shall be provided at supports. Kl

(2) The interaction of shear buckling resistance and moment resistance is shown in Table V. 15 according to the simple postcritical method.

TableV.15 Interaction of shear buckling resistance and moment resistance with the simple postcritical method

1

Vpl.z.Rd

Vba.Rd

OS Vba.Rd

0

, v

\ A I C

I

153


-

EC3 p6.7.21 (3) The web may be assumed to be satisfactory if one of the three following checks A), B) or C)

(according to the loading level of VZ.Sd and My& shall be satisfied:

MySd 5Mf.Rd + (My.Rd -MfRd

A) Ifthe design value of bending moment

EC3 [5.6.7.2 (111 -1 EC4 t4.4.5 (a)] where M f . u is the design plastic moment resistance of a cross-section consisting

of the flanges only (“flanges” meaning both structural steel flanges and reinforcement steel of concrete flange), with effective sections as used in the calculation of my.^ (see chapter V.2.5.1),

& the design value of vertical shear force shall satisfy:

-1 where Vba.u is the design shear resistance buckling of the web according to

simple post-critical method (see chapter V.2.4.2). EC3

p.6.7.2 (211 B) Ifthe design values of bending moment and vertical shear force

the bending moment shall satisfy :

-1 where my.^ is the design bending moment resistance of the cross-section about y

axis depending on the class of cross-section (see chapter V.2.5.1). EC3

p6.7.2 (311 C) Ifthe design values of bending moment and vertical shear force

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

154


V.2.7

V.2.7.1 Generalities

Verification of shear connectors at ULS to longitudinal shear

Shear connectors and transverse reinforcement shall be provided throughout the length of the beam to transmit the lonpitudinal shearforce Ve between the concrete slab and the steel beam at the ultimate limit state, ignoring the effect of natural bond between the materials. The total design longitudinal shear force Ve (see chapter V.2.7.2) have to be resisted by shear connectors :

EC4 [6.1.1 (611

EC4 I6.1.21 (4)

EC4

f4.1.2 (611 ( 5 )

EC4 [6.1.1 (311

1 V e I N . m I where N is the number of studs

PRd is the design shear resistance o f shear connector (see chapter V.2.7.3).

Longitudinal shear Ealure and splitting of the concrete slab due to concentrated forces applied by the shear connectors shall be prevented. The design longitudinal shear force per unit of length ve (see chapter V.2.7.2) to be resisted by the slab shall satify :

I v e s v R d 1 where is the design resistance of any surface ofvotential shear failure &

concrete-flange (see chapter V.2.7.5).

The effects of slip and uplift may be neglected at interfaces between steel and concrete at which shear connection is provided in accordance with rules about headed studs

presented in this chapter V.2.7. Headed studs may be assumed to provide sufficient resistance to uplift unless the shear connection is subjected to direct tension.

Headed studs may be considered as ductile within certain limits (see chapter V.2.7.2.2).

The concepts ‘@I1 shear connection” and ‘partial shear connection” are applicable only to beams in which plastic theory is used for calculating bending resistances of critical cross-sections (i.e. for class 1 or class 2 cross-sections).

A span of a beam or a cantilever has full shear connection when increase in the number of shear connectors would not increase the design bending resistance of the member (see chapter V.2.7.2.1).

Otherwise the shear connection is partial if the design ultimate loading is less than that which could be carried by the member if full shear connection were provided. Limits to the used partial shear connection with ductile connectors are given in chapter V.2.7.2.2.

This chapter V.2.7 focuses on headed studs; Eurocode 4 (Ref. 4) should be consulted for rules about other types of shear connectors listed in chapter 11.3.4.

V.2.7.2 Design longitudinal shear force EC4 [6.2]

The rules presented hereafter applies to beams in which plastic theory is used for resistance of cross-sections : Mpl.m is the plastic resistance moment of a class 1 or class 2 cross-section (see chapter V.2.5.1). For beams with cross-sections in class 3 or 4 and for which elastic theory is used, refer to Eurocode 4 (see Ref. 4 : 6.2.2).

155


where

V.2.7.2.1 Full shear connection I

F d = minimum ; beff hc 0,85 Yc Ys

EC4 t6.2.1.11

(1)

Ref. 8 [4.6]

EC4 [6.2.1.1 (111

For simvlv suvuorted beams :

In simply supported composite beams subject to uniform load, the elastic shear flow defining the shear transfer between the slab and the beam is linear, increasing to a maximum at the ends of the beam. Beyond the elastic limit of the shear connectors, there is a transfer of force along the beam such that, at fhilure, each of the shear connectors is assumed to resist equal force. This implies that the shear connectors possess adequate deformation capacity, i.e. is ductile.

In the plastic design of smgle span composite beams and for full shear C O M ~ O ~ , the total design longitudinal shear force, Vt to be transferred between the points of zero moment (at simple end supports) and maximum sagging moment should be the smaller of the resistance of the concrefe section and of reinforcement in compression, (Fc + Fs) and the resistance of the structural steel section Fa (see Figure V. 12) :

(2) EC4 r6.2.1.1 (211

Ase

is the area of structural steel section (see Table IV.6),

is the effective width of concrete slab (see chapter V.2. l),

is the maximum possible depth of concrete in compression (see chapter V.2.5. l),

is the effective area of any longitudinal reinforcement in compression that is included in the calculation of the sagging bending resistance,

is the yield strength of the structural steel (see Table US),

is the compression strength of the concrete (see Table II. l),


are partial safety fktors at utimate limit states for the structural steel, concrete and reinforcement steel (see Table II.10).

For continuous beams :

For full shear connection, the total design longitudinal shear force Vi to be resisted by shear connectors between the point of maximum sagging bending moment and an intermediate support or a restrained end support shall be calculated as follows (see Figure V. 13) :

where Fd

AS

is as defined above in clause V.2.7.2.1 (1) and is taken as zero for cantilever,

is the effective area of longitudinal slab reinforcement used in the calculation of the hogging bending resistance (at support) (see chapter V.2.5. I),

156

EC4 [4.2.1 (411 is the effective area of any profiled steel sheeting included in the calculalion of the hogging bending resistance, only if ribs run parallel to the beam and ifthe detail design ensures continuify of streagth across joints in the sheeting and appropiate resistance to

k P

longitudinal shear,

fsk

fn YS and Yap


is the yield strength of the profiled steel sheeting (see Table II.9),

are partial safety factors at utimate limit states for the reidorcement steel and the profiled steel deckhg (see Table II. 10).

(a) Moments in simDlv-suDDort ed beam

f = minimum (Fa ; F, + F, )

Figure V.12 Calculation of the longitudinal shear force Ve in simply supported beams

157

IRef. Chapter V - Member in bending I

The number of shear conn&rs for full shear connection shall be at least equal to the design longitudinal shear force Ve, divided by the design resistance of a connector, pRd (see chapter V.2.7.3). Therefore, the number of shear connectors in the zone under consideration is :

Nf =- El pRd takes into accounf the influence V.2.7.3.

of the shape of the profiled sheeting, as given in chapter

(a) Moments in continuous be am Ve = Fcf = minimum (Fa ; F, + F, )

(M P I - R ~ )sagging

:.:;,:,:.: .):, :...: .............................................................................................................................. ............................................................

f F a 3 ''z VP

@) Internal force distribution

Figure V.13 Calculation of the longitudinal shear force Ve in continuous beams

158

I Ref. Chanter V - Members in bendine I

V.2.7.2.2 Partial shear connection with ductile connectors EC4 16.2.1.21

EC4 [6.1.1 (311 (1) Partial shear connection may be used if all cross-sections are in Class 1 or 2.

EC4 16.2.1.2 (111 (2) If connectors are ductile, it may be assumed that sufficient slip at interface between steel and

concrete can occur at the ultimate limit state for moments of resistance at critical sections to be calculated €tom plastic theory (see chapter V.2.5.1).

EC4 [6.1.2] (3) Headed studs (see chapter 11.5.5 and Figure II.4 in chapter II.3.4) may be considered as ductile in

having sufficient deformation capacity to justify the assumption of ideal plastic behaviour, if a minimum degree of shear connection (expressed as N / Nf ratio) is provided (see Figure V. 14).

(4) The moment resistance of a composite beam designed for partial shear connection may be determined by one of the following methods (see Figure V. 15) :

a) Method I :

b) Method 2 : Linear interpolation method,

Plastic stress block (or equilibrium) method.

EC4 [6.2.1.2 (311 (5) Method 1 is more conservative than method 2 but is a simple method of &ermining the moment

resistance. The relationship is defined by the line AC in Figure V. 15. The force transferred by shear connectors, Fc is :

MSd - Mapl.Rd Mpl.Rd - Mapl.Rd

where MM is the applied design sagging bending moment (Msd I Mpi.Rd),

is the design plastic resistance to bending of the structural steel section alone (Wpl fy / ya) (see Table V. 13 b) : Notations),

is the design plastic sagging moment resistance of composite cross- section with full shear connection (see Table V. 13 a)),

is the longitudinal shear force required for full shear connection (see chapter V.2.7.2.1).

Map1.w

Mp1.w

Fcf

159

[kif. Chapter V - Members in bending

EC4 [6.1.2 (2)

to (411

Ref. 7 (Fig. 6.14)

160

0,4

0 . Minimum degree of shear connection :

In all cases -1. case A : - case B : case C : where At is the top flange area,

N / Nf 2 0,4 + 0,03 L N /Nf 2 0,25 + 0,03 L N /Nf 2 0,04 L

where 3 At 2 & where At = Ab where At =

Ab N Nf

is the bottom flange area, is the number of shear connectors, is the number of shear connectors for full shear connection (see clause V.2.7.2.1 (3)). . Conditions of ductile behaviour of headed stuc

- casesAandB: 1) and, 2) [16mm<dI22mml7

w

- caseC: 1) paiq, 2) I19 mm I d I 20 mm 1 , 3) rolled I or H steel section (At = &), 4) composite concrete slab with profiles

steel sheeting that spans pemendicular to the beam and is continuous across it,

5 ) one stud per rib of sheeting, placed centrally within the rib,

6) deck profile with bo / h 2 2 and jpI ,

7) and, the longitudinal shear force Fc is calculated by linear interpolation methad (clause V.2.7.2.2 (5)) .

Figure V.14 Minimum degree of shear connecfion allowing ductile behaviour of headed studs


FC Fcf

MSd 5 MRd = Mapl.Rd +-(Mpl.Rd - Mapl.Rd)

EC4 pig. 6.11

.

M apl.Rd

M pl.Rd

0

MSd M pl.Rd -

"Ductile" shear-connectors

equilibrium method I

1 I I

I ] steel ,F,= 01 I

Lower limit on - W 4 )

1,O- Fcf Nf Degree of shear connection

(6) In Method 2 the force transferred to the concrete is determined by the longitudinal resistance of shear connectors. Equilibrium equations can be established explicitly in a similar manner to chapter V.2.5.1. The relationship is deiined by the curve ABC in Figure V.16.

A good approximation of the reduced bending moment resistance of composite cross-section M m (I Mpl.~d) can be obtained by considering the moment axial force interaction for an I- secdon according to Eurocode 3 (Ref. 3) (see Figure V. 16) and M a should satis6 :

Ref. 7 @. 53)

where MSd is the applied design sagging bending moment ( M u I Mpl.Ild),

is the design plastic sagging moment resistance of composite cross- section with fill shear connection (see Table V. 13 a)),

Mp1.M

161


[form. 6.13 and 6.141

FC is the force transferred by shear co~ectors (Fc = c p R d ) (see chapter V.2.7.3),

N I N f 9

Fa

Mapl.w

is the axial resistance of steel section (= Aa fy / ya) (see Table V.13 b) : Notations), is the design plastic resistance to bending of the structural steel section alone (= Wpl fy / ya) (see Table V. 13 b) : Notations).

[ ;['qd2) ; 0 2 9 a d Yv b d = minimum '9'- -

strain (E) stresses

where zc =S

is the position of first plastic neutral axis in concrete, is the position of second plastic neutral axis in steel section.

Figure V.16 Mu, reduced bending moment resistance of composite cross-section because of partial shear connection

V.2.7.3 Design shear resistance of headed studs

V.2.7.3.1 Headed studs in solid slabs

I I

I I I

I I I

I

Figure V.17 Composite beam with solid slab

(1) The design shear resistance of an automatically welded headed stud with a normal weld collar, should be determined from :

EC4 16.3.2.11

where fu is the specified ultimate tensile strength of the material of the stud but not greater than 500 N/mm2. The commonly specified strength is 450 N / m 2 (see chapter I I S S ) ,

162

[ Ref. Chapter V - Members in bending I

Diameter d

[mm1

22

19

16

Ref. 7 [Table 6.61

First equation

[N/mm21

Second equation of PRd with a = 1,O Of PRd With fu

450 500 C 25/30 C 30137 C 35/45 C40/50 C45l55

109,4 121,6 98,l 110,o 121,6 (132,9) (142,9)

81,6 90,7 73,l 82,l 90,7 (9991) ( l o w )

57,9 64,3 51,9 58,2 64,3 (7033) (75,6)

l

d

h

&k

Ecm

is the diameter of the shank of the stud (d I 22 mm) (see Figure V. 17),

is the overall height of the stud (see Figure V. 17),

is the characteristic cylinder compressive strength of the concrete at the age considered (see Table II. l), is the mean value of the secant modulus of the concrete (see Table II. I),

I

a = 0,2($ + I), if 3 - h 5 4 , d

a= 1 h d , i f ->4 ,

(2) A normal weld collar should comply requirements shown in Figure 11.4. Moreover the weld should have a regular form and be ksed to the shank of the stud.

V.2.7.3.2 Headed studs in composite slabs with profiled steel sheeting EC4 [6.3.3]

EC4 [6.3.3.1] (1) Profiled steel sheetinn with ribs parallel to the suuuortinn beam :

I

U \ centroidal axis of sheet 1

I

Figure V.18 Beams with steel decking ribs parallel to the beam

Where profiled steel sheeting with ribs parallel to the supporting beam is used (see Figure V. 1 S), the headed studs are located within the region of concrete that has the shape of a haunch.

163

IM. ChaDter V - Members in bending

and

EC4 [form. 6.151

EC4

kt I 1,o ifNr = 1 for studs welded

I 0,8 ifNr 2 2 through the steel decking

The design shear resistance should be taken as their resistance in a solid slab (PRd from chapter V.2.7.3.1) multiplied by the reduction factor kt given by the following expression :

k t = 0,6”.(”-;) I1,O hP hP

where bo is the mean width of the ribs (see Figure V. 18),

is the overall height of the stud, but should satisfy : h

hP is the overall depth of the s h e excluding embossments.

[6.3.3.2] ( 2 ) Profiled steel sheetinn with ribs transverse to the sumortinn beam :

[form. 6.161

Ref. 7

[6.3.2.2]

Figure V.19 Beams with steel declung ribs transverse to the beam

Where the headed studs are placed in ribs perpendicular to the supporting beam (see Figure V. 19), the design shear resistance should be taken as their resistance in a solid slab (Pw from chapter V.2.7.3.1) multiplied by the reduction factor kt given by the following expression :

where Nr is the number of stud connectors in one rib at a beam intersection, not to exceed 2 in computations,

is the overall depth of the sheeting excluding embossments and, hP hp I 8 5 1 ~ n

b0 is the mean width of the ribs (see Figure V. 18) and,

bo 2 hp

h is the overall height of the stud, but should satisfy :

164


V.2.7.4 Spacing and detailing of headed studs

Headed studs in accordazlce with chapter V.2.7.3 may be placed uniformly over a length Lm between adjacent critical cross-sections (see chapter V. 1 and Table V. 1) provided that

a) all critical sections in the span considered are in class 1 or class 2,

b) N / Nf satisfies the limits for partial shear connection given in chapter V.2.7.2.2, when L is replaced by Lcr, and,

c) the plastic resistance moment of the composite section does not exceed 2,5 times the plastic resistance moment of the steel member alone (Mpl.m I 2,5 Map1.d (see Tables V. 13 a) and b) respectively for Mp1.m and Mapl.Rd),

EC4 t4.1.2 (S)]

(2) EC4 [6.1.2] (3)

EC4 [6.4.1.5 (211 (4)

For checking the resistance to longitudinal shear critical cross-sections also include free ends of cantilever.

Requirements for dimension of headed studs and its normal weld collar are given in Figure II.4.

When headed studs are expected to be ductile and develop sufficient deformation capacity, specific requirements are provided in chapter V.2.7.2.2 (see Figure V.14).

When a steel compression flange (e.g. due to sagging bending moment) that would otherwise be in a higher class, is assumed to be in class 1 or class 2 because of restraint fiom shear connectors, requirements of spacing for shear connectors are shown in chapter V.2.2.3 (see Figure V.4).

For solid slabs, requirements of spacing for headed studs are given in Figure V.20.

mesh I

shear connector I / I800-mm

I O 220mmt.- 0 4 0 O I

Figure V.20 Detailing of shear connectors in solid slab

165

\Ref. Chapter V - Members in bending

I I I 1

a) Decking ribs trans verse to the beam

b) Decking ribs parallel to the beam

Figure V.21 Types of composite beams with composite slabs

(6) For composite slabs, more detailing rules are provided hereafter about welding and spacing of studs welded through profiled steel decking :

When the decking is continuous and transverse to the beam (Figure V.2 l), the correct placement of studs in relation to the decking rib is of great importance. The most important rules for welded headed studs are repeated here : welded headed studs are normally between 19 mm and 22 mm in diameter. Stud diameters up to 19 mm are generally used for through deck welding only. For welded studs upper flange of the steel

EC4 [6.4.3.1(2)] beam should be clean, dry and unpainted. For satisfactory welding, the deck thichess should not exceed 1,25 mm if galvanized, or 1,5 mm if ungalvanized. In all cases, welding trials shall be performed. The following limitations should also be observed :

- The flange thickness of the supporting beams should not be less than 0,4 times the diameter of the stud, unless the studs are located directly over the web.

- After welding, the top of the stud should extend at least 2 times diameter of the

stud above the top of the decking ribs and should have a concrete cover of at least 20 mm. - The minimum distance between the edge of the stud and edge of the steel flange is 20 mm.

- The transverse spacing between studs should not be less than 4 times the diameter of the stud.

- The longitudinal spacing between studs should not be less than 5 times the stud diameter and not greater than 6 times the overall slab depth nor 800 mm.

Ref. 7

(5.4.1)

EC4 [6.4..2 (411

EC4 [6.4.3.1 (311

EC4 [6.4.1.2 (211

EC4 [6.4.1.6 (2)]

EC4 [6.4.2 (311

EC4 [6.4.3 (3)] EC4 16.4.1.5 (311

166


Ref. 7 (5.4.2) For composite slabs, additional requirements for steel decking :

Studs must be properly placed in decking ribs. A summii~y of these rules are shown in Figure V.22, and listed below :

- Studs are usually attached in every decking rib, in alternate ribs, or in some cases, in pairs in every rib. If more studs are needed than are given by a standard pattern these additional studs should be positioned in equal numbers near the two ends of the span.

- Some modem decks have a central stiffener in the rib which means that it is impossible to attach the stud centrally. In such cases it is rmmmended that studs are attached to the side of each stiffener closest to the end of the beam shown as the favourable side in Figure V.22. This means that a change in location at midspan is needed.

- Alternatively, studs can be "staggered" so that they are attached on each side of the stiffener in adjacent ribs.

- At diswntinuities in the decking, studs should be attached in such a way that both edges of the decking at the discontinuity are properly "anchored". If the decking is considered to act as transverse reinforcement this may mean placing studs in zigzag pattern along the beam, as shown in Figure V.22.

- The minimum distance of the centre of the stud to the edge of the decking is defined as 2,2 times the stud diameter.

EC4 [7.6.1.4 (311

167

IRef. O t e r V - Members in bending

Ref. 7

favourable side I mesh unfavourable side

~

endofs an . -stiffener in decking ,7

4 1 5 d *j

mesh -

I

stiffener in decking /

Figure V.22 Detailing of shear connectors in composite slabs with steel decks including central stiffener

V.2.7.5 Design shear resistance of concrete slab

Sufiicient fruwerse reinforcement shall be provided in the slab so that premature longitudinal shear failure (see chapters V.2.7.5.1 to V.2.7.5.3) or longitudinal splitting (see Eurocode 4, chapter 6.6.5) is prevented at ultimate limit states.

168

L Ref. Chapter V - Members in bending I

V.2.7.5.1 Longitudinal shear in the slab vsd

(1) The design longitudinal shear per unit length of the beam for any potential surface of longitudinal shear failure within the slab (see Figure V.23), vsd, shall not exceed the design resistance to

EC4 [6.6.1]

longitudinal shear, v~d, of the shear surface considered : (VSdIvRdj.

EC4 pig. 6.121

EC4 [6.6.1 (211

v~ should be determined in accordance with chapter V.2.7.2 (determination of Vt) and be consistent with the design of the shear connectors at the ultimate limit state. A model to evaluate

is given in chapter V.2.7.5.2.

At a At 1 a

Case 1) C a ! a

Remark : the length of shear sur fm b-b should be taken as equal to : - (2 h + cph) for a single row of headed studs or staggered

stud connectors, or, (2 h + st + cph) for headed studs arranged in pairs. -

Figure V.23 Typical potential surfhces of shear failure in slabs

(2) Potential failure surfaces are shown in Figure V.23. Top (area At) and bottom (area At,) reinforcement in the slab may be considered to be effective. Where steel decking is continuous over the beam, or is effectively anchored by shear connectors, it may also be considered to act as transverse reinforcement. Failure surface a-a controls in these cases.

Failure surface b-b is not considered critical in Eurocode 4 in cases where steel decking is used transverse to the beam (see Figure V.23, case 2)), provided that the design resistances of the studs are determined using the appropriate reduction factor as given in clause V.2.7.3.2 (2).

(3) In determining vsd, account may be taken of the variation of longitudinal shear across the width of the concrete flange. Longitudinal shear is considered to be transferred uniformly by the shear connectors.

E C ~ [6.6.1(3)]

EC4 [6.6.1 I

(4)syS)l

169


<

Concrete strength C 20/25 C 25/30 C 30/37 C 35/45 C 40/50 C 45/55 C 50/60

tRd 0,25 0,30 0,33 0,37 0,42 0,45 0,48

V.2.7.5.2 Design resistance to longitudinal shear m d

The design resistance of the concrete flange (shear planes a-a illustrated in Figure V.23) shall be determined in accordance with the principles in clause 4.3.2.5 of Eurocode 2 (Ref. 2). Profiled steel sheeting with ribs transverse to the steel beam (see Figure V.23, case 2)) may be assumed to contribute to resistance to longitudinal shear, provided it is continuous across the top flange of the steel beam or if it is welded to the steel beam by stud shear connectors.

In the absence of more accurate calculation the design resistance of any surface of potential shear failure in the flange or a haunch should be determined from :

I f Formula6.25 Formda6.26 \I

(3)

where md O J 5 fct k 0,OS

Yc is the basic shear strength to be taken as TRd = Y

170

I M. Chapter V - Members in bending]

(4) Transverse reinforcement considered to resist longitudinal shear shall be anchored so as to develop its yield strength in accordance with Eurocode 2 (Ref. 2). At edge beams, anchorage may be provided by means of U-bars looped around the shear connectors.

V.2.7.5.3 Contribution of profiled steel sheeting as transverse reinforcement, vpd EC4 t6.6.31

EC4

[6.6.3(1)] (1) Where the profiled steel sheets are continuous across the top flange of the steel beam, the contribution of profiled steel sheeting with ribs transverse to the beam should be taken as

EC4 [form. (6.2711 El I I

EC4 [7.6.1.4]

(3)

where vpd is per unit length of the beam for each intersection of the shear suhce by the sheeting,

AP

fYP

is the cross-sectional area of the profiled steel sheeting per unit length of the beam,

is the sheeting yield strength (see chapter 11.9),

'yap is a partial safety factor (see chapter 11.10).

Where the profiled steel sheeting with ribs transverse to the beam is discontinuous across the top flange of the steel beam, and stud connectors are welded to the steel beam directly through the profiled steel sheets, the contribution of profiled steel sheeting should be taken as :

AP fYP

Yap 1 vpd =- p*r I but vpd I-,

where s is spacing centre-tocentre of the stud along the beam,

ppb.Rd is the design bearing resistance of a headed stud against tearing through the steel sheet :

kq ddo tp fyp PpbRd = 9

Yap

a k, = 1 +- but I4,0, where ddo

&o is the diameter of the weld collar (= 1,l d),

d is the diameter of the shank of the stud,

a is the distance from the centre of the stud to the end of the sheeting (a 2 2 &o),

tp is the thickness of the sheeting,

fYP is the sheeting yield strength (see chapter II.9).

In all other cases, vpd should be neglected. Note that, in a certain number of NAD's, the contribution of Drofiled steel sheeting to shear resistance. v d is never activated.

171

~

pGf. Chapter V - Members in bending

V.2.7.5.4 Minimum transverse reinforcement

(1) The area of reinforcement in a solid slab should be not less than 0,002 times the concrete area being reinforced and should be uniformly distributed.

EC4 [6.6.4]

where As is the cross-sectional area of transverse reinforcement and,

Ac is the effective area of concrete flange.

(2) Where the & are parallel to the beam svan, the area of transverse reinforcement should be not less than 0,002 times the concrete cover slab area in the longitudinal direction and should be uniformly distributed.

(3) Where the & are transverse to the beam man, the area of transverse reinforcement should be not less than 0,002 times the concrete slab area in the longitudinal direction and should be uniformly distributed. Profiled steel sheeting continuous across the top flange of the steel beam may be assumed to contribute to this requirement.

v.3 Verifications at Serviceability Limit States SLS E C ~ PI

V.3.1 Generalities about SLS EC4 [5.1]

Ref. 7 [7.1] (1) The serviceability requirements for composite beams concern the control of :

- deflections (see chapter V.3.2), - cracking of concrete (see chapter V.3.3),

- vibration response (see chapter V.3.4).

Deflections are important in order to prevent cracking or deformation of the partitions and cladding, or to avoid noticeable deviations of floors or ceilings. Floor vibrations may be important in long span applications, but these calculations are outside the scope of Eurocode 4 (Ref. 4).

(2) Loads to be used at the serviceability limit state are presented in chapter III. Normally unfactored loads are used.

E C ~ [5.1(2)] (3) Calculation of stresses and deformations at the serviceability limit states shall take into account the effects of :

- Shear@; - increased flexibility resulting from significant incomplete interaction, due to slip andor

uplift; - cracking and tension stiffening of concrete in hogging moment regions;

- creep and shrinkage of concrete;

- yielding of steel, if any, especially when unpropped construction is used;

- yieldmg of reinforcement, if any, in hogging moment regions.

These effects shall be established by test or analysis, where practicable.

172

I Ref. ChaDter V - Members in bendine; I

(4) Most designers base assessments at the serviceability limit state on elastic behaviour (with certain modifications for creep and cracking etc). In the absence of a more rigorous analysis, the effects of creep may be taken into account by using modular ratios (as given in Table II.3) for the calculation of f l e d stiffnesses. To avoid consideration of postelastic effects, limits are often placed on the stresses existmg in beams at the serviceability limit state.

Ref. 7 [7.1] (5) No stress limitations are made in Eurocode 4 (Ref. 4) because : - postelastic effects in the mid-span region are likely to be small and have little influence on

deflections, - the influence of the connections on the deflection of simply supported beams has been

neglected, - account is taken of plasticity in the support region of continuous beams.

V.3.2 Deflections EC4 [5.2]

EC3 [4.2] (1) Composite structures and components shall be so proportioned that deflections are within limits agreed between the clients, the designer and the competent authority as being appropriate to the intended use and occupancy of the building and the nature of the materials to be supported.

(2) In buildings it will normally be satisfactory to consider the deflections under the rare combination EC4 [5.2.1(2)]

EC4 [5.2.1(4)]

of loading.

(3) The design values for the vertical deflections (&) should be lower limiting values given in Table V. 18. Deflection limits are not specified in Eurocode 4. Reference is made to E u r d e 3 (Ref. 3) (see Tables V. 18 and V. 19) for limits on deflections due to permanent and variable loads. Those limiting values are illustrated by reference to the simply supported beam shown in Table V.19. The sagging vertical deflection (&)- for unpropped beams should be detennined for the underside of the beam, only where the deflection can impair the appearance of the building. In all other cases the reference level is the upperside of the beam. Against excessive maximum deflection (6max) a usual solution consists in introducing an initial precambering (60) of structural steel beam (see Table V. 19).

(4) The values given in Table V. 18 are empirical values. They are intended for comparison with the results of calculations and should not be interpreted as performance criteria.

Ref. 7 [7.2.1](5) Deflections are calculated knowing the moment of inertia of the composite section based on elastic properties (see Figure V.2). Under -inn moment the concrete may be assumed to be uncracked, and the moment of inertia of the composite section (expressed as a transformed equivalent steel section) is given by a formula in clause V.2.1 (5).

Ref. 7 [p. 61](6) The ratio / Ia (=I1 / Ia) therefore defines the improvement in the stifhess of the composite section relative to the steel section. This ratio is presented in Figure 1.4 for all IPE and HE sections (up to 600 mm deep) for typical slab depth. Typically, Ic / Ia is in the range of 2,s to 4,0, indicating that one of the main benefits of composite action is in reduction of deflections.

173


Conditions Ref. 6 [Table 4.21

LimitS

roofs generally

roofs frequently canying personnel other than for maintenance

floors generally

floors and roofs supporting brittle finish or non-flexible partitions

floors supporting columns (unless the deflection has been included in the global analysis for the ultimate limit state)

~~

where Gm can impair the appearance of the building

U200

U250

U250

U250

U400

Ll250

L = span of the beam; for cantilever beams : L = twice cantilever span

U250

U300

U300

U350

U500

Discharge of rainwater : slope of the roof less than 5% check that rainwater cannot collect in pools. slope of the roof less than 3% additional check that incremental collapse cannot occur due to

the weight of water.

Table V.19 Vertical deflections to be considered

Gm is the sagging in the final state relative to the straight line joining the supports,

/State 0

822\ state State 2

4 b

is the pre-camber (hoging) of the beam in the unloaded state (state O),

is the variation of the deflection of the beam due to permanent (G) immediately after loading (state 117

is the variation of the deflection of the beam due to the variable loading (Q) (state 2).

Ref. 7 [P. 611

174

(7) It is not usually necessary to calculate the "cracked" moment of inertia under sagsing b e n d q moment as the elastic neutral axis will normally lie in the steel beam, or near the base of the slab. Where it is necessary to know the "cracked" moment of inertia Iqn ('12) under honninn bending -7 moment a simple formula may be derived from Figure V.2. Assuming that the reinforcement is placed at mid-height of the slab above the sheeting, a formula is provided for E7n in clause V.2.1 (5).

This formula may be used in establishing the moments in elastic global analysis (method 2 in chapter V.2.3), or in crack control calculations (see chapter V.3.3).

Ref. Chapter V - Members in bending I

EC4 (8) Modular ratio :

Ref. 7 [7.2.2] [3.1.4.2]

The values of elastic modulus of concrete under short term loads, Em, are given in Table II. 1. The elastic modulus under long term loads is affected by creep, which causes a reduction in the stiffness of the concrete. The modular ratio, n, is the ratio of the elastic modulus of steel to the timedependent elastic modulus of concrete (see Table II.3).

The modular ratio n for normal-weight concrete is typically, 6,s for short term (variable) l-.

The elastic modulus of concrete for long term (permanent) loads is taken as one-third of the short term value, leading to a modulus ratio n of approximately 20 for long term (permanent) loading in an internal environment. Details of different n values are provided in Table II.3.

For building of n o d usage, surveys have shown that the proportions of variable and permanent imposed loads rarely exceed 3: 1. Although separate deflection calculations may be needed for the variable and permanent deflections, a representative modular ratio is usually appropriate for calculation of imposed load deflection. This value of n may be taken as twice the short term modular ratio (i.e. approximately 13) for buildings of normal usage.

EC4 [5.2.2(6)] (9) Influence of partial shear connection :

Deflections increase due to the effects of slip in the shear connectors. These effects are ignored in composite beams designed for full shear connection. For cases of partial shear connection using headed stud shear connectors and class 1 or 2 cross-section (see chapter V.2.7.2), the deflection, 6, is increased according to :

- for propped construction,

($=i+o,5 (I-$) (2-i)l - for unpropped construction,

where 6a

6c N

is the deflection of the steel beam acting alone under the same loads,

is the deflection of the composite beam with full shear interaction.

is the degree of shear connection at the ultimate state (with NMf 2 0,4). - Nf

EC4 [5.2.2(6)]

EC4 [5.2.2(5)]

The difference between the formulas arises from the higher force in the shear connectors at serviceability in propped construction.

An additional simplification is that slip effects can usually be ignored when N / Nf 2 0,5 or forces on the shear connectors do not exceed 0,7 P R ~ , in unpropped construction and in case of a ribbed slab with ribs transverse to the beam (with the height of ribs : hp I 80 mm). This is because of beneficial effects that are ignored in calculating deflections making the above equation too conservative in many cases.

175

(Ref. Chapter V - Members in bending

EC4 [5.2.2(9)] (10) Shrinkape vieldinn deflections :

Eurocode 4 states that shnnkage deflections need only be calculated for staticallydeterminate beams in buildings (simply supported beams or cantilever) when the span : depth ratio of the beam exceeds 20 ( L / b + h p + b ) > 20 ), and when the free shnnkage strain of the concrete exceeds 400 10-6 (see Table II.2). In practice, these deflections will only be significant for spans greater than 12 m in exceptionally warm dry atmospheres.

The curvature, Ks, due to a free shnnkage strain, ES (see Table II.2) is :

Ref. 7 [7.2.4]

where n is the modular ratio appropriate for shnnkage calculations (n = 20) (see Table II.3),

h, &, hp, Aa, E and r are defined in chapter V.2.1.

The deflection due to this curvature is :

1 6 s = 0,125 Ks L2 I This deflection formula ignores continuity effects at the supports and probably overestimate shnnkage deflections by a considerable margin.

Ref. 7 [7.2.5] (1 1) Continuous beams :

The deflection of a continuous beam is modified by the influence of cracking in the negative moment region. Analyses with uncracked section or cracked section may be used.

EC4 [5.2.2(7)@)] This may be taken into account by calculating the moment of inertia of the cracked section under hogging bending moment (ignoring the

assumed to vary as a reduction factor

bending moment at the supports is

the hogging bending moment at the serviceability limit state based on analysis of the uncracked section, where I1 is the uncracked moment of inertia, and I2 is the cracked moment of inertia (see clause V.2.1 (5)) . The lower limit to this reduction factor on hogging bending moment is which is applicable where there is minimum reinforcement in the slab. This method may be used where the difference in adjacent spans is less than 25%.

In continuous beams, there is a possibility of yielding in the hogging bending moment region. To take accouIlt of this effect the hogging bending moments may be further reduced. In reality, this reduction is a function of the moment resistance of the composite section under hogging and sagging bending moment. A conservative way of taking this into account is to multiply the “elastic7’ hogging bending moments at the supports by a further reduction factor. This factor is given in Eurocode 4 as lo,7b where load sufficient to cause yielding is applied to the section with hardened concrete, which is the normal design case. Together with the minimum factor of 10,61 due to concrete crackmg, the final hogging bending moment may be conservatively taken as 10,421 times the elastic moment based on uncrucked unulvsis.

EC4 [5.2.2(8)]

176


The mid-span deflection of a beam, as influenced by the support moments, may be calculated from :

where C = 0,6 for uniform load, = 0,5 for central point load,

are the midspan moment and deflection of the equivalent simply- supported beam,

are the hogging moments at the supports (for the same loading condition), reduced for cracking and yielding as noted above.

and 60

M1 and M2

As an approximation, a deflection coefficient of 3/384 is usually appropriate for determining the deflection of a continuous composite beam subjected to uniform loading on equal adjacent spans. This may be reduced to 4/384 for end spans. The moment of inertia of the section is based on the uncracked value.

Alternatively, a more precise method is to use the “cracked section ” analvsis model of elastic global analysis described in chapter V.2.3 in order to determine the hogging bending moments directly. No further reduction in hogging bending moments should be made in this case.

EC4 [7.5.2(2)&(3)]( 12)In order to avoid the need to consider additional loading due to ponding of the wet concrete in the

design of the floor and supporting structure, the total deflection of the profiled sheet decking submitted to its own weight plus the weight of wet concrete (but without construction loads) at the construction stage should be limited by :

I 6 IL /180or20mm. 1 where L is the effective span between supports (props being supports in this

context).

V.3.3 Cracking of concrete EC4 [5.3] Ref. 7 [7.4] (1) It is necessary to control cracking of concrete only in cases where the proper functioning of the

structure or its appearance would be impaired. Internally within buildings, durability is not a f f e c t e d by cracking. Similarly when raised floors are used, cracking is not visually important.

EC4 p 3 . 1 (511 (2) Minimum reinforcement without controt ofcrack width :

Where a composite beam is subjected to hogging bending moment and if no attempt is made to control the width of cracks in the concrete of its top flange, the longitudinal reinforcement within the effective width beff of that flange should be at least :

- -1, for propped construction or,

- -1, for unpropped construction,

where As is the cross-sectional area of longitudinal reinforcement and,

& is the effective area of the concrete flange. For information the Table V.20 gives the percentage of reinforcement (As / &) for specific bar diameters, spacings and solid slab thicknesses.

The reinforcement should extend over a length span/4 each side of an internal support, or length/2 for a cantilever as shown in Figure V.24.

177

IM. Chapter V - Members in bending

U /Rm

U - mm

, 1 L1 1 L 2 1 L3 I I 1 1

0,25 L1 0,25 L2 0,25 L2 0,5 L3 1 .IL 1

i r\ n

Figure V.24 Reinforcement length at supports for a composite beam

TableV.20 Minimum percentage of reinforcement bars for propped and unpropped ~ l l S t l - U C t i O n S

EC4 [5.3.1 (S)]

Reinforcement bars

8 6 8 10 8 10 12 12 14 10 16 14 12 18 16 14 20 18 22 16 20 22 18 26 20 30 26 22 30 26

Condition :

spacing [ml 200 100 150 200 100 150 200 150 200 100 200 150 100 200 150 100 200 150 200 100 150 150 100 200 100 200 150 100 150 100

Percentage of reinforcement (%) for different thichesses of solid slab & [mm]

100

0,so 0,52 0,57 0,75 0,77 0,79 1,Ol 1,03 1,13 1,27 1,34 1,54 1,57 1,70 1 9 2,o 1 2,09 2,53 2,54 2,65 3,14 3,53 3,54 3,80 -

120

0,42 0344 0,47 0,63 0,64 0,65 0,84 0,86 0,94 1,06 1,12 1,28 1,31 1,41 1,58 1,68 1,75 2,11 2,12 2,2 1 2,62 2,95 2,95 3,17 3,93

for prouved construction :

150

0,50 0,5 1 0,52 0,67 0,68 0,75 0,85 0,89 1,03 1,05 1,13 1,27 1,34 1,40 1,69 1,70 1,77 2,09 2,36 2,36 2,53 3,14 3,54

200

0,50 0,5 1 0,57 0364 0,67 0,77 0,79 0,85 0,95 1,Ol 1,05 1,27 1,27 1,33 1,57 1,77 1,77 1,90 2,36 2,65

A, I & 2 0,4%

250

0,40 0,41 0,45 0,5 1 0,54 0,62 0,63 0,68 0,76 0,80 0984 1,01 1,02 1906 1,26 1,41 1,42 1,52 1,88 2,12

for unvropDed construction : A, I & 2 0,2%

300

0,42 0,45 0,5 1 0,52 0,57 0,63 0,67 0,70 0984 0,85 0,88 1,05 1,18 1,18 1,27 1,57 1,77

178


EC4 p 3 . 1 (5)] (3) Minimum reinforcement with control ofcrack width :

Where it is necessary to control cracking, a minimum amount of reinforcement should be imposed in order to avoid the presence of large cracks in the hogging moment region.

This minimum percentage of reinforcement area to concrete slab area, pmin is given by : EC4 [5.3.2]

Pmin =- = k c k -

where As is the cross-sectional area of reinforcement,

Ac kc

k

is the effective area of the concrete flange,

is a coefficient due to the bending stress distribution in the section (kc 2 (491, is a coefficient accounting for the decrease in tensile strength of concrete (k = 0,8),

is the effective tensile strength of concrete : a value of 3 N/mm2 is the minimum adopted, is the maximum stress permitted in the reinforcement immediately after cracking, depending on the chosen bar size and with QS < f& ,

where f& is the characteristic yield strength of reinforcement (see Table 11.8).

h e

Ost

A typical value of Pmin is 0,4% to 0,6% which is well in excess of the minimum of 0,2% necessary in unpropped construction for shnnkage control and transverse load distribution. However, these bars need only be placed in the hogging bending moment region of the beams or slabs. This reinforcement may also act as fire reinforcement or transverse reinforcement.

At least half of the required minimum reinforcement should be placed between middepth of the slab and the face subjected to the greater tensile strain.

(4) An additional criterion is that the bars should be of small diameter and should be spaced relatively closely together in order to be more effective in crack control. Maximum bar diameters of high bond bars are given in Table V.21 as a function of the maximum reinforcement stress, CJG and the maximum allowed crack width, w. If detailed crack control is necessary, more information is given in Eurocode 4 (Ref. 4 . clause 5.3.4).

179

[Ref. Chapter V - Members in bending I

Table V.21 Maximum bar diameters for high bond bars for different maximum reinforcement stresses and crack widths at SLS

EC4 [Table 5.11

V.3.4 Vibrations EC4 [5.1 (111

(1) A check of the potential vibration response may be necessary for long span beams designed for light imposed loads. A simple measure of the natural frequency f given in m] or [cycles/sec] of abeamis:

Ref. 7 [7.3]

where 6sw is the instantaneous deflection [mm] caused by reapplication of the self weight of the floor and beam to the composite member.

A minimum limit on natural frequency, f, is proposed as 3 cycles/sec for most building applications except where there is vibrating machinery. The limit may be raised to 5 cycledsec for special buildings such as sports halls.

180

~~

Chapter VI - Members with combined axial compressive force and bending moment I

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

181

I Ref. Chapter VI - Members with combined axial compressive force and bending moment I

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

VI.1 Generalities

(1) For each load cuse (see chapter III) the design values of the following internal forces and moments may be applied to members with combined axial force and bending moment, that shall be checked at ultimate limit states :

EC4 Figure VI.1 Internal forces and bending moments applied to composite member

[4.8.1(1)] (2) This chapter VI only deals with composite members which are of two main types : - totally (Figure W.2 a)) or partially (Figure VI.2 b)) concrete encased steel sections and, - concrete filled steel sections (Figures VI.2 c) and d)).

Y 4 - ezr a>

J bC .I r

b r

I J b = b c r

.I

Figure VI.2 Type of cross-sections of composite columns

Previous page is blank 183

[Ref. Chapter VI - Members with combined axial compressive force and bending moment I Ref. 12

0 . 5 1 ) (3)

Ref. 10 @. 57)

EC4 [4.8.3.1] (6)

(7)

The design for members in compression and bending is done in the following steps : The composite member is examined isolated from the system. Then the end moments which may result from the analysis of the system as a whole are taken up. These end moments may also have been determined by second-order theory in the analysis of the whole system according to the respective requirements. With the end moments and possible horizontal forces within the member length, as well as with the normal force, action effects are determined. For slender member this must be done considering second-order effects (see chapter VI. 1.1). In the simplified method of E u r d 4 imperfections need not to be considered in the analysis of action effects for the composite members. They are taken into account in the determination of the resistauce. The resistance of the composite member to compression and bending (see chapters VI.3 to VIS) is determined by help of the cross-section interaction curve (see chapter VI.2). The influence of transverse shear forces may be considered in the interaction curve (see chapter VI.6).

This chapter VI only applies to isolated non-sway composite members with combined axial load and bending moments.

This chapter VI presents the simplified method of design (EC4 : [4.8.3]) for composite members of double symmetrical (Figure VI.2) and uniform cross-section over the column length. This simplified method uses the European buckling curves for steel columns (Eurocode 3) as the basic design curves for composite members. Application rules for composite members of mono-symmetrical cross-section are given in Annex D of Eurocode 4 (Ref. 4). When the limits of applicability of the simplified method are not fblfilled (see chapter IV. 1. l), the general method (EC4 : [4.8.3]) has to be applied. That general method includes composite members with non-symmetrical or non-uniform cross- section over the column length. The method assumes that composite members are not suceptible to lateral-torsional buckling.

Design assumptions : Both approaches for the design of composite columns (general and simplified methods) are based on the following main assumptions :

- fbll interaction between concrete and steel up to the point of collapse,

- allowances must be made for imperfections which are consistent with those adopted for assessing the strength of bare steel columns,

- proper account must be taken of the steel and concrete stresse-strain curves,

- plane sections remain plane.

The Table VI.1 provides a list of checks to be performed at Ultimate Limit States for the composite member submitted to combined axial compressive force and bending moment (N , M). A member shall have sufficient bearing capacity if all general checks about the design method (list of checks @) are satisfied and if checks are hlfilled according to the loading applied to that member. All the checks have both references to Eurocode 4 and to the design handbook. Beside general checks about the design method (list of checks @), the Table VI. 1 proposes the following loading applied to the member :

@ Axial compressive force and uniaxial bending moment (Nx.Sd, My.sd) or (Nx.s& Mz.sd, @ Axial compressive force and biaxial bending moment (NX.%, my.^ and MZ.Sd).

The influence of transverse shear forces (VZ.s& Vy.sd) is explained in chapter VI.6.

184

[Ref. Chapter VI - Members with combined axial compressive force and bending moment I

EC4 [4.8.3.1 (511

r4.8.3.1 (311 [4.8.2.5] [4.8.2.4] t4.8.2.61 to [4.8.2.8] [4.8.3.10]

[4.8.3.3]

[4.8.3.8]

t4.8.3.111

[Figure 4.121

[4.8.3.13]

[4.8.3.13 (811

[4.8.3.3]

[4.8.3.8]

[4.8.3.11]

[Figure 4.121 [4.8.3.14]

[4.8.3.14 (511

Table VI.1 List of checks to be performed at ULS for the composite member submitted to combined axial compressive force and bending moment (N,M)

3 General checks about the design method Check the limits of applicability of the simplified design methd Check concrete cover and reinforcement Check for local buckling of steel members Check the load introduction and the longitudinal shear

Secondader effects on bending moments Specific remarks for N-M checks

Axial COmDressive force and uniuxid bending moment

Resistance of cross-section to Nx.Sd :

(1) (2) (3) (4)

(5) (6)

@ (Nx.sdY My.sd) or (NX.S& MZ.sd) :

(1) N x . ~ I N p l . ~ (design plastic resistance to compression of

the composite cross-section)

(2) Stability of member to N x . ~ , for both buckling axes : Nx.M I minimUm (Nby.Rd ; NbZ.Rd) (design f l e d buckling

resistances of the composite member about y and z axes)

(3) Resistance of cross-section to (Nx.Sd My.& or (Nx.Sd Mz.Sd) : interaction (Nx.sd My.sd)

- or interaction (Nx.m MZ.sd)

(4) Stability of member to (Nx.Sd My.& or (Nx.Sd MZ.sd) :

My.Sd I 079 Py Mpl.y.Rd

- or MZ.Sd I 099 Pz Mp1.z.M Axial comDressive force and biaxiuZ bending moment

Resistance of cross-section to Nx.Sd :

Nx.Sd I Np1.u

Stability of member to Nx.Sd7 for both buckling axes :

(Nxsd Y My.M and Mz.Sd)

(design plastic resistance to compression of the composite cross-section)

N x . ~ I minimum (Nby.M ; Nbz.Rd) (design f l e d buckling resistances of the composite member about y and z axes)

Resistance of cross-section to (Nx.Sd My.Sd and Mz.sd), for each separate bending plane (xz) and (xy) :

interaction (Nx.sd My.& and interaction (Nx.sd 7 Mz.Sd)

Stability of member to (Nx.sd My.Sd and Mz.s~) : My.,% I 079 Py Mpl.y.Rd Mz.Sd 5 079 Pz Mpl.z.Rd

+ M*d I l,o y.Sd and C’yMpl.y.Rd C’zMpl.z.Rd

References to lesim handbook

Iv.l.l [v 1.1 (4)to(6)

Iv.1.2 lV.1.3 & Iv.1.4

vI.l.l vI.1.2

Iv.2

Iv.3

vI.2

vI.3

Iv.2

Iv.3

vI.4

vI.5

185

IRef. ChaDter VI - Members with combined axial compressive force and bending moment 1

VI.l.1 Second order effects on bending moments

EC4 [4.8.3.10 (211 (1) Columns generally should be checked for second-order effects. For memory, second-order theory

takes into accounf the influence of the deformation of a structure in order to determine internal forces and moments, whereas first-order theory uses the initial geometry of the structure.

Ref. 9 [5.3.2](2) In slender isolated non-sway columns under combined compression and bending, second-order effects on the bendmg may be s i d c a n t . Eurocode 4 requires that the second-order effects on ben- moments about each relevant axis should be considered if the following both conditions (a) and b)) are satisfied :

EC4 [4.8.3.10 (311 a) 1;; - > O , l I an4

where Nx.Sd is the applied design axial load,

are the elastic critical loads for the column length about relevant axis (yy or zz) (see clause IV.3 (4) and additional comments in clause VI. 1.2 (2)),

- h is the non-dimensional slenderness of the composite member for

flexural buckling mode about relevant axis (x,,,x,) (see clause N.3 (4) and additional comments in clauses VI. 1.2 (1) and (2)),

is the ratio of the lesser to the greater end moments : r

for transverse loading within the column length : r = 1.

For simplification, the bending moment according to second-order theory ( M L ) can be

calculated by increasing the greatest first-order bending moment (MSd in Table VI.2) with a correction fixtor k :

EC4 [4.8.3.10 (411 and k 2 1,0,

where N ~ . L is the elastic critical load of the composite column for the relevant axis (yy or zz) and with the effective length taken as the column length (see clause IV.3 (4) and additional comments in clause VI. 1.2 (2)),

is an equivalent moment factor given in Table VI.2. P The composite member is then designed for combined compression (Nx.sd) and bending with the

bendmg moment accounting for second-order e f f i equal to -1. 186

I Ref. Chapter VI - Members with combined axial compressive force and bending moment 1

If any one of the conditions (a) or b)) is not satisfied, the second-order effects may be regarded as insignificant and the applied design moment obtained from first-order theory may be used for the subsequent check of member to combined compression and bending.

Table VI.2 Factors p for the determination of moments according to second-order theory

Line

1

2

3

Moment distribution

First-order ben- moments fiom lateral loads in isolated non-sway CQlUmn

End moments in a non-sway frame

MSd r MSd

- 1 S r I l

Moment factors p

p = 1,o

p = 0,66 + 0,44 r

but p 2 0,44

p 2 1,o

comment

MM is the maximum bending moment within the column length due to lateral forces ignoring second-order effects

MSd and r MM are the end moments

Combined action of end moments and moments from lateral loads

VI.1.2 Specific remarks for N-M calculations

EC4 [4.8.3.3 (311 (1) Increase ofNpl.Rdfor concrete-filled tubes :

In case of concrete-filled circular hollow profile (see Figure VI.2 d)) submitted to N-M loading, the load bearing capacity Npl.Rd of the composite cross-section may be increased because of confinement and triaxial containment of concrete, if both following conditions (a) and b)) are satisfied :

a) the relative slenderness % of composite member is limited to :

I I

b) the greatest design bending moment calculated by first-order theory, M-.M is limited to :

Mmax.Sd - < d which is equivalent to : e = NxSd l0 '

187

EC4 [4.8.3.3 (4)]

where n is the non-dimensional slenderness of composite member (see chapter IV.3 and additional comments in clause VI. 1.2 (2)),

is the applied design normal force,

is the external diameter of the column, is the excentricity of the normal force Nx.Sd related to M-a.

NX. sd

d e

In chapter IV.2 this effect is already presented for cross-section submitted to centered axial compressive force Nx=. In this chapter VI. 1.2 concerning loading of combined axial force and ben- moment, a supplementary condition (the second one : b)) is introduced considering the effect of bending moment amplitude. The following rule for Npl.u evaluation replaces the one presented in chapter IV.2 (Table IV.5):

EC4

[4.8.3.3 (5) and (611

where Npl.u is the design plastic resistance to compression of the composite cross-section,

are the cross-sectional areas of the structural steel, the concrete and the reinforcement (see Table IV.6),

is the yield strength of the structural steel (see Table n.9, is the compression strength of the concrete (see Table II. l),


is the wall thickness of the circular hollow profile,

are partial s a f i i factors at ultimate limit states for the structural steel, concrete and reinforcement steel (see Table 11. lO),

&, &, As

fY

&k

fsk

t

' y~a , yc, ys

*For 0 S e S d/loand h 0,s :

where q l o and 7120 values related to e = 0,O , depend on h as follows :

qlo = 4,9 - 183 x+ 17 2 , q20 = 0,25 (3 + 2%) ,

and qlo 2 0 (see Table IV.4),

and q20 I 1,O (see Table IV.4),

*Fore > d/10or h 2 0 , S :

q l = 0,O and q 2 = 1,O.

188


(2) Secant modulus of elasticitv of the concrete for lonn-term loading :

The effective elastic flexural stifhess (E I)e of a cross-section of a composite column should be calculated from :

EC4

[4.8.3.5] ((E I)e = E, I, + 078 Ecd I, + E, Is1 7

as presented in clause IV.3 (4) where the effects of short-term and long-term loading are taken into account.

In clause IV.3 (5) this effect is already presented for cross-section submitted to centered axial compressive force N x . ~ . In this chapter VI. 1.2 concerning loading of combined axial compression and bending moment , an additional condition (about the eccentricity e of axial load Nx.Sd) is considered to decide if the influence of long-term behaviour of the concrete (creep and shnnkage of concrete) has to be allowed for.

EC4 [4.8.3.5 (l)] - for short-term loading :

EC2 [A.3.1] [A.3.4]

EC4 [4.8.3.5 (211 -

where &m is the secant modulus of elasticity of the concrete according to Table 11. l),

according to Eurocode 2 (Ref. 2). yc = 1,35

for low-term loading and slender columns:

if

and, ifeld 2:

exceeds the limits given in Table IV.9,

where Ecm and 'yc

Nx. Sd

NG.Sd

e

Mmax. Sd

d

are defined for short-term loading,

is the applied design axial force,

is the part of the applied design axial force (Nx.sd) that is permanently acting on the column,

is the non-dimensional relative slenderness for flexural buckling about relevant axis (h.y,h.z)(see clause IV.3 (4) and additional comments in clause VI. 1.2 (l)),

- - M m a x ~ ~ d , is the excentricity ofthe axial force, NXSd

is the greatest design bendug moment calculated by first-order theory, is the overall depth of the cross-section in the bending plane.

This effective elastic flexural stiffness of cross-section of a composite column is used to evaluate the elastic critical load Ncr and the relative slenderness h , for relevant buckling axis (see clause IV.3 (4)).

189

I Ref. Chapter VI - Members with combined axial compressive force and bending moment

vI.2 Resistance of cross-sections to combined compression and uniaxial bending (NLSd ; My.Sd) O r (Ns.Sd ; MzSd)

Ref. 7 [8.3.3] (1) The resistance of composite member to combined compression and bending is detennined with the

help of a cross-section interaction curve. The different combined effects of actions applied to the composite cross-section (Nx.~; My.& or (Nx.~; MZ.sd), shall be situated in the validity area delimited by the N-Mcross-section interaction curve (see Figure VI.3).

In a typical interaction curve of a member with steel section only, it is observed that the moment resistance undergoes a continuous reduction with increase of the axial load (see Ref. 3 chapter 5). However, it is shown in the interaction curve of a composite cross-section that the moment resistauce may be increased by the presence of axial load. This is because the prestressing effect of an axial compression may in certain circumstances, prevent concrete cracking and make the

concrete more effective in resisting moments [ ztd > 1) (see Figure VI.3).

(2) The cross-section interaction curve can be found by considering different positions of the neutral axis over the whole cross-section and by determining the internal action effects from the resulting stress blocks. This approach can only be carried out by computer analysis.

But, with the simplified method of Eurocode 4, it is possible to calculate by hand four or five points (A, C, D, B and E) of the interaction curve. The exact interaction curve may be replaced by the polygonal diagram (A(E)CDB) through these points as shown in Figure VI.4. This simplified method is applicable to the design of composite columns with cross-sections that are symmetrical about both principal axes (y and 2).

EC4 [4.8.3.11]

1

Figure M.3 Cross-section interaction curve for compression and uniaxial bending

190


EC4 Figure 4.12:

EC4 [4.8.3.11 (111

[4.8.3.11 (3)]

EC4 [4.8.3.11 (511

N

Npl.Rd

Npm.Rd

1 - N p . R d 2

c

D I / I

Figure VI.4 Cross-section interaction curve (with polygonal approximation) for compression and uniaxial bending

The points on the interaction curve may be calculated assuming rectangular stress blocks and concrete zones under tension as cracked.

The stress distributions corresponding to points A, B, C, D and E are given in Figure VIS for a totally concreteencased I-section with bending about the major axis of the steel section.

I I

For concrete filled hollow sections the plastic resistances may be calculated with 0,85 f& being replaced by f& (see Figure VIS (a = 0,85 or I), clause VI.2 (3) and Table VI.3 c)).

. -

In general, the additional point E should be determined approximately midway between point A and point C if the resistance of the member to axial compression (x Npl.Rd) is greater than Npm.Rd, where Npm.Rd is the plastic resistance of the concrete section alone.

For encased I sections with bending about major axis (yy) it is not necessary to calculate the point E, because the interaction curve is almost linear between points A and C.

Y

191

IRef. Chapter VI - Members with combined axial compressive force and bending moment 1 EC4 Figure 4.1 31

Point A (compression resistance Npl.Rd )

Point B (bending resistance Mpl.Rd )

M pl.Rd

Point c

M pl.Rd

4- Npm.Rd

Point D

M max.Rd

+ Npm.Rd

2

Point E

ME 4-

N E

Notations : "-" means compression stresses ; "+" means tension stresses

Figure VI.5 Stresses distributions corresponding to the interaction curve (Figure VI.4)

192


( 3 ) Determination of cross-section polygonal interaction curve (see Figures V. 4 and V. 5) : - Point A marks the resistance to normal compressive axial force :

INA = N pl.u I (see chapter W.2 and additional comments in clause VI. 1.2 (l)),

~ M A = 0 1 - Point B shows the stress distribution for bending moment resistance

where Wp, Wpc, Wpsare the plastic section moduli of the whole cross-section for structural steel, for concrete part of the section (for the calculation of Wpc the concrete is assumed to be uncracked) and for the reinforcement (see Table VI.3),

are the plastic section moduli of the cross-section parts within the region of 2 hn (see Figure VIS) for structural steel, for concrete part of the section (for the calculation of Wpm the concrete is assumed to be uncracked) and for the reinforcement (see Table VI.3),

Wpan, Wpcn, Wpsn

fY

fkk

is the yield strength of the structural steel (see table IIS),

is the compression strength of the concrete (see table II. l),

a is a reduction factor depending on the type of cross-section :

fsk is the yield strength of the reinforcement (see table 11.8),

are the partial d e t y factors at ultimate limit states for the structural steel, concrete and reinforcement steel (see table II.10).

yc, ys

193

IRef. Chapter VI - Members with combined axial compressive force and bending moment I - Point C also corresponds to the bending moment resistance but with additional compressed

region (over 2 hn) creating a normal compressive axial force :

where & is the whole area of concrete (see table IV.6),

a, f& and yc are defined for point B.

The stress difference between point C and point B is :

. *I-

- Point D : at this point, the stress neutral axis lies within the centroidal axis of the cross- section ; the axial resistance (over hn) is half the one of point C and the greatest bending resistance is reached :

p/ (see point C),

fsk +wps -

Y h h 2Y c Ys

tY +Wp- fck MrnaxRd =wp-

where all parameters are defined for point B. The stress difference between point D and point B is :

2

fsk where Mn.Rd = W p - fY +Wpcn 2 afck +Wpsn - YMa Yc Ys

- Point E : details are provided in Annex C of Eurocode 4 (Ref. 4: see C.6.3 (5) to (7) for concreteencased I-sections or see C.6.4 (3) to (5) for concrete-filled hollow sections).

The equations for the position of the neutral axis, hn, are given for selected positions in the cross- sections. The resulting value of hn should lie within the limits of the assumed region.

194


EC4 [Annex C]

Table VI.3 a) Neutral axes and plastic section moduli for totally and partially concreteencased steel profile bent about major axis (yy)

Y 9 4- Y ezL For the whole cross-section :

4-n 2 311-10 3 + (b - t )(h - t f ) t f +-r (h - 2tf)+- r t h2 wpa =w 4 2 3

For the cross-section Darts within the region of 2 hn :

case 1 :

case2 :

case 3 :

Wpan = t, h i

Neutral axis in the flange :

h 2 Neutral axis outside the steel section : (- < h n 5 $)

hn = Ac fcd-Asn(2fsd-fcd)+Aa(2fyd-fcd)

2bc fcd wpan =wpa

Notations : see Table VI.3 c)

195

IRef. ChaDter VI - Members with combined axial compressive force and bending moment 1

Table VI.3 b) Neutral axes and plastic section moduli for totally and partially concreteencased steel profile bent about minor axis (zz)

t h = h c , tf

For the whole cross-section : t f b 2 h-2tf 2 4 - x 2 31~-10 3 +- t, +- r t,-- r

w p = 2 4 2 3

For the cross-section parts within the region of 2 hn :

case 1 :

case 2 :

case 3 :

Neutral axis in the web : (hn 5%)

Ac fcd -Asn (2fsd -fed) 2hc fcd +2h(2fyd - f d )

hn =

Wpan=hh, 2

Neutral axis in the flange :

b Neutralaxisoutsidethesteelsection: (T<h, sh) 2

Ac fcd -Asn (2fsd - f ~ I ) - ~ a (2 fyd -fed) hn =

2hc fcd Wpan"Wpa

Notations : see Table VI.3 c)

196


TableVI.3 c) Neutral axes and plastic section moduli for concrete-filled circular and rectanmlar hollow sections ' EC4

[Annex C] i

1) bend in^ about maior axis Cw) : - Rectangular hollow sections :

. For the whole cross-section : h

(r + t)3 -(r + t)2 (4 - XI ( - - t - r) - wPc - wPs wPa = 4 - 5 2

b h 2 2

n Wps = C A s i lezil

1=1

For the cross-section arts within the region of 2 hn : .

n

- Circular hollow sections : The same equations may be used with good approximation by substituting h=b=d and r =d/2-t. 2) Bending about minor axis Czz) : For bending about minor axis (iz) the same equations as for major axis @y) may be used with exchanging the dimensions h and b as well as the subscript z and y.

Notations : fyd

&A

fsd ' y~a , yc, ys are the partial safety factors at ULS (see Table 11. lO), Aa, &, As are the cross-sectional areas defined in Table IV.6, n Asi A s i Asn

= fy / ' y ~ a (see Table 11.5 for fy), = 0,85 f& / yc , for tables VI.3 a) and b), = f& / yc , for table VI.3 c) (see Table II.1 for fck), = f& / ys (see Table 11.8 for fsk),

is the number of reinforcement bars, is the area of re-bar i (= n cp2 / 4 , with cp = re-bar diameter), is the area of re-bar i situated within the region of 2 hn, is the sum of different areas Asi ,

or ezi distance of the rebar i of area Asi to the relevant middle line (z or y axis)

197

[Ref. Chapter VI - Members with combined axial compressive force and bending moment

c c 3 c c c c 3

vI.3 Stability of members to combined compression and uniaxial bending (N,Sd;My.Sd) or &Sd;Mz.Sd)

1 0

0 0725 x

-1 03 x

EC4 [4.8.3.13] Ref. 9 [4.5.3] (1)

EC4 [4.8.3.13(2)] (2)

EC4 [4.8.3.13(4)] (3)

The principle for checking the stability of composite member under combined compression and uniaxial bending according to the Eurocode 4 simplified method is illustrated graphically in Figure VI.6 where NM and MM are axial force resistance and bending moment resistance of the composite member. Figure VI.6 is derived from cross-section interaction curve (see chapter VI.2) for the same bendmg plane of the applied moment.

Firstly, the resistance of the composite member under axial load has to be determined in the

absence of bending moment. This resistance ratio is given by x = b-Rd where Nb.M k the 1 Nd.Rd 1 I I

design flexural buckling resistance of the member (see chapter IV.3 and additional comments in clauses V. 1.2 (1) and (2)), Npl.Rd is the design plastic resistance to compression of the composite cross-section (see chapter IV.2 and additional comment in clause V.1.2 (1)) and where x factor accounts for the influence of member imperfections and slenderness. In Figure VI.6 the bearing capacity to axial load is represented by the value x . At the level of x a corresponding value for bending can be read from the cross-section interaction curve. This bending moment resistance pk Mpl.Rd is meant to be the “moment of imperfection” of the composite member, representing the second-order moment due to imperfections of the member (Mpl.u is the plastic moment resistance of the composite cross-section : see chapter VI.2).

The influence of the imperfections decreases when the axial load ratio (NRd / Npl.Rd) is less than x and is assumed to vary linearly between x and Xn. For an axial load ratio less than xn, the effects of imperfections is neglected. The value Xn accounts for the Eact that the imperfections and the bending moment do not always act unfavourably together. For end moments the ratio Xn may

where r is the ratio of the lesser to the greater end moment as shown in Table VI.4 and x d is defined hrther in clause VI.3 (4).

In other cases of bending moment distribution within the member length (for instance, transverse loads)

Table vI.4

should be taken as zero.

Typical values of Xn

11 Bending moment distribution within the member length 1 Ratio r I Value xn

EC4

[4.8.3.13(3)] (4) With a design axial force applied to the member Nx . s , the axial load ratio is defined as

198

I Ref. Chanter VI - Members with combined axial ComDressive force and bendine moment I

The corresponding bending resistance of the cross-section is given by pd Mpl.Rd , where issued from the interaction curve (see Figure VI.6).

EC4 [4.8.3.13(5)] (5) By reading off the horizontal distance from the interaction curve (see Figure VI.6), the moment

resistance ratio, p, may be obtained and the moment resistance of the composite member under combined compression and bending may then be evaluated.

The value p defines the ultimate moment resistance that is still available, having taken into account the influence of second-order effects in the member. According to Figure VI.6 the length p is calculated from :

is

"t Npl.Rd

7- t------ 0' I \

Figure VI.6 Design procedure for compression and uniaxial bending interaction

III certain regions of the interaction curve, the moment resistance ratio is allowed to be greater than unity in the presence of axial load. This is due to the fact that in the presence of axial load, the amount of concrete in tension and thus cracked is reduced, and more concrete is included in the evaluation of the moment resistance. However, if the bending moment and the applied load are independent of each other, the value of p must be limited to 1,0 : p I 1,0 . On the countrary the value of p may be greater than 1,0 if the bending moment MSd is due solely to the action of the eccentricity of the force Nx.Sd, e.g. in an isolated cohmn without transverse loads acting between the column ends.

[4.8.3.13(8)] (6) Eurocode 4 considers that the member in combined compression and uniaxial bending has sufficient resistance ifthe following condition is satisfied :

[4.8.3.13 (7)]

LM Sd 5 039 Cc M pl.Rd I where MSd is the maximum design bending moment applied within the column

length, which may be hctored to allow for secondader effects, if necessary (see chapter VI. 1 . l),

is the moment resistance ratio obtained from the cross-section interaction curve (see clause VI.3 (5)),

is the plastic moment resistance of the composite cross-section (see chapter VI.2).

P

Mp1.M

199

p. Chapter VI - Members with combined axial compressive force and bending moment

Ref. 12 @p. 58-59) (7)

Ref. 9 @. 25)

The interaction curve has been determined without considering the strain limitations in the concrete. Hence the moments, including secondader effects if necessary, are calculated using the effective elastic flexural stiflkess, (E I)e , and taking into account the entire concrete area of the cross-section (i.e. concrete is uncracked). Consequently, a reduction factor of O,9 is applied to the moment resistance as shown in equation aforementioned to allow for the simplifications in this approach.

The advantage of this simplified method of calculation is its applicability for any double- symmetrical cross-section. Althrough the polygonal course lies beneath the exact interaction curve, the design not always lies on the conservative side. If the deviation between polygonal course and exact curve is very large in the region of the moment of imperfection (at the height of x in Figure VI.6), an small on the other side at the normal force (at Xd in Figure VI.6), a too small imperfection is taken into account. In this case the fifth point E of the interaction curve presented in chapter VI.2 has to be determined nearly in the middle between point A and point C. For concreteencased I-sections with bending about the strong axis of the section the exact interaction curve takes an almost linear course between point A and C, so that point E need not be determined in this case.

For concrete-filled hollow sections, the interaction curve AECDB as shown in Figure VI.4 may be preferred as it will give more economical design, especially for columns under high axial load and low end moments, although much calculation effort is required. For better approximation, the position of point E may be chosen to be closer to point A rather than being mid-way between points A and C. Refer to Eurocode 4 for more infoxmation.

M.4 Resistance of cross-sections to combined compression and biaxial bending (NLSd, My.Sd and MaSd)

For the design of a composite member under combined compression and biaxial bending, verification of cross-section resistance has to be performed separately for each bending axis. The applied effects of actions combined as (Nx.Sd, My.sd) and (Nx.Sd, MZ.sd), have to lie in the valid area of the respective cross-section interaction curves calculated for bending about major axis (yy) and for bending about minor axis (zz) (see chapter VI.2).

vI.5 Stability of members to combined compression and biaxial bending (N,Sd, My&j and

[4.8.3.14(2)]( 1)

EC4 [4.8.3.14(4)] (2)

MaSd) For the design of a composite member under combined compression and biaxial bending, the axial resistance of the member in the presence of bending moment for each axis has to be evaluated separately. In general, it will be obvious which of the axes is more likely to fhil and the imperfectdons need to be considered only for this direction as shown in Figure VI.7 (where failure is expected to occur for bending about z axis). If it is not evident which plane is the most critical, checks should be made for both bending vlanes.

The evaluation of the moment resistance ratios py and pz for both axes is carried out on basis of cross-section interaction curves (see chapter VI.2). If the failure plane is known it is only necessary to consider the effect of geometric imperfections in the critical plane of member buckling (pz in Figure VI.7) and, the moment resistance ratio p in the other plane (py in Figure VI.7) may be evaluated without the consideration of imperfectections. The interaction of the bending moments must also be checked using the moment interaction curve as shown in Figure VI.7. This linear interaction curve is cut off at 0,9 py and 0,9 pz. The design moments, my.^ and MZ.& related to the respective plastic moment resistances, must lie within the moment interaction curve.

200


EC4 14.8.3.14 (5 ) ]

(3) Eurocode 4 considers that the member has sufficient resistance if all the following conditions are satisfied :

Mm I 0,9, P z Mpl.zRd

md, MY.M + Mz.Sd I 1,o Py Mpl.y.Rd PZ Mpl.zRd

where , in the case of Figure W.7,

VZ

W.3)7 is evaluated from cross-section interaction curve (see chapter VI.2), PLY

Mpley.Rd and Mpl.z.Rd are the plastic moment resistanas of the composite cross- section (see chapter VI.2).

1" Npi.Rd

M z.Rd Mpl.z.Rd *

l 'O x z - - - - - - - y . - - - - & - - - A - - - -

M z.Rd I

I 5pl.z.Rd I 1\ 1 I *

0 p d 1,0

t" Npl.Rd

a) Plane (xy) expected to fail, with b) Plane (xz) without consideration consideration of imperfections of imperfections

M y.Rd

I, - M pl.y.Rd 079 CLy p y

z

Figure M.7 Verification for combined compression and biaxial bending

20 1

IRef. Chapter VI - Members with combined axial compressive force and bending moment

M.6

(1) Similary to explanations given in chapter N.1.3, the design transverse shear forces (Vz.w Vy.sd) may be assumed to act on the steel section alone, or to share between the steel section and the concrete. The shear force to be resisted by the concrete must be considered accordmg to Eurocode 2 @f. 2), whereas the shear force to be resisted by the steel section can be checked using the von Mises criterion. Figure VI.8 shows the reduction of normal stresses in the shear area (Av) of the steel section under transverse shear stress, for the case of totally encased I-profile bent about major y-y axis.

Influence of transverse shear forces

- -

where

1 ) MV.y.Rd

VLSd

Figure VI.8 Reduction of normal stresses of steel profile within shear area in the presence of transverse shear stress

EC4 t4.4.3 (111 (2) If the design value of the transverse shear force is allocated to the steel section alone and if :

where V p l . z . ~ , V p l . y . ~ are the design plastic she& resistance about minor axis (zz) and major (yy) axes of steel profile (see chapter V.2.4. l),

no reduction needs to be made in the resistance moments.

(3) For the resistance of the steel cross-section submitted alone to combined shear force (VZ.Sd or Vy.sd) and uniaxial bending moment (My.Sd or MZ.sd) if the design value of transverse shear force

lvSd > o$vpl.Rd I e& shear)

then interaction between shear force and bending moment shall be considered. In this case the design value of bending moment MM shall satisfj at each cross-section :

lMSd 5 MV.Rdl 9 but lMV.Rd Mpl.Rd I where MV.M is the reduced design plastic resistance moment of the composite

cross-section allowing for the transverse shear force (see following clauses VI.6 (3) and (5 ) ) ,

202

1 Ref. Chapter VI - Members with combined axial compressive force and bending moment I

Mp1.m is the design plastic resistance moment of the composite cross- section (see chapter VI.2 and Tables VI.3).

EC4

I p.4.3 (2)] (4) For design purposes, the reduction in the design steel strength (fy.& in the shear area (AV) of the steel section may be transformed into a reduction in steel thickness of that shear area (Av) : tw.red, t f .d or tred (see Table VIS).

Table VIS Reduced steel thickness trd allowing for transverse shear force

EC4 [4.4.3(2)]

Ifhigh shear 1 VSd > 095Vpl.Rd Type of cross-ssctionS and applied loading

iVz.Sd 1Vz.Sd

where Pz

e

P

tf

t W

t

fY Ya

is the flange thickness, is the web thickness, is the wall thickness, is the yield strength of steel profile (see Table US), is the partial safety factor at ULS for structural steel (see Table PI. lO),

Avey and AV are the shear areas about different loading axes (see chapter V.2.4.1, Table V.9).

203

I Ref. Chapter VI - Members with combined axial compressive force and bending moment

EC4 [4.8.3.11 (I)] EC4 [CS]

Using the reduced effective thickness tw.red, t f . d or t d of the web or the flange of the steel section, the moment resistance of the composite cross-section (respectively Mv.~.M, M V . ~ . ~ or Mv.Rd) may be evaluated using the same set of expressions given in chapter VI.2 and Tables VI.3 without any modification. The determination of the cross-section interaction curves for (Nxa Vz.u and My.sa> and (Nxa V y . ~ and MZ.& combined loading can be carried out with the same method given in chapter VI.2 and the checks of composite members should follow the same procedure provided in chapters VI.2 to VIS.

Ref. 9

14.71 ( 5 ) For simplicity, the division of the shear force between the steel section and the concrete may be neglected, and the design shear force is allocated to the steel section alone. In practice, it is unlikely that shear will have any influence on the design of composite columns.

204

Chapter W - Composite slabs or concrete slabs 1

VI1 COMPOSITE SLABS OR CONCRETE SLABS

205

Ref. Chapter VI1 - Composite slabs or concrete slabs

VI1 Composite slabs or concrete slabs ,

:ef. 7 [5]

-1.1 Generalities kef. 7 [5.1]

: ~ 4 [7] (1) This chapter VII reviews the different forms of concrete slab that may be used in conjunction with composite beams, and the factors that influence the design of the beams. The detailed design of composite slabs, which is covered in chapter 7 of Eurocode 4 (Ref. 4), is not treated in this handbook.

(2) Three types of concrete slab are often used in combination with composite beams. These three types are listed as follows :

- Solid slab : this is a slab with no internal voids or ribs openings, normally cast-in place using traditional wooden formwork (see Figure 11.3).

- Cornuosite slab : this is a slab which is cast-in-place using decking (cold-formed profiled steel sheeting) as permanent formwork to the concrete slab. When ribs of the decking have a re-entrant shape andor are provided with embossments that can transmit longitudinal forces between the decking and the concrete, the resulting slab acts as a composite slab in the direction of the decking ribs (see Figure 11.3 and Figure VII. 1).

- Precast concrete slab : this is a slab consisting of prefabricated concrete units and cast-in place concrete. There are two forms that may be used : thin precast concrete plate elements of approximately 50 mm thickness are used as a formwork for solid slabs or alternatively, deep precast concrete elements are used for longer spans with a thin layer of cast-in-place concrete as a wearing surface. Deep precast concrete units often have hollow cores which serve to reduce their dead weight (see Figure 11.3).

I ,

.

No further information is given on solid slabs or precast concrete slabs in this chapter VII. For those cases reference should be made respectively to Eurocode 2 (Ref. 2) and to Eurocode 4 (Ref. 4, chapter 8).

(3) In the design of composite slabs the following aspects have to be considered : :C4 [4.2.2] - The cross-sectional geometry of the slab : In some cases the full cross-sectional area of the

slab cannot be used for composite beam calculations. A reduced or “effective” cross- sectional area must be calculated. Formulae for determining effective slab widths are given in chapter V.2.1.

- The influence of the slab on the shear connection between the slab and the beam : stud behaviour and maximum strength may be modified due to the shape of the ribs in the slab (see chapter V.2.7.3). The correct placement of studs relative to ribs is of great importance (see chapter V.2.7.4).

- The quantity and placement of transverse reinforcement : transverse reinforcement is used to ensure that longitudinal shear failure or splitting of the concrete does not occur before failure of the composite beam itself (see chapter V.2.7.5).

3C4 [6.3.3]

324 [6.6]

‘ Previous page ’ is blank

207

[Ref. Chapter VII - Composite slabs or concrete slabs

a) Composite slab with reentrant deck Drofile

mesh I U U \ I

1 m

1 w

I\ I\ \

1 - 4 I I t” i

I I

of sheet embossments

b) Comwsite slab with trapezoidal deck Drofile. showing the main geometrical Darameters

Figure VII.l Typical composite slabs

208

1 Ref. Chapter VI1 - Composite slabs or concrete slabs I

VI13 Initial slab design

VII.2.1 Proportions of composite slab

Ref. 7 [5.2]

Ref. 7 [5.2.1](1) Typical composite slabs are shown in Figure W. 1. In general such slabs consist of : deckmg (cold formed profiled steel sheeting), concrete and light mesh reinforcement. There are many types of decking currently marketed in Europe. These can be, however, broadly classified into two groups :

- Re-entrant rib geometries. An example of such a profile is shown in Figure W. 1 a). Note that embossements are often placed on the top flange of the deck.

- Ouen or trauezoidal rib geometries. An example of such a profile is shown in Figures W. 1 b). Note that embossements are often placed on the webs of the deck.

(2) Composite slab depths range from 100 to 200 mm; 120 to 180 mm being the most common depending on the fire resistance requirements.

(3) Decking rib geometries may vary considerably in form, width and depth. Typical rib heights, hp are between 40 mm and 85 mm. Centre-line distances between ribs generally vary between 150 mm and 300 mm. Embossment shapes and sheet overlaps also vary between decking manufhcturers .

(4) In general, the sheet steel is hot-dipped galvanised with 0,02 mm of zinc coating on each side. The base material is cold-formed steel with thicknesses between 0,75 mm and 1,5 mm. The yield strength f& of the steel is in the range of 220 to 350 N/mm2.

(5) Deeper decks permit longer spans to be concreted without the need for propping. Ribs deeper than 85 mm, however, are not treated in this handbook. For such ribs composite action with the steel beam may be significantly reduced, thus requiring special attention.

VII.2.2 Construction condition

(1) Normally, decking is first used as a construction platform. This means that it supports construction operatives, their tools and other material commonly found on construction sites. Good construction practice requires that the decking sheets be attached to each other and to all permanent supports using screws or shot-fired nails.

(2) Next, the decking is used as formwork so that it supports the weight of the wet concrete, reinforcement and the concreting gang. The maximum span length of the decking without propping can be calculed according to the rules given in Part 1.3 or Annex A of Eurocode 3. Characteristic loads for the construction phase are intruduced in addition to the self weight of the slab (see chapter III).

(3) Typically, decking with a steel thickness of 1,2 mm, and a rib height hp of 60 mm, can span between 3 m and 3 3 m without propping.

VII.2.3 Composite action

Ref. 7 [5.2.2]

Ref. 7 [5.2.3] After the concrete has hardened, composite action is achieved by the combination of chemical bond and mechanical interlock between the steel decking and the concrete. The chemical bond is unreliable and is not taken into account in design. Composite slab design is generally based on information provided by the decking manufacturer, in the form of allowable imposed load tables. These values are determined from test results and their interpretation as required in Eurocode 4 (Ref. 4 : 10.3). In most catalogues the resistance to imposed load is given as a function of decking type and steel sheet thickness, slab thickness, span length and the number of temporary supports. Generally, these resistances are well in excess of the applied loads, indicating that composite action is satisfactory or that the design is controlled by other limitations. However, care should be taken to read the catalogue for any limitations or restrictions due to dynamic loads, and concentrated point and line loads.

209

I 1R.f. Chapter W - Composite slabs or concrete slabs

Maximum Span : Deph ratios Normal weight concrete Light weight concrete

VII.2.4 Deflections Ref. 7 [5.2.4] EC4 [7.6.2.2] (1) Deflection calculations in reinforced concrete are notoriously inaccurate, and therefore some

approximations are justified to obtain an estimate for the deflections of a composite slab. The stiffhess of a composite slab may be calculated from the cracked section properties of a reinforced concrete slab, by treating the cross-sectional area of declung as an equivalent reinforcing bar.

End span Internal span Single span

35 38 32 30 33 27

(2) However, if the maximum ratio of span length to slab depth @slab (= hp + h&u Figure VII. 1 b)) is within the limits of Table W . l no deflection check is needed. The end span should be considered as the general case for design. In this case it is assumed that minimum anticrack reinforcement exists at the supports. Experience shows that imposed load deflections do not exceed spd350 when using the span to depth ratios shown in Table W.1. More rehed deflection calculations will lead to greater span to depth ratios than those given in Table W. 1.

Table VII.l Maximum span to depth ratios of composite slabs (L / hslab)

VII.3 Influence of decking on the design of composite beams Ref. 7 [5.3]

(1) Profiled steel decking performs a number of important roles, and influences the design of the composite beam in a number of ways. It :

- may provide lateral restraint to the steel beams during constructions (see chapter V.2.5.2),

- causes a possible reduction in the design resistance of the shear connectors (see chapter V.2.7.3),

- may act under some conditions as transverse reinforcement leading to a reduction in the amount of bar reinforcement needed (see chapter V.2.7.5).

(2) The orientation of the sheeting is important. Decking ribs may be oriented in two ways with respect to the composite beam :

- decking ribs transverse to the steel beam. The decking may be discontinuous (see Figure VII.2 a)), or continuous (see Figure VII.2 b)) over the top flange of the beam ,

- decking ribs parallel to the steel beam (see Figure VII.2 c) and d)).

The shear connectors may be welded through the decking, or placed in holes formed in the troughs of the declung. In the latter case the shear connectors can also be welded to the steel beam off-site. When the through welding procedure is used on site, studs may not be welded through more than one sheet and overlapping of sheets is not permitted (see chapter V.2.7.4).

210

I Ref. Chapter VI1 - Composite slabs or concrete slabs I

I

a) discontinuous declang b) continuous declung @ Deckinp ribs transverse to the beam

c) 4 @ Deckinp ribs parallel to the beam

~

Figure VII.2 Orientation of profiled steel decking

VII.3.1 Ribs transverse to the beam Ref. 7 [5.3.1]

The concrete slab in the direction of the beam is not a homogeneous (solid) slab (see Figure VII.2 a) and b)). This has important consequences for the design of the composite beam, as only the depth of concrete over the ribs acts in compression (see chapter V.2.5.1). Additionally, there is often a significant influence on the resistance of the shear connectors due to the shape of the deck profile (see chapter V.2.7.3).

VII.3.2 Ribs parallel to the beam Ref. 7 [5.3.2]

In the construction phase, decking with this orientation is not considered effective in resisting lateral torsional buckling of the steel beam (see Figure MI.2, c) and d)),

In this case, the complete cross-section of the slab may be used in calculating the moment resistance of the beam (see chapter V.2.5.1). The orientation of the ribs also implies that there will be little reduction in the studs due to the ribs in the concrete slab (see chapter V.2.7.3).

211

IRef. Chapter VII - Composite slabs or concrete slabs 1

VII.4 Minimum transverse reinforcement Ref. 7 [5.5]

(1) Transverse reinforcement must be provided in the slab to ensure that longitudinal shearing failure or splitting does not occur before the failure of the composite beam itself (see chapter V.2.7.5).

(2) The steel decking is not allowed to participate as transverse reinforcement unless there is an effective means of transferring tension into the slab, such as by throughdeck welding of the shear connectors. Where the decking is continuous, the decking is effective in transferring tension and can act as transverse reinforcement. This is not necessarily the case if the ribs are parallel to the beam because of overlaps in the sheeting.

(3) Minimum amounts of transverse reinforcement are required. The reinforcement should be distributed uniformly. The minimum amount is 0,002 times the concrete section above the ribs.

2 12

STRUCTURAL STEEL RESEARCH REPORTS established by RPS DEPARTEMENT / ProfilARBED RECHERCHES

k d y J.C. ,Schleich J.B.; Elasto Plastic Behaviour of Steel Frames with Semi-Rigid Connections / NORDIC STEEL COLLOQUIUM on Research and Development within The Field of steel Construction; Odense, Denmark , 9-1 1 September 1991, RPS ReportN0101/91. Geardy J.C. , Schleich J.B.;Semi-Rigid Action in Steel Frames Structures / CEC agreement NO7210-SA / 507 ; Final Report EUR 14427 EN, Luxembourg 1992, RPS ReportNo102/91. Pbin R,Schleich J.B.; Seismic Resistance of Composite Structures, SRCS / CEC agreement N"7210-SA / 506 ; Final Report EUR 14428 EN, Luxembourg 1992, RPS Report N0103/91. Chantrain Ph.,Schleich J.B.; Interaction Diagrams between Axial Load N and Bending Moment M for Columns submitted to Bucklug / CEC agreement N"721oSA / 510 ; Final Report EUR 14546 EN, November 1991, RPS ReportN0104/91. Schaumann P., Steffen A.; Verbundbriicken auf Basis von Walztriigem, Versuch Nr. 1 Einstegiger Verbundmger / HRA, &hum, Juli 1990, HRA M c h t A 89199, RFS Report No105/90. Schaumann P., Steffen A.; Verbundbriicken auf Basis von Walztriigern, Versuch Nr. 2 Realistischer Verbundbrockenwger

Bruls A., Wang J.P. ; Composite Bridges with Hot Rolled Beams in High Strength Steel Fe E 460 , and Spans up to 50 m / Service Ponts et Charpentes, Universitk de Liege; Liege, November 1991,RF'S Report N0107/91. Schleich J.B., Witq A.; Acier HLE pour Ponts Mixtes a Portks Moyennes de 20 a 50 m / Journ6e S i h g i q u e ATS 1991; Paris, 4 et 5 decembre 1991, RPS ReportN0108/91. Schaumann P, Steffen A.; Verbundbriicken auf Basis von Walztriigern, Versuch Nr. 5 Hauptmgerstoss mit

Schaumann P, Schleich J.B., Kulka H., Tilmanns H.; Verbundbriicken unter Verwendung von Walztriigern / Zusammenstellung der V0-e anlhsslich des Seminars "Verbundbrtkkentag" am 12.09.90 an der Ruhruniversittit Bochum, RPS Report No 1 10192. Schaumann P., Steffen A.; Verbundbriicken auf Basis von Walztriigern, Versuche Nr. 3 U. 4 Haupth%gerstoss mit geschraubten Steglaschen / HRA, Bochum 1992, HRA Bericht 90232-B, Rps Report NO1 11/92. Schleich J.B., Witry A.; Neues Konzept filr einfache Verbundbriicken mit Spannweiten von 20 bis 50 m / E. Leipziger Metallhau-Kolloquiq Leipzig, 27. Mtin 1992, RPS Report NO1 12/92. Berg~nann R., Kindmatm R.; Auswertung der Versuche zum Tragverhalten von Verbundprofden mit ausbetonierten Kammern; Verbundstiitzen / Ruhruniversittit Bochum, Bericht N"9201, Februarl992, RPS Report NO1 13/92. Bergmann R., Kindmann R.; Auswertung der Versuche zum Tragverhalten von Verbundprofilen mit ausbetonierten Kammern; Verbundtriiger / Ruhruniversittit Bochum, Bericht NO9202, Matz 1992, RPS Report NO1 14/92. Mang F., Schleich J.B., Wippel H, Witry A.; Untersuchungen an stegparallel versteiften Rahmenknoten, ausgemhrt aus dicknanschien hochfesten Walzprofilen . Entwurf hochbelasteter Vierenklmger im Rahmen des Neubaus des Zentrums fb Kunst und Medientechnologie ( ZKM ), Karlsruhe / RPS Report NO1 15/92. Chantrain Ph., Becker A., Schleich J.B.; Behaviour of HISTAR hot-rolled profiles in the steel construction - Tests / RPS Report NO1 16/91. Bode H., Kilnzel R; Composite Beams of Fe E 460 Quality, Research report 2/90; University of Kaiserslautem, Mach 1990; RPS Report No 1 17/92. Bruls A., Wang J.P. ; Composite Bridges with Hot Rolled Beams in High Strength Steel Fe E 460, Fe E 600 up to 60 meters / Service Ponts et Charpentes, Universitk de Liege, Liege, August 1992, RPS Report NO1 18/92. Chantrain Ph., Geardy J.C., Schleich J.B. ; Elasto-Plastic Behaviour of Steel Frame Works / CEC agreement NO7210-SA/508 ; Final Report EUR 15627 EN , Luxembourg 1992, RPS Report No 1 19/92. Chantrain Ph., Schleich J.B.; Design Handbook for Braced or Non-Sway Steel Buildings according to Eurocode 3 / CEC agreement NO72 1 O-SNS 1 3 and No PHIN-94-002 1, ECCS Publication No 85; December 1996, RPS Report 120196. Chantrain Ph., Schleich J.B.; Simplified version of Eurocode 4 for usual buildmgs / CEC agreement N07210-SN516 ; Final Report EUR (to be published), April 1996, RPS Report 121/96. Chantrain Ph., Schleich J.B.; Improved classification of steel and composite cross-sections : New rules for local buckling in Eurocodes 3 and 4 / CEC agreement N"721oSN519/319/934; Final Report EUR (to be published), April 1996, RFS Report 122/96. Chantrain Ph., Schleich J.B.; Promotion of plastic design for steel and composite cross-dons : new required conditions in Eurocodes 3 and 4, practical tools for designers (Rotation capacities of profiles ...) / CEC agreement NO7210- SN520/321/935 ; Part I of the Final Report EUR (to be published) , July 1996, RPS Report 123196. Chantrain Ph., Schleich J.B.; Ductility of plastic binges in steel structures - Guide for plastic analysis ; Part II of the Final Report of the CEC agreement N"7210-SN520/321/935; July 1996, RPS Report 124/96. Schleich J.B., Conan Y., Quazmtti S., Dubois C.; L'acier dans le logement ; Rapport final ; Juillet 1998, RPS Report 12998. Conan Y.., Schleich J.B.; Design Handbook for Braced or Non-Sway Steel Buildings according to Eurocode 4 / July 1999, RPS Report 126/99. Chabrolin B..; Partial Safety Factors for Resistance of Steel Elements to EC3 and EC4 / CTICM, CEC agreement NO7210-SN322.422.936.123.521.124.838.622; Intermediate reports 94-97, RPS Report 127/99. Schleich J.B., Conan Y., Klosak M.; Modelling and Predesign of Steel and Composite Structures / CEC agreement NO7210-SN525.326.132; Intermediate reports 96-98, RPS Report 128/99.

/ HRA, &hum, November 1991, HRA Bericht A 89199-2, RPS Report No 106/91.

Stahlbetondl~erqUeltriQer / HRA, &hum, 1992, HRA Bericht A 90232-A, RPS Report N0109/92.

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