Reinforced concrete design theory and example

Reinforced Concrete
The third edition of this popular textbook has been extensively rewritten and expanded to
conform to the latest versions of BS8110. It sets out design theory for concrete elements
and structures, and illustrates practical applications of the theory.
Reinforced Concrete includes more than 60 clearly worked out design examples and
over 600 diagrams, plans and charts. Backgrounds to the British Standard and Eurocode
are given to explain the ‘why’ as well as the ‘how’, and differences between the codes
are highlighted. New chapters on prestressed concrete and water retaining structures are
included in this edition, and the most commonly encountered design problems in structural concrete are covered. Additional worked examples are available on an associated
website at www.sponpress.com/civeng/support.htm.
This book is written for students on civil engineering degree courses, to explain the
principles of element design and the procedures for design of concrete buildings, and is
also a useful reference for practising engineers.
Prab Bhatt is an Honorary Senior Research Fellow at the Department of Civil Engineering
at the University of Glasgow, UK.
Thomas J.MacGinley (late) was formerly of Nanyang Technological University,
Singapore.
Ban Seng Choo (late) was formerly Professor of Timber Engineering at the School of
Built Environment, Napier University, Edinburgh, UK.



Reinforced Concrete
Design theory and examples
Third edition

Prab Bhatt, Thomas J.MacGinley
and Ban Seng Choo

LONDON AND NEW YORK

First published 1978 by E&FN Spon
Second edition 1990
Third edition published 2006 by Taylor & Francis
2 Park Square, Milton Park, Abingdon, Oxon OX 14 4RN
Simultaneously published in the USA and Canada
by Taylor & Francis
270 Madison Ave, New York, NY 10016, USA
Taylor & Francis is an imprint of the Taylor & Francis Group
This edition published in the Taylor & Francis e-Library, 2009.
To purchase your own copy of this or any of
Taylor & Francis or Routledge’s collection of thousands of eBooks
please go to www.eBookstore.tandf.co.uk.
© 1978 T.J.MacGinley
© 1990 T.J.MacGinley and B.S.Choo
© 2006 P.Bhatt, T.J.MacGinley and B.S.Choo
All rights reserved. No part of this book may be reprinted or reproduced
or utilised in any form or by any electronic, mechanical, or other means,
now known or hereafter invented, including photocopying and recording,
or in any information storage or retrieval system, without permission in
writing from the publishers.
The publisher makes no representation, express or implied, with regard to
the accuracy of the information contained in this book and cannot accept
any legal responsibility or liability for any efforts or omissions that may
be made.
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloging in Publication Data
Bhatt, P.

Reinforced concrete: design theory and examples/P.Bhatt,
T.J.MacGinley, and B.S.Choo.—3rd ed.
p. cm.
Rev. ed. of: Reinforced concrete/T.J.MacGinley, B.S.Choo.
London; New York: E & F.Spon, 1990.
ISBN 0-415-30796-1 (pbk.: alk. paper)—ISBN 0-415-30795-3
(hardback: alk. paper)
1. Reinforced concrete construction. I. MacGinley, T.J.
(Thomas Joseph) II. Choo, B.S. III. MacGinley, T.J.
(Thomas Joseph). Reinforced concrete. IV. Title.
TA683.2.M33 2005
624.1′834–dc22
2005021534
ISBN 0-203-40438-6 Master e-book ISBN
ISBN10: 0–415–30795–3
ISBN13: 978-0-415-30795-6 (hbk)
ISBN10: 0–415–30796–1
ISBN13: 978–0–415–30796–3 (pbk)


Dedicated with love and gratitude to
my mother Srimati Sharadamma
who taught us to ‘never disown the poor’.



CONTENTS
 
xxvii

 
 
 
 
 
 
 
 

1

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 

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viii  Contents

 
 
 
 
 
 
 
 
 
 
 
 
 

  2.7   Failures in concrete structures
2.7.1   Factors affecting failure
 
2.7.1.1   Incorrect selection of materials
 
2.7.1.2   Errors in design calculations and detailing
 
2.7.1.3   Poor construction methods
 
2.7.1.4   Chemical attack
 
2.7.1.5   External physical and/or mechanical factors

 
  2.8   Durability of concrete structures
2.8.1   Code references to durability
 
  2.9   Concrete cover
2.9.1   Nominal cover against corrosion
 
2.9.2   Cover as fire protection
 
  2.10   References
3   Limit state design and structural analysis
 
  3.1   Structural design and limit states
3.1.1   Aims and methods of design
 
 
3.1.2   Criteria for a safe design: limit states
 
 
3.1.3   Ultimate limit state
 
 
3.1.4   Serviceability limit states
 
 
 
  3.2   Characteristic and design loads
 
  3.3   Materials: Properties and design strengths
 

  3.4   Structural analysis
3.4.1   General provisions
 
 
3.4.2   Methods of frame analysis
 
 
3.4.3   Monolithic braced frame
 
 
3.4.4   Rigid frames providing lateral stability
 
 
3.4.5   Redistribution of moments
 
 
4   Section design for moment
 
  4.1   Types of beam section
 
  4.2   Reinforcement and bar spacing
4.2.1   Reinforcement data
 
 
4.2.2   Minimum and maximum areas of reinforcement in beams
 
 
4.2.3   Minimum spacing of bars
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 
 
 

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Contents   ix

 
 
 
 

  4.3   Behaviour of beams in bending
  4.4   Singly reinforced rectangular beams
4.4.1   Assumptions and stress-strain diagrams
 
4.4.2   Moment of resistance: Rectangular stress block
 

 

 

 

 

 
 

 
 

 

 

 
 

 

4.5.1   Design formulae using the simplified stress block

 

4.5.2   Examples of rectangular doubly reinforced concrete beams

4.4.3   Procedure for the design of singly reinforced rectangular
beam
4.4.4   Examples of design of singly reinforced rectangular
sections
4.4.5   Design chart
4.4.5.1   Examples of use of design chart

4.4.6   Moment of resistance using rectangular parabolic stress
block
4.5
 
Doubly
reinforced beams
 

 
 
 
 
 
 
 
 
 
 
 

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57
58
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60

 

62

  4.6   Flanged beams
4.6.1   General considerations
 
4.6.2   Stress block within the flange
 
4.6.3   Stress block extends into the web
 
4.6.3.1   Code formula
 
4.6.4   Steps in reinforcement calculation of a T- or an L-beam
 
4.6.5   Examples of design of flanged beams
 
  4.7   Checking existing sections
4.7.1   Examples of checking for moment capacity
 
4.7.2   Strain compatibility method
 
4.7.2.1   Example of strain-compatibility method
 
5   Shear, bond and torsion
 
  5.1   Shear forces
5.1.1   Shear in a homogeneous beam

 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

64

5.1.2   Shear in a reinforced concrete beam without shear reinforcement
5.1.3   Shear reinforcement in the form of links

 

 
 
 
 
 

 
 
 
 
 
 
 

 

 

 

 

 

 

5.1.3.1   Examples of design of link reinforcement in
beams

 
 

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x  Contents

 
 
 

 
 
 

5.1.4   Shear reinforcement close to a support

 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

5.1.6.1   Example of design of shear reinforcement using
bent up bars
5.1.7   Shear resistance of solid slabs

 
5.1.8   Shear due to concentrated loads on slabs
 
5.1.8.1   Example of punching shear design
 
  5.2   Bond, laps and bearing stresses in bends
5.2.1   Example of calculation of anchorage lengths
 
5.2.2   Hooks and bends

 
5.2.2.1   Examples of anchorage length calculation
 
5.2.2.2   Curtailment and anchorage of bars
 
5.2.3   Laps and joints
 
5.2.4   Bearing stresses inside bends
 
5.2.4.1   Example of design of anchorage at beam support
 
  5.3   Torsion
5.3.1   Occurrence and analysis of torsion
 
5.3.2   Structural analysis including torsion
 
5.3.3   Torsional shear stress in a concrete section
 
5.3.4   Torsional reinforcement
 

 

 

 

5.1.5   Examples of design of shear reinforcement for beams
5.1.6   Shear reinforcement in the form of bent-up bars

5.3.4.1   Example of design of torsion steel for rectangular
beam
5.3.4.2   Example of T-beam design for torsion steel

 
6   Serviceability limit state checks
 
  6.1   Serviceability limit state
 
  6.2   Deflection
6.2.1   Deflection limits and checks
 
 
6.2.2   Span-to-effective depth ratio
 
 
6.2.2.1   Example of deflection check for T-beam
 
 
 
  6.3   Cracking
6.3.1   Cracking limits and controls
 
 
6.3.2   Bar spacing controls in beams
 
 

 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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110
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118

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Contents   xi

 
 
 

6.3.2.1   Examples of maximum bar spacings in beams

 
6.3.3   Bar spacing controls in slabs
 
6.3.3.1   Example of maximum bar spacings in slabs
 
7   Simply supported beams
 
  7.1   Simply supported beams
7.1.1   Steps in beam design
 
 
7.1.2   Curtailment and anchorage of bars
 
 
7.1.3   Example of design of a simply supported L-beam in a
footbridge
7.1.4   Example of design of simply supported doubly reinforced
 
rectangular beam
  7.2   References

 

 
 
 
 
 
 
 

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141
142
142
142
144

 

  146

 
 
 
 

  Reinforced concrete slabs
  8.1   Types of slab and design methods
  8.2   One-way spanning solid slabs
8.2.1   Idealization for design
 
8.2.2   Effective span, loading and analysis
 

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  158
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  158
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8.2.5   Deflection
 
8.2.6   Crack control
 
  8.3   Example of design of continuous one-way slab

  8.4   One-way spanning ribbed slabs
8.4.1   Design considerations
 
8.4.2   Ribbed slab proportions
 
8.4.3   Design procedure and reinforcement
 
8.4.4   Deflection
 
8.4.5   Example of one-way ribbed slab
 
  8.5   Two-way spanning solid slabs
8.5.1   Slab action, analysis and design
 
8.5.2   Rectangular slabs simply supported on all four edges
 
8.5.3   Example of a simply supported two-way slab
 
  8.6   Restrained solid slabs

 
 
8

8.2.3   Section design and slab reinforcement curtailment and
cover
8.2.4   Shear

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xii  Contents

 
 
 
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

8.6.1   Design and arrangement of reinforcement
 
8.6.2   Adjacent panels with markedly different support moments
 
8.6.3   Shear forces and shear resistance
 
8.6.4   Deflection
 
8.6.5   Cracking
 
8.6.6   Example of design of two-way restrained solid slab
 
  8.7   Waffle slabs

8.7.1   Design procedure
 
8.7.2   Example of design of a waffle slab
 
  8.8   Flat slabs
8.8.1   Definition and construction
 
8.8.2   General code provisions
 
8.8.3   Analysis
 
8.8.4   Division of panels and moments
 
8.8.5   Design of internal panels and reinforcement details
 
8.8.6   Design of edge panels
 
8.8.7   Shear force and shear resistance
 
8.8.8   Deflection
 
8.8.9   Crack control
 
8.8.10 Example of design for an internal panel of a flat slab floor
 
  8.9   Yield line method
8.9.1   Outline of Theory
 
8.9.1.1 Properties of yield lines
 

8.9.2   Johansen’s stepped yield criterion
 
8.9.3   Energy dissipated in a yield line
 
8.9.4   Work done by external loads
 
8.9.5   Example of a continuous one-way slab
 
8.9.6   Simply supported rectangular two-way slab
 

 

 

 

 

 

 

8.9.6.1   Example of yield line analysis of a simply supported rectangular slab
8.9.7   Rectangular two-way slab continuous over supports
8.9.7.1   Example of yield line analysis of a clamped rectangular slab

 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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Contents   xiii

 
 
 

 
 
 

8.9.8   Clamped rectangular slab with one long edge free

 

 

 

 

 
 
 
 
 
 
 

 
 
 
 
 
 
 

8.9.8.3   Example of yield line analysis of a clamped rectangular slab with one free long edge
8.9.9   Trapezoidal slab continuous over three supports and free
on a long edge
8.9.10  Slab with hole

 

 

 
 

 
 

 

 

 

 

 
 
 
 
 
 
 
 
 
 
 
 

 
8.9.16.2   Clamped slab
 
8.9.16.3   Slab with two short edges discontinuous
 
8.9.16.4   Slab with two long edges discontinuous
 
8.9.16.5   Slab with one long edge discontinuous
 
8.9.16.6   Slab with one short edge discontinuous
 
8.9.16.7   Slab with two adjacent edges discontinuous
 
8.9.16.8   Slab with only a short edge continuous
 
8.9.16.9   Slab with only a long edge continuous

 
  8.10   Hillerborg’s strip method
8.10.1 Simply supported rectangular slab
 
8.10.2 Clamped rectangular slab with a free edge
 

8.9.8.1   Calculations for collapse mode 1
8.9.8.2   Calculations for collapse mode 2

8.9.10.1   Calculations for collapse mode 1
8.9.10.2   Calculations for collapse mode 2
8.9.10.3   Calculations for collapse mode 3
8.9.10.4   Calculation of moment of resistance
8.9.11  Slab-beam systems
8.9.12  Corner levers
8.9.13 C
 ollapse mechanisms with more than one independent
variable
8.9.14  Circular fans
8.9.14.1   Collapse mechanism for a flat slab floor
8.9.15  Design of a corner panel of floor slab using yield line
analysis
8.9.16 Derivation of BS 8110 moment and shear coefficients for
the design of restrained slabs
8.9.16.1   Simply supported slab

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xiv  Contents

 

 

 
 

 
 

 

 

 
 
 
 
 
 
 
 
 
 
 
 

8.10.3  A slab clamped on two opposite sides, one side simply
supported and one edge free
8.10.4  Strong bands

8.10.5 Comments on the strip method

8.11   Design of reinforcement for slabs in accordance with a predetermined field of moments
8.11.1
 Rules for designing bottom steel
 

8.11.1.1  Examples of design of bottom steel
 
8.11.2  Rules for designing top steel
 
8.11.2.1  Examples of design of top steel
 
8.11.3 Examples of design of top and bottom steel
 
8.11.4 Comments on the design method using elastic analysis
 
  8.12   Stair slabs
8.12.1  Building regulations
 
8.12.2  Types of stair slab
 
8.12.3  Code design requirements
 
8.12.4  Example of design of stair slab
 
  8.13   References
9   Columns
 
  9.1   Types, loads, classification and design considerations

9.1.1   Types and loads
 
 
9.1.2   General code provisions
 
 
9.1.3   Practical design provisions
 
 
 
  9.2   Short braced axially loaded columns
9.2.1   Code design expressions
 
 
9.2.1.1   Examples of axially loaded short column
 
 
9.3   Short columns subjected to axial load and bending about one
axis-symmetrical reinforcement
9.3.1   Code provisions
 

 

 

 
 
 
 

 
 

 
 
 
 
 

9.3.2   Section analysis
9.3.2.1   Parabolic-rectangular stress block
9.3.2.2   Rectangular stress block
9.3.2.3   Stresses and strains in steel
9.2.3.4   Axial force N and moment M

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Contents   xv
9.2.3.5   Example of a short column subjected to axial load
and moment about one axis
9.3.3   Construction of column design chart

 

 

 

 

 

 

 
 
 

 
 
 

 

 

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9.3.3.1   Typical calculations for rectangular-parabolic

stress block
9.3.3.2   Typical calculations for rectangular stress block
9.3.3.4   Column design using design charts
9.3.4   Further design chart

9.4   Short columns subjected to axial load and bending about one
axis: unsymmetrical reinforcement
9.4.1   Example of a column section subjected to axial load and
 
moment unsymmetrical reinforcement
  9.5   Column sections subjected to axial load and biaxial bending

 

 

 

 

 
 

 
 

 

 

 
 
 
 
 

 
 
 
 

9.5.1   Outline of the problem
9.5.1.1   Expressions for contribution to moment and axial
force by concrete
9.5.1.2   Example of design chart for axial force and biaxial moments
9.5.1.3   Axial force biaxial moment interaction curve
9.5.2   Approximate method given in BS 8110

9.5.2.1   Example of design of column section subjected to
axial load and biaxial bending: BS 8110 method
  9.6   Effective heights of columns
9.6.1   Braced and un-braced columns
9.6.2   Effective height of a column
9.6.3   Effective height estimation from BS 8110
9.6.4   Slenderness limits for columns

9.6.4.1   Example of calculating the effective heights of
column by simplified and rigorous methods
  9.7   Design of slender columns

 

 

 
 

 

9.7.1   Additional moments due to deflection

 

 

 
 
 

 
 
 

9.7.2   Design moments in a braced column bending about a
single axis
9.7.3   Further provisions for slender columns
9.7.4   Unbraced structures
9.7.4.1   Example of design of a slender column

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xvi  Contents

 
 
 

 
 
 
 

  Walls in buildings
  10.1  Functions, types and loads on walls
  10.2 Types of wall and definitions
  10.3 Design of reinforced concrete walls
10.3.1  Wall reinforcement
 
10.3.2 General code provisions for design
 
10.3.3  Design of stocky reinforced concrete walls
 
10.3.4  Walls supporting in-plane moments and axial loads
 

 

 

 

 

 

 

 

 

10

10.3.4.1   Example of design of a wall subjected to axial
load and in-plane moments using design chart
10.3.4.2   Example of design of a wall subjected to axial
load and in-plane moments with concentrated
steel in end zones/columns
10.3.4.3   Example of design of a wall subjected to axial
load, transverse and in-plane moments
10.3.5  Slender reinforced walls

 
 
 
 
 
 
 
 

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10.3.6  Deflection of reinforced walls
 
 
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  10.4  Design of plain concrete walls
  379
10.4.1  Code design provisions
 
 
  379
10.4.1.1   Example of design of a plain concrete wall
 
 

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11   Foundations
  385
 
  11.1  General considerations
  385
 
  11.2  Isolated pad bases
  385
11.2.1 General comments
 
 
  385
11.2.2  Axially loaded pad bases
 
 
  386
11.2.2.1  Example of design of an axially loaded base
 
 
  390
 
  11.3  Eccentrically loaded pad bases
  393
11.3.1 Vertical pressure
 
 
  393
11.3.2 Resistance to horizontal loads
 

 
  394
11.3.3  Structural design
 
 
  396
11.3.3.1 Example of design of an eccentrically loaded base   396
 
 
 

11.3.3.2 Example of design of a footing for pinned base
steel portal
  11.4  Wall, strip and combined foundations

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Contents   xvii

 
 
 
 
 
 
 
 
 

 
 
 

11.4.1 Wall footings
 
11.4.2  Shear wall footing
 
11.4.3  Strip footing
 
11.4.4  Combined bases
 
11.4.4.1   Example of design of a combined base
 
  11.5 Piled foundations
11.5.1  General considerations
 
11.5.2  Loads in pile groups
 
11.5.2.1  Example of loads in pile group
 
11.5.3  Design of pile caps
 
11.5.3.1 Example of design of pile cap
 
  11.7 References
12   Retaining walls
 
  12.1  Wall types and earth pressure
12.1.1 Types of retaining wall

 
 
12.1.2 Earth pressure on retaining walls
 
 
 
  12.2 Design of cantilever walls
12.2.1  Initial sizing of the wall
 
 
12.2.2  Design procedure for a cantilever retaining wall
 
 
12.2.3  Example of design of a cantilever retaining wall
 
 
 
  12.3   Counterfort retaining walls
12.3.1 Stability check and design procedure
 
 
12.3.2  Example of design of a counterfort retaining wall
 
 
12.3.3  Design of wall slab using yield line method
 
 
12.3.4  Design of base slab using yield line method
 
 

12.3.5  Base slab design using Hillerborg’s strip method
 
 
12.3.5.1  Horizontal strips in base slab
 
 
12.3.5.2  Cantilever moment in base slab
 
 
12.3.6  Wall design using Hillerborg’s strip method
 
 
12.3.6.1  Cantilever moment in wall slab
 
 
12.3.7  Counterfort design using Hillerborg’s strip method
 
 
13   Design of statically indeterminate structures
 
  13.1  Introduction

 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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xviii  Contents

 
 
 
 
 
 
 
 
 
 
 
 
 

  13.2 Design of a propped cantilever
  13.3 Design of a clamped beam
  13.4 Why use anything other than elastic values in design?
  13.5 Limits on departure from elastic moment distribution in BS 8110
13.5.1  Moment of resistance
 
13.5.2  Serviceability considerations
 
  13.6  Continuous beams
13.6.1  Continuous beams in in-situ concrete floors
 
13.6.2  Loading on continuous beams
 

13.6.2.1 Arrangement of loads to give maximum moments
 
13.6.2.2 Example of critical loading arrangements
 
13.6.2.3 Loading from one-way slabs
 
13.6.2.4 Loading from two-way slabs
 

 

 

 
 
 
 
 
 
 
 
 
 
 

13.6.2.5 Alternative distribution of loads from two-way
slabs
13.6.3   Analysis for shear and moment envelopes

 

  13.7 Example of elastic analysis of a continuous beam
  13.8 Example of moment redistribution for a continuous beam
  13.9 Curtailment of bars
  13.10 Example of design for the end span of a continuous beam
  13.11 Example of design of a non-sway frame
  13.12 Approximate methods of analysis
13.12.1  Analysis for gravity loads
 
13.12.2  Analysis of a continuous beam for gravity loads
 
13.12.3 Analysis of a rectangular portal frame for gravity loads
 
13.12.4  Analysis for wind loads by portal method
 
14   Reinforced concrete framed buildings
 
  14.1 Types and structural action
 
  14.2 Building loads
14.2.1   Dead load
 
 
14.2.2   Imposed load
 
 
14.2.3   Wind loads
 
 
14.2.4   Load combinations
 

 

 
 
 
 
 
 
 
 
 
 
 
 
 

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Contents   xix

 
 
 
 
 
 
 

 
 
 
 

14.2.4.1   Example on load combinations
 
  14.3 Robustness and design of ties
14.3.1 Types of tie
 
14.3.2 Design of ties
 
14.3.3 Internal ties
 
14.3.4 Peripheral ties
 
14.3.5 Horizontal ties to columns and walls
 
14.3.6 Corner column ties
 
14.3.7 Vertical ties
 
  14.4 Frame analysis
14.4.1 Methods of analysis
 

 
 
 
 

 
 
 
 
 
 
 

 

 

14.4.2 Example of simplified analysis of concrete framed
building under vertical load
14.4.3 Example of simplified analysis of concrete framed
 
building for wind load by portal frame method
  14.5 Building design example

  541

 
 
 

 
 
 
 
 

 
 
 
 
 
 
 
 

14.5.1 Example of design of multi-storey reinforced concrete
framed buildings
15 Tall buildings
  Modified version of initial contribution by J.C.D. Hoenderkamp,
formerly of Nanyang Technological Institute, Singapore
  15.1 Introduction

 

  15.2 Assumptions for analysis
  15.3 Planar lateral load resisting elements
15.3.1 Rigid-jointed frames
 
15.3.2 Braced frames
 
15.3.3 Shear walls
 
15.3.4 Coupled shear walls
 
15.3.5 Wall-frame structures
 

15.3.6 Framed-tube structures
 
15.3.7 Tube-in-tube structures
 
15.3.8 Outrigger-braced structures
 
  15.4 Interaction between bents
  15.5 Three dimensional structures

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xx  Contents

 

 

 

 

 
 
 
 
 

15.5.1 Classification of structures for computer modelling

15.5.1.1   Category I: Symmetric floor plan with identical
parallel bents subject to a symmetrically applied
lateral load q
15.5.1.2   Category II: Symmetric structural floor plan with
non-identical bents subject to a symmetric hori 
zontal load q
15.5.1.3   Category III: Non-symmetric structural floor
plan with identical or non-identical bents subject
 
to a lateral load q
  15.6 Analysis of framed-tube structures

  15.7 Analysis of tube-in-tube structures
  15.8 References
16   Prestressed concrete

 
  16.1 Introduction
 
  16.2 How to apply prestress?
16.2.1 Pre-tensioning
 
 
16.2.1.1 Debonding
 
 
16.2.1.2 Transmission length
 
 
16.2.2 Post-tensioning
 
 
16.2.3 External prestressing
 
 
16.2.4 Un-bonded construction
 
 
16.2.5 Statically indeterminate structures
 
 
16.2.6 End-block
 
 
 
  16.3 Materials

16.3.1 Concrete
 
 
16.3.2 Steel
 
 
16.3.2.1   Relaxation of steel
 
 
 
  16.4 Design of prestressed concrete structures
 
  16.5 Limits on permissible stresses in concrete
16.5.1 Definition of class
 
 
16.5.1.1 Partial prestressing
 
 
16.5.2 Permissible compressive stress in concrete at transfer
 
 
16.5.3 Permissible tensile stress in concrete at transfer
 
 

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Contents   xxi

 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

16.5.4  Permissible compressive stress in concrete at

serviceability limit state
16.5.4  Permissible tensile stress in concrete at serviceability limit
 
state
  16.6 Limits on permissible stresses in steel

 

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16.6.1 Maximum stress at jacking and at transfer
 
  16.7   Equations for stress calculation
16.7.1 Transfer state
 
16.7.2 Serviceability limit state
 
16.7.3 Example of stress calculation
 
  16.8 Design for serviceability limit state
16.8.1 Initial sizing of section
 
16.8.1.1 Example of initial sizing
 
16.8.2  Choice of prestress and eccentricity
 
16.8.2.1 Example of construction of Magnel diagram
 
16.8.2.2 Example of choice of prestress and eccentricity
 

16.8.2.3 Example of debonding
 
  16.9 Composite beams
16.9.1 Magnel equations for a composite beam
 
  16.10 Post-tensioned beams: cable zone
16.10.1 Example of a post-tensioned beam
 
  16.11 Ultimate moment capacity
16.11.1 Example of ultimate moment capacity calculation
 

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16.11.2 Ultimate moment capacity calculation using tables in
BS8110
16.11.2.1 Example of ultimate moment capacity
 
calculation using tables in BS8110
  16.12 Ultimate shear capacity of sections cracked in flexure

 

  632

16.12.1 Example of calculation of Vcr
 
  16.13 Ultimate shear capacity Vco of sections uncracked in flexure
16.13.1 Example of calculating ultimate shear capacity Vco
 
16.13.1.1 Calculation of Vco from first principles
 
  16.14  Design of shear reinforcement
16.14.1 Example of shear link design
 

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xxii  Contents

 
 
 
 
 
 
 
 
 
 
 

  16.15   Horizontal shear
16.15.1   Shear reinforcement to resist horizontal shear stress
 
16.15.2   Example of design for horizontal shear
 
  16.16   Loss of prestress in pre-tensioned beams
16.16.1   Loss at transfer
 
16.16.1.1   Example on calculation of loss at transfer
 
16.16.2   Long term loss of prestress

 
  16.17   Loss of prestress in post-tensioned beams
  16.18   Design of end-block in post-tensioned beams
16.18.1   Example of end-block design
 
  16.19   References
17   Design of structures retaining aqueous liquids
 
  17.1   Introduction
17.1.1   Load factors
 
 
17.1.2   Crack width
 
 
17.1.3   Span/effective depth ratios
 
 
17.1.4   Cover
 
 
17.1.5   Mix proportions
 
 
17.1.6   Minimum reinforcement
 
 
 
  17.2   Bending analysis for serviceability limit state
17.2.1   Example of stress calculation at SLS

 
 
 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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17.2.2   Crack width calculation in a section subjected to flexure only
17.2.2.1   Example of crack width calculation in flexure
only
17.2.3   Crack width calculation in a section subjected to
bending moment and direct tension
17.2.3.1   Example of calculation of crack width under
bending moment and axial tension
17.2 4  Crack width calculation in direct tension

  660

17.2.4.1   Example of crack width calculation in direct
tension
17.2.4   Deemed to satisfy clause

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17.2.5   Design tables

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Contents   xxiii

 
 
 
 
 

  17.3   Control of restrained shrinkage and thermal movement cracking
17.3.1   Movement joints
 
17.3.2   Critical amount of reinforcement
 
17.3.3   Crack spacing
 
17.3.4   Width of cracks
 

 
 
 
 
 

 

 

17.3.5   Design options for control of thermal contraction and
restrained shrinkage
17.3.6   Example of options for control of thermal contraction
 
and restrained shrinkage
  17.4   Design of a rectangular covered top under ground water tank

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  17.5   Design of circular water tanks
17.5.1   Example of design of a circular water tank
 
  17.6   References

18   Eurocode 2
 
  18.1   Load factors
18.1.1   Load factors for ultimate limit state
 
 
18.1.2   Load factors for serviceability limit state
 
 
 
  18.2   Material safety factors
 
  18.3   Materials
 
  18.4   Bending analysis
18.4.1   Maximum depth of neutral axis x
 
 
18.4.2   Stress block depth
 
 
18.4.3   Maximum moment permitted in a rectangular beam with
no compression steel
18.4.4   Lever arm Z

 

 

 

 
 
 
 
 
 
 
 
 

 
18.4.5   Moment redistribution
 
  18.5   Examples of beam design for bending
18.5.1   Singly reinforced rectangular beam
 
18.5.2   Doubly reinforced beam
 
18.5.3   T-beam design
 
  18.6   Shear design: Standard method
18.6.1   Maximum permissible shear stress
 
18.6.2   Permissible shear stress in reinforced concrete
 
18.6.3   Total shear capacity
 

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xxiv  Contents

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

18.6.4   Shear reinforcement in the form of links
 
18.6.5   Maximum permitted spacing of links
 
18.6.6   Minimum area of links
 
18.6.7   Example of shear design
 

  18.7   Punching shear
18.7.1   Location of critical perimeter
 
18.7.2   Maximum permissible shear stress, Vmax
 
18.7.3   Permissible shear stress, vc
 
18.7.4   Shear reinforcement
 
18.7.5   Example
 
  18.8   Columns
18.8.1   Short or slender column?
 
18.8.2   Example
 
  18.9   Detailing
18.9.1   Bond
 
18.9.2   Anchorage lengths
 
18.9.3   Longitudinal reinforcement in beams
 
  18.10   References
19   Deflection and cracking
 
  19.1   Deflection calculation
19.1.1   Loads on the structure
 
 

19.1.2   Analysis of the structure
 
 
19.1.3   Method for calculating deflection
 
 
19.1.4   Calculation of curvatures
 
 
19.1.5   Cracked section analysis
 
 
19.1.5.1   Simplified approach
 
 
19.1.6   Uncracked section
 
 
19.1.7   Long-term loads: Creep
 
 
19.1.8   Shrinkage curvature
 
 
19.1.9   Total long-term curvature
 
 
19.1.10 Deflection calculation
 
 

19.1.10.1   Evaluation of constant K
 
 
 
  19.2   Example of deflection calculation for T-beam

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 

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