2014_Reinforced Concrete Design to Eurocodes-Design Theory and Examples_Bhatts et. al.

ReinfoRced
concRete design
to euRocodes
design theoRy and examples
fourth Edition

Prab Bhatt
Thomas J. MacGinley
Ban Seng Choo


Reinforced
Concrete Design
to Eurocodes
Design Theory and Examples
fourth Edition


Reinforced
Concrete Design
to Eurocodes
Design Theory and Examples
fourth Edition

Prab Bhatt
Thomas J. MacGinley
Ban Seng Choo

A SPON BOOK

First published 1978 as Reinforced Concrete: Design Theory and Examples by E&FN Spon © 1978 T.J. MacGinley
Second edition published 1990 © 1990 T.J. MacGinley and B.S.Choo
Third edition published 2006 by Taylor & Francis © 2006 P. Bhatt, T.J. MacGinley and B.S. Choo

CRC Press
Taylor & Francis Group
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© 2014 by P. Bhatt and the estates of T.J. MacGinley and B.S. Choo
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Version Date: 20130801
International Standard Book Number-13: 978-1-4665-5253-1 (eBook - PDF)
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Dedicated with love and affection to our grandsons

Veeraj Rohan Bhatt Verma
Devan Taran Bhatt
Kieron Arjun Bhatt


CONTENTS
Preface
About the Authors
1

Introduction
1.1
Reinforced concrete structures
1.2
Structural elements and frames
1.3
Structural design
1.4
Design standards
1.5
Calculations, design aids and computing
1.6
Detailing

1.7
References

2

Materials, Structural Failures and Durability
2.1
Reinforced concrete structures
2.2
Concrete materials
2.2.1
Cement
2.2.1.1
Types of cement
2.2.1.2
Strength class
2.2.1.3
Sulphate-resisting cement
2.2.1.4
Low early strength cement
2.2.1.5
Standard designation of cements
2.2.1.6
Common cements
2.2.2
Aggregates
2.2.3
Concrete mix design
2.2.4
Admixtures

2.3
Concrete properties
2.3.1
Stress−strain relationship in compression
2.3.2
Compressive strength
2.3.3
Tensile strength
2.3.4
Modulus of elasticity
2.3.5
Creep
2.3.6
Shrinkage
2.4
Tests on wet concrete
2.4.1
Workability
2.4.2
Measurement of workability
2.5
Tests on hardened concrete
2.5.1
Normal tests
2.5.2
Non-destructive tests
2.5.3
Chemical tests
2.6
Reinforcement

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Reinforced concrete design to EC 2
2.7
2.8

2.9
2.10
2.11

Exposure classes related to environmental conditions
Failures in concrete structures
2.8.1
Factors affecting failure
2.8.1.1
Incorrect selection of materials
2.8.1.2
Errors in design calculations and detailing
2.8.1.3

Poor construction methods
2.8.1.4
External physical and/or mechanical factors
Durability of concrete structures
Fire protection
References

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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 safe design: Limit states
3.1.3
Ultimate limit state
3.1.4

Serviceability limit states
3.2
Actions, characteristic and design values of actions
3.2.1
Load combinations
3.2.2
Load combination EQU
3.2.3
Load combination STR
3.2.4
Examples
3.2.4.1
Checking for EQU (stability)
3.2.4.2
Load calculation for STR (design)
3.2.5
Partial factors for serviceability limit states
3.3
Partial factors for materials
3.4
Structural analysis
3.4.1
General provisions
3.5
Reference

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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
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
4.4.2.1
U.K. National Annex formula
4.4.3
Procedure for the design of singly reinforced
rectangular beam

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Contents

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4.4.4

4.5

4.6

4.7

4.8
5

Examples of design of singly reinforced
rectangular sections
4.4.5
Design graph
Doubly reinforced beams
4.5.1
Design formulae using the rectangular stress block
4.5.2
Examples of rectangular doubly reinforced
concrete beams
Flanged beams
4.6.1
General considerations
4.6.2
Stress block within the flange
4.6.3
Stress block extends into the web
4.6.4
Steps in reinforcement calculation for a T-beam or

an L-beam
4.6.5
Examples of design of flanged beams
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
Reference

Shear, Bond and Torsion
5.1
Shear forces
5.1.1
Shear in a homogeneous beam
5.1.2
Shear in a reinforced concrete beam without shear
reinforcement
5.1.3
Shear reinforcement in the form of links
5.1.4
Derivation of Eurocode 2 shear design equations
5.1.4.1
Additional tension force due to shear
in cracked concrete
5.1.5
Minimum shear reinforcement
5.1.6

Designing shear reinforcement
5.1.7
Bent-up bars as shear reinforcement
5.1.7.1 Example of design of bent-up bars and link
reinforcement in beams
5.1.8
Loads applied close to a support
5.1.8.1
Example
5.1.9
Beams with sloping webs
5.1.10 Example of complete design of shear reinforcement for
beams
5.1.11 Shear design of slabs
5.1.12 Shear due to concentrated loads on slabs
5.1.13 Procedure for designing shear reinforcement against
punching shear
5.1.13.1 Example of punching shear design: Zero
moment case

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5.1.14

5.2
5.3

5.4

5.5

6

Shear reinforcement design: Shear and moment
combined
5.1.14.1 Support reaction eccentric with regard to
control perimeter for rectangular columns
5.1.14.2 Support reaction eccentric with regard to
control perimeter for circular columns
5.1.14.3 Support reaction eccentric with regard to
control perimeter about two axes for
rectangular columns
5.1.14.4 Rectangular edge columns
5.1.14.5 Support reaction eccentric toward the
interior for rectangular corner column
5.1.14.6 Approximate values of  for columns of a
flat slab
Bond stress
Anchorage of bars
5.3.1
Design anchorage length
5.3.2

Example of calculation of anchorage length
5.3.3
Curtailment and anchorage of bars
5.3.4
Example of moment envelope
5.3.4.1 Anchorage of curtailed bars and
anchorage at supports
5.3.4.2
Anchorage of bottom reinforcement at an
end support
5.3.5
Laps
5.3.5.1 Transverse reinforcement in the lap
zone
5.3.5.2
Example of transverse reinforcement in the
lap zone
5.3.6
Bearing stresses inside bends
Torsion
5.4.1
Occurrence and analysis of torsion
5.4.2
Torsional shear stress in a concrete section
5.4.2.1
Example
5.4.3
Design for torsion
5.4.3.1
Example of reinforcement design for

torsion
5.4.4
Combined shear and torsion
5.4.4.1
Example of design of torsion steel for a
rectangular beam
Shear between web and flange of T-sections
5.5.1
Example

Serviceability Limit State Checks
6.1
Serviceability limit state

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6.2

6.3

7

8

xi
Deflection
6.2.1
Deflection limits and checks

6.2.2
Span-to-effective depth ratio
6.2.2.1
Examples of deflection check for beams
Cracking
6.3.1
Cracking limits and controls
6.3.2
Bar spacing controls in beams
6.3.3
Minimum steel areas
6.3.3.1
Example of minimum steel areas
6.3.4
Bar spacing controls in slabs
6.3.5
Surface reinforcement

Simply Supported Beams
7.1
Simply supported beams
7.1.1
Steps in beam design
7.1.2
Example of design of a simply supported L-beam
in a footbridge
7.1.3
Example of design of simply supported doubly
reinforced rectangular beam
7.2

References
Reinforced Concrete Slabs
8.1
Design methods for slabs
8.2
Types of slabs
8.3
One-way spanning solid slabs
8.3.1
Idealization for design
8.3.2
Effective span, loading and analysis
8.3.3
Section design, slab reinforcement curtailment
and cover
8.4
Example of design of continuous one-way slab
8.5
One-way spanning ribbed or waffle slabs
8.5.1
Design considerations
8.5.2
Ribbed slab proportions
8.5.3
Design procedure and reinforcement
8.5.4
Deflection
8.5.5
Example of one-way ribbed slab
8.6

Two-way spanning solid slabs
8.6.1
Slab action, analysis and design
8.6.2
Rectangular slabs simply supported on all four edges:
Corners free to lift
8.6.3
Example of a simply supported two-way slab:
Corners free to lift
8.7
Restrained solid slabs
8.7.1
Design and arrangement of reinforcement

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8.8
8.9

8.10

8.7.2
Shear forces and shear resistance
8.7.3
Deflection
8.7.4
Cracking
8.7.5
Example of design of two-way restrained solid slab
8.7.6
Finite element analysis
Waffle slabs
8.8.1
Design procedure
8.8.2
Example of design of a waffle slab
Flat slabs
8.9.1
Definition and construction
8.9.2
Analysis
8.9.3
General Eurocode 2 provisions
8.9.4
Equivalent frame analysis method
8.9.5
Shear force and shear resistance
8.9.6
Deflection

8.9.7
Crack control
8.9.8
Example of design for an internal panel of a flat
slab floor
Yield line method
8.10.1 Outline of theory
8.10.1.1 Properties of yield lines
8.10.2 Johansen’s stepped yield criterion
8.10.3 Energy dissipated in a yield line
8.10.4 Work done by external loads
8.10.5 Example of a continuous one-way slab
8.10.6 Simply supported rectangular two-way slab
8.10.6.1 Example of yield line analysis of a simply
supported rectangular slab
8.10.7 Rectangular two-way clamped slab
8.10.7.1 Example of yield line analysis of a clamped
rectangular slab
8.10.8 Clamped rectangular slab with one long edge free
8.10.8.1 Calculations for collapse mode 1
8.10.8.2 Calculations for collapse mode 2
8.10.8.3 Example of yield line analysis of a clamped
rectangular slab with one long edge free
8.10.9 Trapezoidal slab continuous over three supports and
free on a long edge
8.10.10 Slab with a symmetrical hole
8.10.10.1 Calculations for collapse mode 1
8.10.10.2 Calculations for collapse mode 2
8.10.10.3 Calculations for collapse mode 3
8.10.10.4 Calculation of moment of resistance

8.10.11 Slab-and-beam systems
8.10.12 Corner levers

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Contents
8.10.13 Collapse mechanisms with more than one
independent variable
8.10.14 Circular fans
8.10.14.1 Collapse mechanism for a flat slab floor
8.10.15 Design of a corner panel of floor slab using yield
line analysis
8.10.16 Derivation of moment and shear coefficients for the
design of restrained slabs
8.10.16.1 Simply supported slab
8.10.16.2 Clamped slab
8.10.16.3 Slab with two discontinuous short edges
8.10.16.4 Slab with two discontinuous long edges
8.10.16.5 Slab with one discontinuous long edge
8.10.16.6 Slab with one discontinuous short edge

8.10.16.7 Slab with two adjacent discontinuous edges
8.10.16.8 Slab with only a continuous short edge
8.10.16.9 Slab with only a continuous long edge
8.11 Hillerborg’s strip method
8.11.1 Simply supported rectangular slab
8.11.2 Clamped rectangular slab with a free edge
8.11.3 Slab clamped on two opposite sides, one side
simply supported and one edge free
8.11.4 Strong bands
8.11.5 Comments on the strip method
8.12 Design of reinforcement for slabs using elastic analysis
moments
8.12.1 Rules for designing bottom steel
8.12.1.1 Examples of design of bottom steel
8.12.2 Rules for designing top steel
8.11.2.1 Examples of design of top steel
8.12.3 Examples of design of top and bottom steel
8.12.4 Comments on the design method using elastic
analysis
8.13 Stair slabs
8.13.1 Building regulations
8.13.2 Types of stair slabs
8.13.3 Design requirements
8.13.4 Example of design of stair slab
8.13.5 Analysis of stair slab as a cranked beam
8.14 References
9

Columns
9. 1 Types, loads, classification and design considerations

9.1.1
Types and loads
9.1.2
Braced and unbraced columns
9.1.3
General code provisions

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9.2

9.3

9.4

9.5

9.6

10

9.1.3
Practical design provisions
Columns subjected to axial load and bending
about one axis with symmetrical reinforcement
9.2.1
Code provisions
9.2.2
Section analysis: Concrete
9.2.3
Stresses and strains in steel
9.2.4
Axial force N and moment M
9.2.5
Construction of column design chart
9.2.5.1 Typical calculations for rectangular stress
block
9.2.5.2
Column design using design chart
9.2.5.3
Three layers of steel design chart
Columns subjected to axial load and bending about
one axis: Unsymmetrical reinforcement
9.3.1
Example of a column section subjected to axial load

and moment: Unsymmetrical reinforcement
Column sections subjected to axial load and biaxial bending
9.4.1
Outline of the problem
9.4.1.1
Expressions for contribution to moment and
axial force by concrete
9.4.1.2
Example of design chart for axial force
and biaxial moments
9.4.1.3
Axial force−biaxial moment interaction
curve
9.4.2
Approximate method given in Eurocode 2
9.4.2.1
Example of design of column section
subjected to axial load and biaxial
bending: Eurocode 2 method
Effective length of columns
9.5.1
Effective length
9.5.2
Long and short columns
9.5.3
Slenderness ratio
9.5.3.1 Example of calculating the effective length
of columns
9.5.4
Primary moments and axial load on columns

Design of slender columns
9.6.1
Additional moments due to deflection

Walls in Buildings
10.1 Functions, types and loads on walls
10.2 Design of reinforced concrete walls
10.2.1 Wall reinforcement
10.2.2 General code provisions for design
10.2.3 Design of stocky reinforced concrete walls

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10.3

10.4
10.5
11

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Walls supporting in-plane moments and axial loads
10.3.1 Wall types and design methods
10.3.2 Interaction chart
10.3.3 Example of design of a wall subjected to axial load
and in-plane moment using design chart
10.3.3.1 Example of design of a wall with

concentrated steel in end zones or columns
subjected to axial load and in-plane moment
10.3.4 Design of a wall subjected to axial load and in-plane
moment with columns at the end
10.3.5 Design of a wall subjected to axial load, out-of-plane
and in-plane moments
Design of plain concrete walls
10.4.1 Code design provisions
Reference

Foundations
11.1 General considerations
11.2 Geotechnical design
11.2.1 Geotechnical design categories
11.2.2 Geotechnical design approaches
11.2.3 Load factors for Design 1 approach
11.2.3.1 Example of calculation of bearing capacity
by Design 1 approach
11.2.3.2 Example of calculation of bearing capacity
by Design 2 approach
11.2.3.3 Example of calculation of bearing capacity
by Design 3 approach
11.2.3.4 Comments on the calculation of bearing
capacity by three design approaches
11.3 Spread foundations
11.4 Isolated pad bases
11.4.1 General comments
11.4.2 Axially loaded pad bases
11.4.2.1 Example of design of an axially loaded base
11.5 Eccentrically loaded pad bases

11.5.1 Vertical soil pressure at base
11.5.2 Resistance to horizontal loads
11.5.3 Structural design
11.5.3.1 Example of design of an eccentrically
loaded base
11.5.3.2 Example of design of a footing for a
pinned base steel portal
11.6 Wall, strip and combined foundations

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11.6.1
11.6.2
11.6.3
11.6.4

11.7

12

13

Wall footings
Shear wall footings
Strip footings

Combined bases
11.6.4.1 Example of design of a combined base
Piled foundations
11.7.1 General considerations
11.7.2 Loads in pile groups
11.7 2.1 Example of loads in pile group
11.7.3 Design of pile caps
11.8
References

Retaining Walls
12.1 Wall types and earth pressure
12.1.1 Types of retaining walls
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 slab design using Hillerborg’s strip method
12.3.6.1 Cantilever moment in vertical wall slab
12.3.7 Counterfort design using Hillerborg’s strip method
12.4 Reference
Design of Statically Indeterminate Structures
13.1 Introduction
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 Design using redistributed elastic moments in Eurocode 2
13.6 Design using plastic analysis in Eurocode 2
13.7 Serviceability considerations when using redistributed elastic
moments

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13.8

13.9

13.10
13.11
13.12
13.13
13.14

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xvii
Continuous beams
13.8.1 Continuous beams in cast-in-situ concrete floors
13.8.2 Loading on continuous beams
13.8.2.1 Arrangement of loads to give maximum
moments
13.8.2.2 Eurocode 2 arrangement of loads to give
maximum moments
13.8.2.3 The U.K. National Annex arrangement of
loads to give maximum moments
13.8.2.4 Example of critical loading arrangements
13.8.2.5 Loading from one-way slabs
13.8.2.6 Loading from two-way slabs
13.8.2.7 Analysis for shear and moment envelopes
Example of elastic analysis of continuous beam
Example of moment redistribution for continuous beam
Curtailment of bars
Example of design for the end span of a continuous beam
Example of design of a non-sway frame
Approximate methods of analysis
13.14.1 Analysis for gravity loads
13.14.2 Analysis of a continuous beam for gravity loads

13.14.3 Analysis of a rectangular portal frame for gravity
loads
13.14. 4 Analysis for wind loads by portal method

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
14.2.3.1 Wind load calculated using U.K. National
Annex
14.2.3.2 Wind load calculated using the Eurocode
14.2.4 Use of influence lines to determine positioning of
gravity loads to cause maximum design moments
14.2.5 Use of sub-frames to determine moments in members
14.2.6 Load combinations
14.2.6.1 Example of load combinations
14.3 Robustness and design of ties
14.3.1 Types of ties
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

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14.4

14.5
14.6
15

16

14.3.6 Vertical ties
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
Building design example
14.5.1 Example of design of multi-storey reinforced
concrete framed buildings
References

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Tall Buildings
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
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 horizontal 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

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642
642
642
642
643
644
645
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646
648
648

Prestressed Concrete
16.1 Introduction
16.2 Applying prestress

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Contents

xix
16.2.1

16.3

16.4
16.5

16.6
16.7

16.8

16.9
16.10
16.11
16.12

16.13

Pretensioning
16.2.1.1 Debonding
16.2.1.2 Transmission length
16.2.2 Posttensioning
16.2.3 External prestressing
16.2.4 Unbonded construction
16.2.5 Statically indeterminate structures
16.2.6 End block
Materials
16.3.1 Concrete
16.3.2 Steel
16.3.2.1 Relaxation of steel
Design of prestressed concrete structures
Limits on permissible stresses in concrete
16.5.1 Permissible compressive and tensile stress in concrete
at transfer
16.5.2 Permissible compressive and tensile stress in concrete
at serviceability limit state
Limits on permissible stresses in steel
16.6.1 Maximum stress at jacking and at transfer
Equations for stress calculation
16.7.1 Transfer state
16.7.2 Serviceability limit state
16.7.3 Example of stress calculation
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
Composite beams
16.9.1 Magnel equations for a composite beam
Posttensioned beams: Cable zone
16.10.1 Example of a posttensioned beam
Ultimate moment capacity
16.11.1 Example of ultimate moment capacity calculation
Shear capacity of a section without shear reinforcement and
uncracked in flexure
16.12.1 Example of calculating ultimate shear capacity VRd ,c
16.12.2 Example of calculating ultimate shear capacity VRd ,c
for a composite beam
Shear capacity of sections without shear reinforcement and
cracked in flexure

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Reinforced concrete design to EC 2
16.13.1 Example of calculating ultimate shear capacity VRd ,c
16.14 Shear capacity with shear reinforcement
16.14.1 Example of calculating shear capacity with shear
reinforcement
16.14.2 Example of design for shear for a bridge beam
16.14.3 Example of design for shear for a composite beam
16.15 Horizontal shear
16.15.1 Example of checking for resistance for horizontal shear
stress
16.16 Loss of prestress in pretensioned beams
16.16.1 Immediate loss of prestress at transfer
16.16.1.1 Example of calculation of loss at transfer
16.16.2 Long term loss of prestress
16.17 Loss of prestress in posttensioned beams
16.18 Design of end block in posttensioned beams
16.19 References

17

Deflection and Cracking
17.1 Deflection calculation
17.1.1 Loads on structure
17.1.2 Analysis of structure
17.1.3 Method for calculating deflection
17.1.4 Calculation of curvatures
17.1.5 Cracked section analysis
17.1.6 Uncracked section analysis
17.1.7 Long-term loads: Creep

17.1.7.1 Calculation of φ(∞,to)
17.1.7.2 Example of calculation of φ(∞,to)
17.1.8 Shrinkage
17.1.8.1 Calculation of final shrinkage strain εcd, ∞
17.1.8.2 Calculation of final autogenous shrinkage
strain εca, ∞
17.1.8.3 Calculation of final total shrinkage strain εcs, ∞
17.1.8.4 Curvature due to shrinkage
17.1.9 Curvature due to external loading
17.1.9.1 Evaluation of constant K
17.2 Checking deflection by calculation
17.2.1 Example of deflection calculation for T-beam
17.3 Calculation of crack widths
17.3.1 Cracking in reinforced concrete beams
17.4 Example of crack width calculation for T-beam
17.5 References

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713
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717

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Contents

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18

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19

A General Method of Design at Ultimate Limit State
18.1 Introduction
18.2 Limit theorems of the theory of plasticity
18.3 Reinforced concrete and limit theorems of the theory of
plasticity
18.4 Design of reinforcement for in-plane stresses
18.4.1 Examples of reinforcement calculations
18.4.2 An example of application of design equations
18.4.3 Presence of prestressing strands
18.5 Reinforcement design for flexural forces
18.6 Reinforcement design for combined in-plane and flexural
forces
18.6.1 Example of design for combined in-plane and flexural
forces
18.7 Out-of-plane shear
18.8 Strut−tie method of design
18.8.1 B and D regions
18.8.1.1 Saint Venant’s principle
18.8.2 Design of struts
18.8.3 Types of nodes and nodal zones
18.8.4 Elastic analysis and correct strut−tie model

18.8.5 Example of design of a deep beam using
strut−tie model
18.8.6 Example of design of a half joint using
strut−tie model
18.9 References
Design of Structures Retaining Aqueous Liquids
19.1 Introduction
19.1.1 Load factors
19.1.2 Crack width
19.2.2.1 Crack width control without direct
calculation
19.2 Bending analysis for serviceability limit state
19.2.1 Example of stress calculation at SLS
19.2.2 Crack width calculation in a section subjected to
flexure only
19.3 Walls subjected to two-way bending moments and tensile force
19.3.1 Analysis of a section subjected to bending moment
and direct tensile force for serviceability limit state
19.3.1.1 Example of calculation of stresses under
bending moment and axial tension
19.3.2
Crack width calculation in a section subjected
to direct tension
19.3.3
Control of cracking without direct calculation

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Reinforced concrete design to EC 2
19.4

19.5

19.6
19.7
20

Control of restrained shrinkage and thermal movement
cracking
19.4.1 Design options for control of thermal contraction and
restrained shrinkage
19.4.2 Reinforcement calculation to control early-age
cracking and thermal contraction and restrained
shrinkage
19.4.3 Reinforcement calculation to control early-age
cracking for a member restrained at one end
19.4.4 Example of reinforcement calculation to control
early-age cracking in a slab restrained at one end
19.4.5 Reinforcement calculation to control early-age
cracking in a wall restrained at one edge
19.4.6 Example of reinforcement calculation to control
early-age cracking in a wall restrained at one edge
Design of a rectangular covered top underground water tank
19.5.1 Check uplift
19.5.2 Pressure calculation on the longitudinal wall
19.5.3 Check shear capacity
19.5.4 Minimum steel area

19.5.5 Design of walls for bending at ultimate limit state
19.5.5.1 Design of transverse/side walls
19.5.5.2 Crack width calculation in transverse walls
19.5.5.3 Design of longitudinal walls
19.5.5.4 Crack width calculation in longitudinal walls
19.5.5.5 Detailing at corners
19.5.6 Design of base slab at ultimate limit state
Design of circular water tanks
19.6.1 Example of design of a circular water tank
References

U.K. National Annex
20.1 Introduction
20.2 Bending design
20.2.1 Neutral axis depth limitations for design using
redistributed moments
20.3 Cover to reinforcement
20.4 Shear design
20.4.1 Punching shear
20.5 Loading arrangement on continuous beams and slabs
20.6 Column design
20.7 Ties
20.8 Plain concrete
20.9 ψ Factors

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Contents

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Additional References

833

Index

835


Preface
The fourth edition of the book has been written to conform to Eurocode 2 covering
structural use of concrete and related Eurocode 1. The aim remains as stated in the
first edition: to set out design theory and illustrate the practical applications of code
rules by the inclusion of as many useful examples as possible. The book is written
primarily for students in civil engineering degree courses to assist them to
understand the principles of element design and the procedures for the design of
complete concrete buildings. The book will also be of assistance to new graduates
starting their careers in structural design and to experienced engineers coming to
grips with Eurocodes.
The book has been thoroughly revised to conform to the Eurocode rules. Many
new examples and sections have been added. Apart from referring to the code
clauses, reference to the full code has been made easier by using the equation
numbers from the code.
Grateful acknowledgements are extended to:
 The British Standards Institution for permission to reproduce extracts

from Eurocodes. Full copies of the standards can be obtained from
BSI Customer Services, 389, Chiswick High Road, London W4 4AL,
Tel: +44(0)20 8996 9001. e-mail:
 Professor Christopher Pearce, Deputy Head, School of Science and
Engineering , University of Glasgow, Scotland for use of the facilities.
 Mr. Ken McColl, computer manager of School of Engineering, Glasgow
University for help with computational matters.
 Dr. Lee Cunningham, Lecturer in Engineering, University of Manchester
for reviewing Chapter 19.
 Sheila, Arun, Sujaatha, Ranjana and Amit for moral support.
P. Bhatt
2 October 2013 (Mahatma Gandhi’s birthday)


ABOUT THE AUTHORS
Prab Bhatt is Honorary Senior Research Fellow at Glasgow University, UK and
author or editor of eight other books, including Programming the Dynamic
Analysis of Structures, and Design of Prestressed Concrete Structures, both
published by Taylor & Francis.
He has lectured on design of reinforced and prestressed concrete structures and
also on structural mechanics to undergraduate and postgraduate classes in
universities in India, Canada and Scotland. He has also carried out research,
theoretical and experimental, in the area of behaviour of concrete structures, and
has also been extensively involved in design office work.
Tom MacGinley and Ban Seng Choo, both deceased, were academics with
extensive experience of teaching and research in Singapore, Newcastle,
Nottingham and Edinburgh.


CHAPTER 1

INTRODUCTION
1.1 REINFORCED CONCRETE STRUCTURES
Concrete is arguably the most important building material, playing a part in all
building structures. Its virtue is its versatility, i.e. its ability to be moulded to take
up the shapes required for the various structural forms. It is also very durable and
fire resistant when specification and construction procedures are correct.
Concrete can be used for all standard buildings both single-storey and multi-storey
and for containment and retaining structures and bridges. Some of the common
building structures are shown in Fig. 1.1 and are as follows:
1. The single-storey portal supported on isolated footings.
2. The medium-rise framed structure which may be braced by shear walls or
unbraced. The building may be supported on isolated footings, strip
foundations or a raft.
3. The tall multi-storey frame and core structure where the core and rigid
frames together resist wind loads. The building is usually supported on a
raft which in turn may bear directly on the ground or be carried on piles or
caissons. These buildings usually include a basement.
Complete designs for types 1 and 2 are given. The analysis and design for type
3 is discussed. The design of all building elements and isolated foundations is
described.
1.2 STRUCTURAL ELEMENTS AND FRAMES
The complete building structure can be broken down into the following elements:
 Beams: horizontal members carrying lateral loads
 Slab: horizontal plate elements carrying lateral loads
 Columns: vertical members carrying primarily axial load but generally
subjected to axial load and moment
 Walls: vertical plate elements resisting vertical, lateral or in-plane loads
 Bases and foundations: pads or strips supported directly on the ground
that spread the loads from columns or walls so that they can be supported

by the ground without excessive settlement. Alternatively the bases may
be supported on piles.
To learn about concrete design it is necessary to start by carrying out the design
of separate elements. However, it is important to recognize the function of the
element in the complete structure and that the complete structure or part of it needs
to be analysed to obtain actions for design. The elements listed above are