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Reinforced concrete design to Eurocode 2 Other bestselling titles from Palgrave Macmillan Reinforced Concrete Design to Eurocode 2 seventh edition Bill Mosley Formerly Senior Teaching Fellow, Nanyang Technological Institute, Singapore John Bungey Emeritus Professor of Civil Engineering, University ...

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Reinforced concrete design to Eurocode 2

Other bestselling titles from Palgrave Macmillan

Reinforced Concrete Design to Eurocode 2 seventh edition

Bill Mosley Formerly Senior Teaching Fellow, Nanyang Technological Institute, Singapore

John Bungey Emeritus Professor of Civil Engineering, University of Liverpool, UK

Ray Hulse Formerly Associate Dean, Faculty of Engineering and Computing, Coventry University, UK

# W. H. Mosley and J. H. Bungey 1976, 1982, 1987, 1990 # W. H. Mosley, J. H. Bungey and R. Hulse 1999, 2007, 2012 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No portion of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, Saffron House, 6-10 Kirby Street, London EC1N 8TS. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages. The authors have asserted their rights to be identified as the authors of this work in accordance with the Copyright, Designs and Patents Act 1988. First published 2012 by PALGRAVE MACMILLAN Palgrave Macmillan in the UK is an imprint of Macmillan Publishers Limited, registered in England, company number 785998, of Houndmills, Basingstoke, Hampshire RG21 6XS. Palgrave Macmillan in the US is a division of St Martin’s Press LLC, 175 Fifth Avenue, New York, NY 10010. Palgrave Macmillan is the global academic imprint of the above companies and has companies and representatives throughout the world. Palgrave1 and Macmillan1 are registered trademarks in the United States, United Kingdom, Europe and other countries ISBN-13: 978–0–230–30285–3 paperback This book is printed on paper suitable for recycling and made from fully managed and sustained forest sources. Logging, pulping and manufacturing processes are expected to conform to the environmental regulations of the country of origin. A catalogue record for this book is available from the British Library. A catalog record for this book is available from the Library of Congress. 10 21

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Printed in China

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Dedicated to all our families for their encouragement and patience whilst writing this text

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Contents Preface Acknowledgements Notation

1 Introduction to design and properties of reinforced concrete 1.1 1.2 1.3 1.4 1.5 1.6 1.7

Design processes Composite action Stress–strain relations Shrinkage and thermal movement Creep Durability Specification of materials

2 Limit state design 2.1 2.2 2.3 2.4 2.5

Limit states Characteristic material strengths and characteristic loads Partial factors of safety Combination of actions Global factor of safety

3 Analysis of the structure at the ultimate limit state 3.1 3.2 3.3 3.4 3.5 3.6

Actions Load combinations and patterns Analysis of beams Analysis of frames Shear wall structures resisting horizontal loads Redistribution of moments

4 Analysis of the section 4.1 4.2 4.3 4.4

Stress–strain relations Distribution of strains and stresses across a section in bending Bending and the equivalent rectangular stress block Singly reinforced rectangular section in bending at the ultimate limit state

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1 2 6 8 11 15 16 16 20 21 22 23 28 32 33 34 35 36 43 53 58 63 64 65 67 68

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Contents

4.5

Rectangular section with compression reinforcement at the ultimate limit state 4.6 Flanged section in bending at the ultimate limit state 4.7 Moment redistribution and the design equations 4.8 Bending plus axial load at the ultimate limit state 4.9 Rectangular–parabolic stress block 4.10 Triangular stress block

5 Shear, bond and torsion 5.1 5.2 5.3 5.4

Shear Anchorage bond Laps in reinforcement Analysis of section subject to torsional moments

6 Serviceability, durability and stability requirements 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8

Detailing requirements Span–effective depth ratios Calculation of deflection Flexural cracking Thermal and shrinkage cracking Other serviceability requirements Limitation of damage caused by accidental loads Design and detailing for seismic forces

7 Design of reinforced concrete beams 7.1 7.2

Preliminary analysis and member sizing Design for bending of a rectangular section with no moment redistribution 7.3 Design for bending of a rectangular section with moment redistribution 7.4 Flanged beams 7.5 One-span beams 7.6 Design for shear 7.7 Continuous beams 7.8 Cantilever beams, corbels and deep beams 7.9 Curtailment and anchorage of reinforcing bars 7.10 Design for torsion 7.11 Serviceability and durability requirements

8 Design of reinforced concrete slabs 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9

Shear in slabs Span–effective depth ratios Reinforcement details Solid slabs spanning in one direction Solid slabs spanning in two directions Flat slab floors Ribbed and hollow block floors Stair slabs Yield line and strip methods

72 77 84 88 96 98 104 105 117 121 123 129 130 140 142 154 159 163 166 171 176 178 180 185 189 193 194 198 204 210 212 216 217 218 224 225 226 231 236 244 250 253

Contents

9 Column design 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8

Loading and moments Column classification and failure modes Reinforcement details Short columns resisting moments and axial forces Non-rectangular sections Biaxial bending of short columns Design of slender columns Walls

10 Foundations and retaining walls 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8

Pad footings Combined footings Strap footings Strip footings Raft foundations Piled foundations Design of pile caps Retaining walls

11 Prestressed concrete 11.1 11.2 11.3 11.4 11.5

Principles of prestressing Methods of prestressing Analysis of concrete section under working loads Design for the serviceability limit state Analysis and design at the ultimate limit state

12 Water-retaining structures 12.1 12.2 12.3 12.4 12.5

Scope and principles Joints in water-retaining structures Reinforcement details Basements and underground tanks Design methods

13 Composite construction 13.1 13.2 13.3 13.4 13.5 13.6

The design procedure Design of the steel beam for conditions during construction The composite section at the ultimate limit state Design of shear connectors Transverse reinforcement in the concrete flange Deflection checks at the serviceability limit state

Appendix Further reading Index

261 262 263 267 269 279 282 285 289 292 296 303 307 308 311 312 316 320 331 333 334 336 341 365 381 382 385 388 389 390 407 410 411 414 419 423 426 431 442 444

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Preface

The purpose of this book is to provide a straightforward introduction to the principles and methods of design for concrete structures. It is directed primarily at students and young engineers who require an understanding of the basic theory and a concise guide to design procedures. Although the detailed design methods are generally according to European Standards (Eurocodes), much of the theory and practice is of a fundamental nature and should, therefore, be useful to engineers in countries outside Europe. The search for harmonisation of Technical Standards across the European Community (EC) has led to the development of a series of these Structural Eurocodes which are the technical documents intended for adoption throughout all the member states. The use of these common standards is intended to lower trade barriers and enable companies to compete on a more equitable basis throughout the EC. Eurocode 2 (EC2) deals with the design of concrete structures and, in the UK, has replaced BS8110. Eurocode 2 consist of 4 parts and adopts the limit state principles established in British Standards. This book refers primarily to part 1, dealing with general rules for buildings. Eurocode 2 must be used in conjunction with other European Standards including Eurocode 0 (Basis of Design) that deals with analysis and Eurocode 1 (Actions) that covers loadings on structures. Other relevant Standards are Eurocode 7 (Geotechnical Design) and Eurocode 8 (Seismic Design). Several UK bodies have also produced a range of supporting documents giving commentary and background explanation. Further supporting documentation includes, for each separate country, the National Annex which includes information specific to the individual member states and is supported in the UK by the British Standards publication PD 6687:2006 which provides background information. Additionally, the Concrete Centre has produced The Concise Eurocode for the Design of Concrete Buildings which contains material that has been distilled from EC2 but is presented in a way that makes it more user-friendly than the main Eurocode and contains only that information which is essential for the design of more everyday concrete structures. The Institution of Structural Engineers has also produced a new edition of their Design Manual. These latter two documents also contain information not included in EC2 such as design charts and design methods drawn from previous British Standards. The presentation of EC2 is oriented towards computer solution of equations, encompasses higher concrete strengths and is quite different from that of BS8110.

Preface

However the essential feature of EC2 is that the principles of design embodied in the document are almost identical to the principles inherent in BS8110. Hence, although there are some differences in details, engineers who are used to designing to the previous British Standard should have no difficulty in grasping the essential features of EC2. New grades of reinforcing steel are used and design is now based on concrete cylinder strength, with both of these features incorporated in this edition. Changes in terminology, arising partly from language differences, have resulted in the introduction of a few terms that may be unfamiliar to UK engineers. The most obvious of these is the use of actions to describe the loading on structures and the use of the terms permanent and variable actions to describe dead and imposed loads. Throughout this text, terminology has been kept as consistently as possible in line with accepted UK practice and hence, for example, loads have commonly, but not exclusively, been used instead of actions. Other ‘new’ terminology is identified at appropriate points in the text. The subject matter in this book has been arranged so that chapters 1 to 5 deal mostly with theory and analysis while the subsequent chapters cover the design and detailing of various types of member and structure. In order to include topics that are usually in an undergraduate course, there are sections on seismic design, earth-retaining structures as well as chapters on prestressed concrete and composite construction. A new chapter on water retaining structures has been added together with other new sections including the design of deep beams. Additions and modifications have also been made to reflect UK interpretation and practice in the use of EC2 since its introduction. Additional figures and examples have been added to assist understanding and a new section has been added to Chapter 1 to provide an introduction to design processes. This includes consideration of conceptual design, Sustainability and Health & Safety as well as the role of computer software in design. Important equations that have been derived within the text are highlighted by an asterisk adjacent to the equation number and in the Appendix a summary of key equations is given. Where it has been necessary to include material that is not directly provided by the Eurocodes, this has been based on currently accepted UK good practice. In preparing this new edition one aim has been to retain the structure and features of the earlier 5th edition of the well-established book Reinforced Concrete Design by Mosley, Bungey and Hulse (Palgrave) which is based on British Standards. By comparing both books it is possible to compare the essential differences between Eurocode 2 and previous British Standards and to contrast the different outcomes when structures are designed to either codes. It should be emphasised that Codes of Practice are always liable to be revised, and readers should ensure that they are using the latest edition of any relevant standard. Finally, the authors would like to thank Mr Charles Goodchild (The Concrete Centre) and Dr Steve Jones (Liverpool University) for their helpful comments and suggestions during the writing of this edition.

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Acknowledgements Permission to reproduce extracts from BS EN 1992-1-1: 2004 and BS EN 1990: 2002 is granted by British Standards Institution (BSI). No other use of this material is permitted. British Standards can be obtained in pdf or hard copy formats from the BSI online shop: http://shop.bsigroup.com or by contacting BSI Customer Services for hard copies only: Tel. +44 (0)20 8996 9001, Email: [email protected]. We would also like to acknowledge and thank ARUP for permission to reproduce the photographs shown in chapters 2 to 7. Permission to reproduce the photograph of Minworth Sewage Treatment Works in chapter 12 is by courtesy of Pick Everard. The photograph of The Tower, East Side Plaza, Portsmouth (chapter 1) is reproduced by courtesy of Stephenson RC Frame Contractor, Oakwood House, Guildford Road, Bucks Green, Horsham, West Sussex. The photographs in chapters 8, 9 and 13 were supplied by iStock.com.

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Notation Notation is generally in accordance with EC2 and the principal symbols are listed below. Other symbols are defined in the text where necessary. The symbols " for strain and f or  for stress have been adopted throughout, with the general system of subscripts such that the first subscript refers to the material, c – concrete, s – steel, and the second subscript refers to the type of stress, c – compression, t – tension. E Ed F G I K M N Q T V

modulus of elasticity design value of action at the ultimate limit state load (action) permanent load second moment of area prestress loss factor moment or bending moment axial load variable load torsional moment shear force

a b d d0 e f h i k l n 1=r s t u x z

deflection breadth or width effective depth of tension reinforcement depth to compression reinforcement eccentricity stress overall depth of section in plane of bending radius of gyration coefficient length or span ultimate load per unit area curvature of a beam spacing of shear reinforcement or depth of stress block thickness punching shear perimeter neutral axis depth lever arm

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Notation

Ac Ap As A0s As; req As; prov Asw Ecm Es Gk Ic Mbal MEd Mu Nbal NEd P0 Qk TEd VEd Wk bw fck fcm fctm fpk fs fsc fst fyk gk k1 k2 la l0 qk  e

c

f

G

Q

s  "  

concrete cross-sectional area cross-sectional area of prestressing tendons cross-sectional area of tension reinforcement cross-sectional area of compression reinforcement cross-sectional area of tension reinforcement required at the ultimate limit state cross-sectional area of tension reinforcement provided at the ultimate limit state cross-sectional area of shear reinforcement in the form of links or bent-up bars secant modulus of elasticity of concrete modulus of elasticity of reinforcing or prestressing steel characteristic permanent load second moment of area of concrete moment corresponding to the balanced condition design value of moment ultimate moment of resistance axial load on a column corresponding to the balanced condition design value of axial force initial prestress force characteristic variable load design value of torsional moment design value of shear force characteristic wind load minimum width of section characteristic cylinder strength of concrete mean cylinder strength of concrete mean tensile strength of concrete characteristic yield strength of prestressing steel steel stress compressive steel stress tensile steel stress characteristic yield strength of reinforcement characteristic permanent load per unit area average compressive stress in the concrete for a rectangular parabolic stress block a factor that relates the depth to the centroid of the rectangular parabolic stress block and the depth to the neutral axis lever-arm factor ¼ z=d effective height of column or wall characteristic variable load per unit area coefficient of thermal expansion modular ratio action combination factor partial safety factor for concrete strength partial safety factor for loads (actions), F partial safety factor for permanent loads, G partial safety factor for variable loads, Q partial safety factor for steel strength moment redistribution factor strain stress bar diameter

Notation

Notation for composite construction, Chapter 13 Aa Av b beff d Ea Ec; eff Ecm fctm fy fu h ha hf hp hsc Ia Itransf k1 kt L Mc n nf PRd R cf R cx Rs R sf R sx Rv Rw R wx tf tw Wpl; y x z  "

vEd 

Area of a structural steel section Shear area of a structural steel section Width of the steel flange Effective width of the concrete flange Clear depth of steel web or diameter of the shank of the shear stud Modulus of elasticity of steel Effective modulus of elasticity of concrete Secant modulus of elasticity of concrete Mean value of the axial tensile strength of concrete Nominal value of the yield strength of the structural steel Specified ultimate tensile strength Overall depth; thickness Depth of structural steel section Thickness of the concrete flange Overall depth of the profiled steel sheeting excluding embossments Overall nominal height of a shear stud connector Second moment of area of the structural steel section Second moment of area of the transformed concrete area and the structural steel area Reduction factor for resistance of headed stud with profiled steel sheeting parallel with the beam Reduction factor for resistance of headed stud with profiled steel sheeting transverse to the beam Length, span Moment of resistance of the composite section Modular ratio or number of shear connectors Number of shear connectors for full shear connection Design value of the shear resistance of a single connector Resistance of the concrete flange Resistance of the concrete above the neutral axis Resistance of the steel section Resistance of the steel flange Resistance of the steel flange above the neutral axis Resistance of the clear web depth Resistance of the overall web depth ¼ R s ¼ 2R sf Resistance of the web above the neutral axis Thickness of the steel flange Thickness of the steel web Plastic section modulus of a steel structural section Distance to the centroid of a section Lever arm Deflection at mid span pffiffiffiffiffiffiffiffiffiffiffiffiffi Constant equal to 235=fy where fy is in N/mm2 factor of safety Longitudinal shear stress in the concrete flange Degree of shear connection

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1 Introduction to design and properties of reinforced concrete Chapter introduction Structural design may be considered ...