PP 1990:2010 Structural Eurocodes

Transcription

1 PP 1990:2010 Structural Eurocodes Extracts from the Structural Eurocodes for students of structural design Third Edition

2 First published in the UK in 2004 Second edition published in 2007 Third edition published in 2010 by BSI 389 Chiswick High Road London W4 4AL British Standards Institution 2004, 2007, 2010 All rights reserved. Except as permitted under the Copyright, Designs and Patents Act 1988, no part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, photocopying, recording or otherwise without prior permission in writing from the publisher. Whilst every care has been taken in developing and compiling this publication, BSI accepts no liability for any loss or damage caused, arising directly or indirectly in connection with reliance on its contents except to the extent that such liability may not be excluded in law. Whilst every effort has been made to trace all copyright holders, anyone claiming copyright should get in touch with the BSI at the above address. BSI has no responsibility for the persistence or accuracy of third-party websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. The right of the compilers to be identified as the authors of this work has been asserted by the compilers in accordance with sections 77 and 78 of The Copyright, Designs and Patents Act British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN Typeset in Verdana by Monolith Printed in Great Britain by Berforts Group,

3 Acknowledgments Compilers BSI thanks Professor Norman Bright and Professor John Roberts for overseeing the authoring of the first edition of this guide (2004), and Professor John Roberts for co-ordinating the update for the second edition (2007) and third edition (2010). Contributors Chapter 0 Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Professor Haig Gulvanessian (all editions) Professor Haig Gulvanessian (all editions) Anthony Threlfall (first edition); Professor Norman Bright (second edition) Owen Booker (third edition) Dr Mike Gardner (first and second editions) Professor Gerry Parke (third edition) Dr J B (Buick) Davidson (all editions) Christopher Mettem (first edition); Professor Norman Bright (second edition) Peter Watt (third edition) Professor John Roberts (all editions) Dr Andrew Bond and Andrew Harris (all editions) Costas Georgopoulos (all editions) Dr Anton Fried (all editions) iii

4

5 Contents Foreword Introduction Chapter 0 Extracts from Eurocode: Basis of structural design Chapter 1 Extracts from Eurocode 1: Actions on structures Chapter 2 Extracts from Eurocode 2: Design of concrete structures Chapter 3 Extracts from Eurocode 3: Design of steel structures Chapter 4 Extracts from Eurocode 4: Design of composite steel and concrete structures Chapter 5 Extracts from Eurocode 5: Design of timber structures Chapter 6 Extracts from Eurocode 6: Design of masonry structures Chapter 7 Extracts from Eurocode 7: Geotechnical design Chapter 8 Extracts from Eurocode 8: Design of structures for earthquake resistance Chapter 9 Extracts from Eurocode 9: Design of aluminium structures v

6

7 Foreword This Foreword has been adapted from the generic Foreword found in the Structural Eurocodes. Background to the Eurocode programme In 1975, the Commission of the European Community decided on an action programme in the field of construction, based on article 95 of the Treaty of Rome. The objective of the action programme was the elimination of technical obstacles to trade, and the harmonization of technical specifications. Within this action programme, the Commission took the initiative to establish a set of harmonized technical rules for the design of construction works that, in a first stage, would serve as an alternative to the national rules in force in the Member States and, ultimately, would replace them. In 1989, the Commission and the Member States of the EU (European Union) and EFTA (European Free Trade Association) decided, on the basis of an agreement between the Commission and CEN (Committee for European Standardization), to transfer the preparation and publication of the Eurocodes to CEN through a series of mandates, in order to provide them with a future status of European Standard (EN). This links de facto the Eurocodes with the provisions of all the Council s Directives and/or Commission s Decisions dealing with European standards (e.g. the Council Directive 89/106/EEC on construction products CPD and Council Directives 93/37/EEC, 92/50/EEC and 89/440/EEC on public works and services and equivalent EFTA Directives initiated in pursuit of setting up the internal market). The Structural Eurocode programme comprises the following European standards, each generally consisting of a number of parts: EN 1990, Eurocode 0: Basis of Structural Design EN 1991, Eurocode 1: Actions on structures EN 1992, Eurocode 2: Design of concrete structures EN 1993, Eurocode 3: Design of steel structures EN 1994, Eurocode 4: Design of composite steel and concrete structures EN 1995, Eurocode 5: Design of timber structures EN 1996, Eurocode 6: Design of masonry structures EN 1997, Eurocode 7: Geotechnical design EN 1998, Eurocode 8: Design of structures for earthquake resistance EN 1999, Eurocode 9: Design of aluminium structures Eurocode standards-drafting recognizes the responsibility of regulatory authorities in each Member State, and has safeguarded the right of each Member State to determine values related to regulatory safety matters at national level where these continue to vary. The Eurocodes contain nationally determined parameters in order that specific geographical, geological or climatic conditions as well as specific levels of protection applicable in different Member States may be taken into account. For each nationally determined parameter, the Eurocodes provide a recommended value (a default value). However, Member States may choose a different specific value as the nationally determined parameter, if they consider it necessary in order to ensure that building and civil engineering works are designed and executed in a way that does not endanger safety within that Member State. The values or selections chosen by a Member State are contained within a National Annex. Each Eurocode part has a corresponding National Annex for each state in which it is to be used. Status and field of application of Eurocodes The Member States of the EU and EFTA recognize that Eurocodes serve as reference documents for the following purposes: 1) as a means to prove compliance of building and civil engineering works with the essential requirements of Council Directive 89/106/EEC, particularly Essential Requirement N 1: Mechanical resistance and stability, and Essential Requirement N 2: Safety in case of fire; 2) as a basis for specifying contracts for construction works and related engineering services; vii

8 Extracts from the Structural Eurocodes for students of structural design 3) as a framework for drawing up harmonized technical specifications for construction products (ENs and ETAs (European Technical Agreements)). The Eurocode standards provide common structural design rules for everyday use for the design of whole structures and component products of both a traditional and an innovative nature. Unusual forms of construction or design conditions are not specifically covered and additional expert consideration will be required by the designer in such cases. National Standards implementing Eurocodes The National Standards implementing Eurocodes will comprise the full text of the Eurocode (including any annexes), as published by CEN, which may be preceded by a National title page and National foreword, and may be followed by a National Annex. The National Annex may only contain information on those parameters that are left open in the Eurocode for national choice, known as Nationally Determined Parameters, to be used for the design of buildings and civil engineering works to be constructed in the country concerned, i.e.: values and/or classes where alternatives are given in the Eurocode; values to be used where a symbol only is given in the Eurocode; country-specific data (geographical, climatic, etc.), e.g. snow map; the procedure to be used where alternative procedures are given in the Eurocode. It may also contain: decisions on the application of informative annexes; references to non-contradictory complementary information to assist the user to apply the Eurocode. The Eurocodes are European standards that provide a common series of methods for calculating the structural strength of elements used in construction. They enable the structural design of construction works and assessment of stability with a common basis of design, but with approaches that tend to be materials specific. They are supported by European product and test method standards. The disparities between the various calculation methods referred to in national building regulations may hinder the free circulation of engineering and architectural services within the Community. Eurocodes facilitate the freedom to provide services in the field of structural engineering and architecture by providing a harmonized system of general rules. In December 2003, the Eurocodes were formally recommended by the European Commission as a suitable tool for designing construction works, checking the mechanical resistance of components and checking the stability of structures. Member States of the European Community have been recommended to promote instruction in the use of the Eurocodes, especially within higher education and as part of continuous professional development courses for engineers and technicians. viii

9 Introduction This guide This guide contains extracts from some of the principal parts of each of the Eurocodes. It is intended to be a suitable teaching tool for lecturers of students of structural design, and to be suitable as guidance material for undergraduate design projects. The extracts chosen are as concise as possible, focussing on the essential principles in the Eurocodes. Commentary is kept to a minimum and only made on parts of the text that require explanation. The commentary in each chapter is shown as boxed text with a grey background, in order to distinguish it from the Eurocode extracts. This guide does not deal with fire design. Each chapter in this guide corresponds to a particular Eurocode, and has been numbered in accordance with that Eurocode e.g. chapter 1 contains extracts from Eurocode 1: Actions on structures. For consistency with the Eurocodes, EN 1990: Eurocode Basis of structural design, has been labelled as Eurocode (not Eurocode 0 ). In order to facilitate future amendments to this guide, the page numbers in each chapter reflect the chapter that they belong to e.g. the page numbers in chapter 0 are preceded by 0-, whilst the page numbers in chapter 6 are preceded by 6-. The guide is written for students at UK universities and for English-speaking universities worldwide. It is a stand alone publication. However, it is expected that the reader has access to the full published versions of the Eurocodes, either in hard copy in the university library, or electronically through, for example, the university s membership of BSI, that provides access to all published British Standards. Symbols and definitions are covered in each chapter of the guide in the same way they are dealt with in the individual chapter of the Eurocodes. This is because it is recognized that there are differences between each chapter. However, the following note is important: IMPORTANT NOTE: The distinction between Principles and Application Rules described in Clause 1.4 of the Eurocode for Basis of Design (Chapter 0) applies to all parts of the suite of Eurocodes. In the guide the extracts have been taken from the latest version of the Eurocode at the time of writing. The parts of the Eurocodes each have a corresponding National Annex for each Member State, which provides the Nationally Determined Parameters and various allowable choices, such as which Informative Annexes may be used in that Member State. National Annex content that is included in this guide is inserted at the corresponding points of the Eurocode to which the National Annex text refers. All National Annex content is labelled NA.x. ix

10 Extracts from the Structural Eurocodes for students of structural design Complete list of parts of the Eurocodes The following is a complete list of all parts of the Eurocodes. The parts included in this guide are indicated in bold. EN 1990:2002 Eurocode, Basis of structural design EN1991 Eurocode 1: Actions on structures EN :2002, General actions Densities, self-weight, imposed loads for buildings EN :2002, Actions on structures exposed to fire EN :2003, General actions Snow loads EN :2005, General actions Wind actions EN :2003, General actions Thermal actions EN :2005, General actions Actions during execution EN :2006, General actions Accidental actions EN1991-2:2003, Traffic loads on bridges EN1991-3:2006, Actions induced by cranes and machinery EN1991-4:2006, Silos and tanks EN 1992 Eurocode 2: Design of concrete structures EN :2004, General rules and rules for buildings EN :2004, General rules Structural fire design EN1992-2:2005, Concrete bridges Design and detailing EN1992-3:2006, Liquid retaining and containment structures PD :2008, Recommendations for the design of structures to BS EN :2005 EN 1993 Eurocode 3: Design of steel structures EN :2005, General rules and rules for buildings EN :2005, General rules Structural fire design EN :2006, General rules Supplementary rules for cold-formed members and sheeting EN :2006, General rules Supplementary rules for stainless steel EN :2006, Strength and stability of planar plated structures without transverse loading EN :2007, Strength and stability of shell structures EN :2007, Plated structures subject to out of plane loading EN :2005, Design of joints EN :2005, Fatigue EN :2005, Material toughness and through-thickness properties EN :2006, Design of structures with tension components EN :2007, Additional rules for the extension of EN 1993 up to steel grades S 700 EN1993-2:2006, Steel bridges EN :2006, Towers, masts and chimneys Towers and masts EN :2006, Towers, masts and chimneys Chimneys EN :2008, Execution of steel structures and aluminium structures Technical requirements for the execution of steel structures PD :2008, Recommendations for the design of bridges to BS EN 1993 EN :2007, Silos EN :2007, Tanks EN :2007, Pipelines EN1993-5:2007, Piling EN1993-6:2007, Crane supporting structures EN 1994 Eurocode 4: Design of composite steel and concrete structures EN :2004, General rules and rules for buildings EN :2005, General rules Structural fire design EN1994-2:2005, General rules and rules for bridges PD :2007, Background paper to BS EN and the UK National Annex to BS EN Eurocode 4 Design and composite steel and concrete structures General rules and rules for bridges x

11 EN 1995 Eurocode 5: Design of timber structures EN :2004, General Common rules and rules for buildings EN :2004, General Structural fire design EN1995-2:2004, Bridges Introduction EN 1996 Eurocode 6: Design of masonry structures EN :2005, General rules for reinforced and unreinforced masonry structures EN :2005, General rules Structural fire design EN1996-2:2006, Design considerations, selection of materials and execution of masonry EN :2006, Simplified calculation methods and simple rules for masonry structures EN 1997 Eurocode 7: Geotechnical design EN1997-1:2004, General rules EN1997-2:2007, Ground investigation and testing EN 1998 Eurocode 8: Design of structures for earthquake resistance EN1998-1:2004, General rules, seismic actions and rules for buildings EN1998-2:2005, Bridges EN1998-3:2005, Assessment and retrofitting of buildings EN1998-4:2006, Silos, tanks and pipelines EN1998-5:2004, Foundations, retaining structures and geotechnical aspects EN1998-6:2005, Towers, masts and chimneys EN 1999 Eurocode 9: Design of aluminium structures EN :2007, General structural rules EN :2007, Structural fire design EN :2007, Structures susceptible to fatigue EN :2007, Cold-formed structural sheeting EN :2007, Shell structures EN :2008, Execution of steel structures and aluminium structures Technical requirements for aluminium structures xi

12

13 Chapter 4 Extracts from Eurocode 4: Design of composite steel and concrete structures The Eurocode extracts in this chapter are taken from EN :2004 (incorporating corrigendum April 2009), Eurocode 4: Design of composite steel and concrete structures Part 1-1 General rules and rules for buildings. Text altered by CEN corrigendum April 2009 is indicated in the text by ˆ. A useful additional reference is: Designers guide to EN : Eurocode 4: Design of composite steel and concrete structures, Part 1.1 : General rules and rules for buildings [1]. The National Annex extracts are taken from NA to BS EN :2004 UK National Annex to Eurocode 4: Design of composite steel and concrete structures Part 1-1: General rules and rules for buildings. The full list of the contents of EN follows, and is given for reference purposes. (Bold items are covered in this chapter.) Foreword Section 1 General 1.1 Scope Scope of Eurocode Scope of Part 1.1 of Eurocode Normative references General reference standards Other reference standards 1.3 Assumptions 1.4 Distinction between principles and application rules 1.5 Definitions General Additional terms and definitions used in this Standard 1.6 Symbols Section 2 Basis of design 2.1 Requirements 2.2 Principles of limit state design 2.3 Basic variables Actions and environmental influences Material and product properties Classification of actions 2.4 Verification by the partial factor method Design values Design values of actions Design values of material or product properties Design values of geometrical data Design resistances Combination of actions Verification of static equilibrium (EQU) Section 3 Materials 3.1 Concrete 3.2 Reinforcing steel 3.3 Structural steel 3.4 Connecting devices General Headed stud shear connectors 3.5 Profiled steel sheeting for composite slabs in buildings Section 4 Durability 4.1 General 4.2 Profiled steel sheeting for composite slabs in buildings 4-1

14 Guide to the Structural Eurocodes for students of structural design Section 5 Structural analysis 5.1 Structural modelling for analysis Structural modelling and basic assumptions Joint modelling Ground-structure interaction 5.2 Structural stability Effects of deformed geometry of the structure Methods of analysis for buildings 5.3 Imperfections Basis Imperfections in buildings General Global imperfections Member imperfections 5.4 Calculation of action effects Methods of global analysis General Effective width of flanges for shear lag Linear elastic analysis General Creep and shrinkage Effects of cracking of concrete Stages and sequence of construction Temperature effects Pre-stressing by controlled imposed deformations Non-linear global analysis Linear elastic analysis with limited redistribution for buildings Rigid plastic global analysis for buildings 5.5 Classification of cross-sections General Classification of composite sections without concrete encasement Classification of composite sections for buildings with concrete encasement Section 6 Ultimate limit states 6.1 Beams Beams for buildings Effective width for verification of cross-sections 6.2 Resistances of cross-sections of beams Bending resistance General Plastic resistance moment M pl,rd of a composite crosssection Plastic resistance moment of sections with partial shear connection in buildings Non-linear resistance to bending Elastic resistance to bending Resistance to vertical shear Scope Plastic resistance to vertical shear Shear buckling resistance Bending and vertical shear 6.3 Resistance of cross-sections of beams for buildings with partial encasement Scope Bending resistance Resistance to vertical shear Bending and vertical shear 6.4 Lateral-torsional buckling of composite beams General Verification of lateral-torsional buckling of continuous composite beams with cross-sections in Class 1, 2 and 3 for buildings Simplified verification for buildings without direct calculation 4-2

15 Extracts from Eurocode 4: Design of composite steel and concrete structures 6.5 Transverse forces on webs General Flange-induced buckling of webs 6.6 Shear connection General Basis of design Limitation on the use of partial shear connection in beams for buildings Spacing of shear connectors in beams for buildings Longitudinal shear force in beams for buildings Beams in which non-linear or elastic theory is used for resistances of one or more cross-sections Beams in which plastic theory is used for resistance of cross-sections Headed stud connectors in solid slabs and concrete encasement Design resistance Influence of tension on shear resistance Design resistance of headed studs used with profiled steel sheeting in buildings Sheeting with ribs parallel to the supporting beams Sheeting with ribs transverse to the supporting beams Biaxial loading of shear connectors Detailing of the shear connection and influence of execution Resistance to separation Cover and concreting Local reinforcement in the slab Haunches other than formed by profiled steel sheeting Spacing of connectors Dimensions of the steel flange Headed stud connectors Headed studs used with profiled steel sheeting in buildings Longitudinal shear in concrete slabs General Design resistance to longitudinal shear Minimum transverse reinforcement Longitudinal shear and transverse reinforcement in beams for buildings 6.7 Composite columns and composite compression members General General method of design Simplified method of design General and scope Resistance of cross-sections Effective flexural stiffness, steel contribution ratio and relative slenderness Methods of analysis and member imperfections Resistance of members in axial compression Resistance of members in combined compression and uniaxial bending Combined compression and biaxial bending Shear connection and load introduction General Load introduction Longitudinal shear outside the areas of load introduction Detailing Provisions Concrete cover of steel profiles and reinforcement Longitudinal and transverse reinforcement 6.8 Fatigue General Partial factors for fatigue assessment 4-3

16 Guide to the Structural Eurocodes for students of structural design Fatigue strength Internal forces and fatigue loadings Stresses General Concrete Structural steel Reinforcement Shear connection Stress ranges Structural steel and reinforcement Shear connection Fatigue assessment based on nominal stress ranges Structural steel, reinforcement and concrete Shear connection Section 7 Serviceability limit states 7.1 General 7.2 Stresses General Stress limitation for buildings 7.3 Deformations in buildings Deflections Vibration 7.4 Cracking of concrete General Minimum reinforcement Control of cracking due to direct loading Section 8 Composite joints in frames for buildings 8.1 Scope 8.2 Analysis, modelling and classification General Elastic global analysis Classification of joints 8.3 Design methods Basis and scope Resistance Rotational stiffness Rotation capacity 8.4 Resistance of components Scope Basic joint components Longitudinal steel reinforcement in tension Steel contact plate in compression Column web in transverse compression Reinforced components Column web panel in shear Column web in compression Section 9 Composite slabs with profiled steel sheeting for buildings 9.1 General Scope Definitions Types of shear connection 9.2 Detailing provisions Slab thickness and reinforcement Aggregate Bearing requirements 9.3 Actions and action effects Design situations Actions for profiled steel sheeting as shuttering Actions for composite slab 4-4

17 Extracts from Eurocode 4: Design of composite steel and concrete structures 9.4 Analysis for internal forces and moments Profiled steel sheeting as shuttering Analysis of composite slab Effective width of composite slab for concentrated point and line loads 9.5 Verification of profiled steel sheeting as shuttering for ultimate limit states 9.6 Verification of profiled steel sheeting as shuttering for serviceability limit states 9.7 Verification of composite slabs for ultimate limit states Design criterion Flexure Longitudinal shear for slabs without end anchorage Longitudinal shear for slabs with end anchorage Vertical shear Punching shear 9.8 Verification of composite slabs for serviceability limit states Cracking of concrete Deflection Annex A (Informative) Stiffness of joint components in buildings A.1 Scope A.2 Stiffness coefficients A.2.1 Basic joint components A Longitudinal steel reinforcement in tension A Steel contact plate in compression A.2.2 Other components in composite joints A Column web panel in shear A Column web in transverse compression A.2.3 Reinforced components A Column web panel in shear A Column web in transverse compression A.3 Deformation of the shear connection Annex B (Informative) Standard tests B.1 General B.2 Tests on shear connectors B.2.1 General B.2.2 Testing arrangements B.2.3 Preparation of specimens B.2.4 Testing procedure B.2.5 Test evaluation B.3 Testing of composite floor slabs B.3.1 General B.3.2 Testing arrangement B.3.3 Preparation of specimens B.3.4 Test loading procedure B.3.5 Determination of design values for m and k B.3.6 Determination of the design values for s ud Annex C (Informative) Shrinkage of concrete for composite structures for buildings Bibliography 4-5

18 Guide to the Structural Eurocodes for students of structural design Foreword National Annex for EN This standard gives values with notes indicating where national choices may have to be made. Therefore the National Standard implementing EN has a National Annex containing all Nationally Determined Parameters to be used for the design of buildings and civil engineering works to be constructed in the relevant country. Section 1 General 1.1 Scope Scope of Eurocode 4 (1) Eurocode 4 applies to the design of composite structures and members for buildings and civil engineering works. It complies with the principles and requirements for the safety and serviceability of structures, the basis of their design and verification that are given in EN 1990 Basis of structural design. (2) Eurocode 4 is concerned only with requirements for resistance, serviceability, durability and fire resistance of composite structures. Other requirements, e.g. concerning thermal or sound insulation, are not considered. (3) Eurocode 4 is intended to be used in conjunction with: EN 1990 Basis of structural design EN 1991 Actions on structures ENs, hens, ETAGs and ETAs for construction products relevant for composite structures EN 1090 Execution of steel structures Technical requirements EN Execution of concrete structures EN 1992 Design of concrete structures EN 1993 Design of steel structures EN 1997 Geotechnical design EN 1998 Design of structures for earthquake resistance, when composite structures are built in seismic regions. (4) Eurocode 4 is subdivided in various parts: Part 1-1: General rules and rules for buildings Part 1-2: Structural fire design Part 2: Bridges. In 1.1.1(4), the bold text indicates the parts of Eurocode 4 that are covered in this chapter Scope of Part 1-1 of Eurocode 4 (1) Part 1-1 of Eurocode 4 gives a general basis for the design of composite structures together with specific rules for buildings. (2) The following subjects are dealt with in Part 1-1: Section 1: General Section 2: Basis of design Section 3: Materials Section 4: Durability Section 5: Structural analysis Section 6: Ultimate limit states 4-6

19 Extracts from Eurocode 4: Design of composite steel and concrete structures Section 7: Serviceability limit states Section 8: Composite joints in frames for buildings Section 9: Composite slabs with profiled steel sheeting for buildings Scope of Part 1-2 of Eurocode 4 This part deals with the design of composite structures for the accidental situation of fire exposure and identifies differences from, or supplements to, normal temperature design. Scope of Part 2 of Eurocode 4 This part gives the basic rules for the design of composite construction for bridges. 1.5 Definitions Additional terms and definitions used in this standard composite 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 shear connection an interconnection between the concrete and steel components of a composite member that has sufficient strength and stiffness to enable the two components to be designed as parts of a single structural member composite slab a slab in which profiled steel sheets are used initially as permanent shuttering and subsequently combine structurally with the hardened concrete and act as tensile reinforcement in the finished floor propped structure or member a structure or member where the weight of concrete elements is applied to the steel elements which are supported in the span, or is carried independently until the concrete elements are able to resist stresses un-propped structure or member a structure or member in which the weight of concrete elements is applied to steel elements which are unsupported in the span un-cracked flexural stiffness the stiffness E a I 1 of a cross-section of a composite member where I 1 is the second moment of area of the effective equivalent steel section calculated assuming that concrete in tension is un-cracked cracked flexural stiffness the stiffness E a I 2 of a cross-section of a composite member where I 2 is the second moment of area of the effective equivalent steel section calculated neglecting concrete in tension but including reinforcement 4-7

20 Guide to the Structural Eurocodes for students of structural design 1.6 Symbols For the purpose of this Standard the following symbols apply. Latin upper case letters A Cross-sectional area of the effective composite section neglecting concrete in tension A a Cross-sectional area of the structural steel section A b Cross-sectional area of bottom transverse reinforcement A bh Cross-sectional area of bottom transverse reinforcement in a haunch A c Cross-sectional area of concrete A ct Cross-sectional area of the tensile zone of the concrete A p Cross-sectional area of profiled steel sheeting A pe Effective cross-sectional area of profiled steel sheeting A s Cross-sectional area of reinforcement A sf Cross-sectional area of transverse reinforcement A t Cross-sectional area of top transverse reinforcement E a Modulus of elasticity of structural steel E c,eff Effective modulus of elasticity for concrete E cm Secant modulus of elasticity of concrete E s Design value of modulus of elasticity of reinforcing steel F, Design longitudinal force per stud F t Design transverse force per stud I Second moment of area of the effective composite section neglecting concrete in tension I a Second moment of area of the structural steel section I c Second moment of area of the un-cracked concrete section I 1 Second moment of area of the effective equivalent steel section assuming that the concrete in tension is un-cracked I 2 Second moment of area of the effective equivalent steel section neglecting concrete in tension but including reinforcement L Length; span; effective span L e Equivalent span L i Span L s Shear span M Bending moment M a Contribution of the structural steel section to the design plastic resistance moment of the composite section M el,rd Design value of the elastic resistance moment of the composite section M pa Design value of the plastic resistance moment of the effective cross-section of the profiled steel sheeting M pl,a,rd Design value of the plastic resistance moment of the structural steel section M pl,rd Design value of the plastic resistance moment of the composite section with full shear connection M pr Reduced plastic resistance moment of the profiled steel sheeting M Rd Design value of the resistance moment of a composite section or joint M Rk Characteristic value of the resistance moment of a composite section or joint N Compressive normal force; number of stress range cycles; number of shear connectors N a Design value of the normal force in the structural steel section N c Design value of the compressive normal force in the concrete flange N c,f Design value of the compressive normal force in the concrete flange with full shear connection N c,el Compressive normal force in the concrete flange corresponding to M el,rd N pl,a Design value of the plastic resistance of the structural steel section to normal force N s Design value of the plastic resistance of the steel reinforcement to normal force N sd Design value of the plastic resistance of the reinforcing steel to tensile normal force P,,Rd Design value of the shear resistance of a single stud connector corresponding to F, P pb,rd Design value of the bearing resistance of a stud P Rd Design value of the shear resistance of a single connector P Rk Characteristic value of the shear resistance of a single connector P t,rd Design value of the shear resistance of a single stud connector corresponding to F t Design value of the shear force acting on the structural steel section V a,ed 4-8

21 V b,rd V Ed V ld V l,rd V pl,rd V pl,a,rd V Rd V v,rd Extracts from Eurocode 4: Design of composite steel and concrete structures Design value of the shear buckling resistance of a steel web Design value of the shear force acting on the composite section Design value of the resistance of the end anchorage Design value of the resistance to shear Design value of the plastic resistance of the composite section to vertical shear Design value of the plastic resistance of the structural steel section to vertical shear Design value of the resistance of the composite section to vertical shear Design value of the resistance of a composite slab to vertical shear Latin lower case letters a b b b b eff b eff,1 b eff,2 b ei b em b f b i b r b s b 0 c d d do d p d s e e p e s f cd f ck f ct,eff f ctm f ct,0 f lctm f sd f sk f u f y f yd f yp,d h h a h c h f h n h p h s Spacing between parallel beams; diameter or width; distance Width of the flange of a steel section; width of slab Width of the bottom of the concrete rib Total effective width Effective width at mid-span for a span supported at both ends Effective width at an internal support Effective width of the concrete flange on each side of the web Effective width of a composite slab Width of the flange of a steel section Geometric width of the concrete flange on each side of the web Width of rib of profiled steel sheeting Distance between centres of adjacent ribs of profiled steel sheeting Distance between the centres of the outstand shear connectors; mean width of a concrete rib (minimum width for re-entrant sheeting profiles); width of haunch Width of the outstand of a steel flange; effective perimeter of reinforcing bar Clear depth of the web of the structural steel section; diameter of the shank of a stud connector; overall diameter of circular hollow steel section; minimum transverse dimension of a column Diameter of the weld collar to a stud connector Distance between the centroidal axis of the profiled steel sheeting and the extreme fibre of the composite slab in compression Distance between the steel reinforcement in tension to the extreme fibre of the composite slab in compression; distance between the longitudinal reinforcement in tension and the centroid of the beam s steel section Eccentricity of loading; distance from the centroidal axis of profiled steel sheeting to the extreme fibre of the composite slab in tension Distance from the plastic neutral axis of profiled steel sheeting to the extreme fibre of the composite slab in tension Distance from the steel reinforcement in tension to the extreme fibre of the composite slab in tension Design value of the cylinder compressive strength of concrete Characteristic value of the cylinder compressive strength of concrete at 28 days Mean value of the effective tensile strength of the concrete Mean value of the axial tensile strength of concrete Reference strength for concrete in tension Mean value of the axial tensile strength of lightweight concrete Design value of the yield strength of reinforcing steel Characteristic value of the yield strength of reinforcing steel Specified ultimate tensile strength Nominal value of the yield strength of structural steel Design value of the yield strength of structural steel Design value of the yield strength of profiled steel sheeting Overall depth; thickness Depth of the structural steel section Depth of the concrete encasement to a steel section; thickness of the concrete flange; thickness of concrete above the main flat surface of the top of the ribs of the sheeting Thickness of concrete flange; thickness of finishes Position of neutral axis Overall depth of the profiled steel sheeting excluding embossments Depth between the centroids of the flanges of the structural steel section; distance between the longitudinal reinforcement in tension and the centre of compression 4-9

22 Guide to the Structural Eurocodes for students of structural design h sc Overall nominal height of a stud connector k Amplification factor for second-order effects; coefficient; empirical factor for design shear resistance k c Coefficient k, Reduction factor for resistance of a headed stud used with profiled steel sheeting parallel to the beam k s Rotational stiffness; coefficient k t Reduction factor for resistance of a headed stud used with profiled steel sheeting transverse to the beam k z Parameter l Length of the beam in hogging bending adjacent to the joint m Slope of fatigue strength curve; empirical factor for design shear resistance n Modular ratio; number of shear connectors n f Number of connectors for full shear connection n L Modular ratio depending on the type of loading n r Number of stud connectors in one rib n 0 Modular ratio for short-term loading s Longitudinal spacing centre-to-centre of the stud shear connectors; slip s t Transverse spacing centre-to-centre of the stud shear connectors t Age; thickness t f Thickness of a flange of the structural steel section t w Thickness of the web of the structural steel section t 0 Age at loading v Ed Design longitudinal shear stress x pl Distance between the plastic neutral axis and the extreme fibre of the concrete slab in compression y Cross-section axis parallel to the flanges z Cross-section axis perpendicular to the flanges; lever arm Vertical distance z 0 Greek upper case letters Dr Dr c Dr E Dr E,glob Dr E,loc Dr E,2 Dr s Dr s,equ Ds Ds c Ds E Ds E,2 Ds R W Stress range Reference value of the fatigue strength at 2 million cycles Equivalent constant amplitude stress range Equivalent constant amplitude stress range due to global effects Equivalent constant amplitude stress range due to local effects Equivalent constant amplitude stress range related to 2 million cycles Increase of stress in steel reinforcement due to tension stiffening of concrete Damage equivalent stress range Range of shear stress for fatigue loading Reference value of the fatigue strength at 2 million cycles Equivalent constant amplitude stress range Equivalent constant amplitude range of shear stress related to 2 million cycles Fatigue shear strength Coefficient Greek lower case letters a a cr a M a M,y, a Mz a st b b c, b i c C c F c Ff Factor; parameter Factor by which the design loads would have to be increased to cause elastic instability Coefficient related to bending of a composite column Coefficient related to bending of a composite column about the y-y axis and the z-z axis respectively Ratio Factor; transformation parameter Parameters Partial factor for concrete Partial factor for actions, also accounting for model uncertainties and dimensional variations Partial factor for equivalent constant amplitude stress range 4-10

23 Extracts from Eurocode 4: Design of composite steel and concrete structures c M Partial factor for a material property, also accounting for model uncertainties and dimensional variations c M0 Partial factor for structural steel applied to resistance of cross-sections, see EN , 6.1(1) c M1 Partial factor for structural steel applied to resistance of members to instability assessed by member checks, see EN , 6.1(1) c Mf Partial factor for fatigue strength c Mf,s Partial factor for fatigue strength of studs in shear c P Partial factor for pre-stressing action c S Partial factor for reinforcing steel c V Partial factor for design shear resistance of a headed stud c VS Partial factor for design shear resistance of a composite slab d Factor; steel contribution ratio; central deflection d max Sagging vertical deflection d s Deflection of steel sheeting under its own weight plus the weight of wet concrete d s,max Limiting value of d s d u Maximum slip measured in a test at the characteristic load level d uk Characteristic value of slip capacity e 235 / fy, where f y is in N/mm 2 g Degree of shear connection; coefficient g a, g ao Factors related to the confinement of concrete g c, g co, g cl Factors related to the confinement of concrete h Angle k, k v Damage equivalent factors k glob, k ldz Damage equivalent factors for global effects and local effects, respectively λ Relative slenderness λ LT Relative slenderness for lateral-torsional buckling l Coefficient of friction; nominal factor l d Factor related to design for compression and uniaxial bending l dy, l dz Factor l d related to plane of bending m Reduction factor to allow for the effect of longitudinal compression on resistance in shear; parameter related to deformation of the shear connection m a Poisson s ratio for structural steel n Parameter related to deformation of the shear connection q Parameter related to reduced design bending resistance accounting for vertical shear q s Parameter; reinforcement ratio r com,c,ed Longitudinal compressive stress in the encasement due to the design normal force r c,rd Local design strength of concrete r ct Extreme fibre tensile stress in the concrete r max,f Maximum stress due to fatigue loading r min,f Minimum stress due to fatigue loading r s,max,f Stress in the reinforcement due to the bending moment M Ed,max,f r s,min,f Stress in the reinforcement due to the bending moment M Ed,min,f r s Stress in the tension reinforcement r s,max Stress in the reinforcement due to the bending moment M max r s,max,0 Stress in the reinforcement due to the bending moment M max, neglecting concrete in tension r s,0 Stress in the tension reinforcement neglecting tension stiffening of concrete s Rd Design shear strength s u Value of longitudinal shear strength of a composite slab determined from testing s u,rd Design value of longitudinal shear strength of composite slab s u,rk Characteristic value of longitudinal shear strength of a composite slab z Diameter (size) of a steel reinforcing bar; damage equivalent impact factor z* Diameter (size) of a steel reinforcing bar u t Creep coefficient u (t,t 0 ) Creep coefficient, defining creep between times t and t 0, related to elastic deformation at 28 days v Reduction factor for flexural buckling v LT Reduction factor for lateral-torsional buckling Creep multiplier w L 4-11

24 Guide to the Structural Eurocodes for students of structural design Section 2 Basis of design 2.1 Requirements (1)P The design of composite structures shall be in accordance with the general rules given in EN (2)P The supplementary provisions for composite structures given in this Section shall also be applied. 2.2 Principles of limit states design (1)P For composite structures, relevant stages in the sequence of construction shall be considered. The influence of the method of construction propped or un-propped should be carefully considered. In un-propped construction, the bare steel beam (or metal deck in the case of an un-propped composite slab) is required to safely carry the wet concrete and temporary actions arising during construction. See also Basic variables Actions and environmental influences (1) Actions to be used in design may be obtained from the relevant parts of EN (2)P In verification for steel sheeting as shuttering, account shall be taken of the ponding effect (increased depth of concrete due to the deflection of the sheeting). For further guidance on when ponding should be considered and how this may be done, see Material and product properties (1) Unless otherwise given by Eurocode 4, actions caused by time-dependent behaviour of concrete should be obtained from EN Classification of actions (1)P The effects of shrinkage and creep of concrete and non-uniform changes of temperature result in internal forces in cross-sections, and curvatures and longitudinal strains in members; the effects that occur in statically determinate structures, and in statically indeterminate structures when compatibility of the deformations is not considered, shall be classified as primary effects. (2)P In statically indeterminate structures the primary effects of shrinkage, creep and temperature are associated with additional action effects, such that the total effects are compatible; these shall be classified as secondary effects and shall be considered as indirect actions. For buildings the effects of shrinkage may sometimes be ignored see 3.1(4) and 7.3.1(8). 2.4 Verification by the partial factor method Design values of material or product properties (2)P For concrete, a partial factor c C shall be applied. The design compressive strength shall be given by: f = f / c (2.1) cd ck C 4-12

25 Extracts from Eurocode 4: Design of composite steel and concrete structures where the characteristic value f ck shall be obtained by reference to EN , 3.1 for normal concrete and to EN , 11.3 for lightweight concrete. NOTE The value for c C is that used in EN (3)P For steel reinforcement, a partial factor c S shall be applied. NOTE The value for c S is that used in EN (4)P For structural steel, steel sheeting and steel connecting devices, partial factors c M shall be applied. Unless otherwise stated, the partial factor for structural steel shall be taken as c M0. NOTE Values for c M are those given in EN (5)P For shear connection, a partial factor c V shall be applied. NOTE The value for c V may be given in the National Annex. The recommended value for c v is 1,25. The National Annex refers to c V in NA.2.3. NA 2.3 Clause (5) Partial factor, c V The value of c v may vary depending on the form of slab, geometry of decking, and the size and layout of shear studs. Use the recommended value unless shear stud resistances given in non-contradictory complementary information (see NA.4) would justify the use of an alternative value. NA.4 refers the reader to the website for non-contradictory complementary information. The number of studs in a trough, type of decking and other details (e.g. the position of reinforcing mesh) may have a considerable effect on shear stud resistances and the designer should check that the resistance used in calculations is appropriate for the as-built condition. For scheme design, a value of c v of 1,25 is reasonable but the guidance provided in non-contradictory complementary information should be consulted for the final design. (6)P For longitudinal shear in composite slabs, a partial factor c VS shall be applied. NOTE The value for c VS may be given in the National Annex. The recommended value for c VS is 1,25. The National Annex refers to c VS in NA.2.4. NA 2.4 Clause (6) Partial factor, c VS Use the recommended value Design resistances (1)P For composite structures, design resistances shall be determined in accordance with EN 1990, expression (6.6a) or expression (6.6c) Combination of actions (1) The general formats for combinations of actions are given in EN 1990, Section 6. NOTE For buildings, the combination rules may be given in the National Annex to Annex A of EN