Design of reinforced concrete structures

892 Pages·2013·36.72 MB·English

by  Subramanian

DESIGN OF
REINFORCED
CONCRETE
STRUCTURES
N SUBRAMANIAN
Consulting Engineer
Maryland, USA
OXFORD
UNIVERSITY PRESS
3
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First published in 2013
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ISBN-13: 978-0-19-808694-9
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Respectfully dedicated to the memory of my beloved teacher
Prof. P. Purushothaman
PREFACE
According to the World Business Council for Sustainable ABOUT THE BOOK
Development (www.wbcsd.org), concrete is the most widely used
material on earth (apart from water), with nearly three tons being Design of Reinforced Concrete Structures is designed to meet
used annually for each human being. Concrete is a construction the requirements of undergraduate students of civil and structural
material composed primarily of coarse and fi ne aggregates, cement, engineering. This book will also be an invaluable reference to
and water. Nowadays, various chemical and mineral admixtures are postgraduate students, practising engineers, and researchers.
also added to concrete to achieve the required properties. It is also This text is based on the latest Indian Standard code of practice
one of the oldest materials known to humans—the 43.3 m diameter for plain and reinforced concrete (IS 456:2000) released in July
Pantheon dome in Rome, which remains the largest coffered dome 2000 (reaffi rmed 2005) and the three amendments released in
in the world, is nearly 1900 years old. Since concrete is weak in June 2001, September 2005, and August 2007. Even though this
tension and strong in compression, reinforcements are added to fourth revision of the code gives greater emphasis to the limit
make it a composite material called reinforced concrete (RC), states method of design, it also provides working stress method
which can resist both tensile and compressive stresses. The wide in Annex B as an alternative method. SI units have been used
popularity of RC is due to its many advantages over other materials throughout the book.
such as structural steel or wood. Focusing on the modern limit states design, the book covers
The behaviour of RC structural elements is diffi cult to topics such as the properties of concrete, structural forms,
predict; one of my professors (late) Dr S.R. Srinivasan used to loadings, behaviour of various structural elements (compression
quip, the behaviour of RC is comparable to that of a drunken and tension members, beams, slabs, foundations, walls, and
monkey bitten by a scorpion! The design rules for RC structures joints) and design and detailing for fl exure, shear, torsion, bond,
developed in the past were mostly empirical in nature and were tension, compression, and compression with uniaxial and biaxial
based on extensive tests conducted on scaled specimens (which bending. It also discusses the design of fl at plates, footing and
also introduced size effects). Design of an RC structure involves pile caps, shear walls, staircases, RC joints, and multi-storey
the proportioning of different elements of the structure and buildings.
detailing them in such a way that the structure will be able to The following features in the book make it stand out among
resist all the loads that are likely to act on it during its service life, the other books in this area:
without excessive deformation or collapse. Such designs should
also be aesthetic, economical, durable, stable, and sustainable. • Even though IS 456 was revised in 2000, most of the design
RC design is often considered as much an art as a science. It provisions remain unchanged from the previous 1978 edition
must balance theoretical analysis with practical considerations of the code. Hence, IS 456 code provisions are compared
such as the probability of loads acting on it, the actual behaviour with the provisions of other recent codes, especially with the
of the structure as distinguished from the idealized analytical and provisions of ACI 318:2011(in the global economy, many
design model, the actual properties of materials used compared engineers are required to design structures using codes of
to the assumed ones, and the actual behaviour of the material other countries also).
compared to the assumed elastic behaviour. • As per the seismic zone map of India (as given in IS 1893),
Structural knowledge is increasing continuously and rapidly more than 60 per cent of the land area in India is susceptible to
as techniques for analysis, design, fabrication, and erection of seismic damage. Hence, seismic design and ductile detailing
structures are being improved constantly and new types of are given equal importance in this book. The behaviour of
structures are being introduced. Hence, designers need to have a various elements of structures and the basis for the codal rules
sound knowledge of the behaviour—both material behaviour of are also explained.
the reinforced concrete and structural behaviour of the individual • Several topics that are usually not found in other books
elements as well as the complete structure. Unless the structural such as high-strength concrete, high-strength reinforcement,
engineers are abreast of the recent developments and understand structural forms, sustainable design, integrity reinforcement,
the relationship between the structural behaviour and design various shear design procedures, various shear and punching
criteria implied by the rules of the design codes, they will be shear reinforcement, bond of coated and headed bars, space
following the codal rules rigidly and blindly and may even apply truss model of torsion design, size effect in beams and slabs,
them incorrectly in situations beyond their scope. yield line analysis of slabs, design of fl at slabs, pile caps,
This text attempts to guide students and practising structural staircases, joints, shear walls, and strut-and-tie model design
engineers in understanding and using the design codes correctly are discussed in this book.
and wisely. It also strives to make them aware of the recent • Detailed case studies of structural failures and innovations are
developments and the latest technologies and methods in use in the provided in most of the chapters to help students relate to the
area of reinforced concrete. concepts learnt through the book.
viii Preface
• A rich pedagogy provides the required rigour for students to charts available in SP 16 are also explained. Emphasis is given to
excel in this subject in the examinations: over 160 examples ductility and earthquake resistance.
with step-by-step solutions, over 850 review questions, 160
Chapter 6 deals with the design to resist shear forces. In addition
numerical problems, and over 750 illustrative fi gures and 200
to explaining the behaviour of beams under shear, factors
tables. An exhaustive reference list at the end of each chapter
affecting the behaviour, design and maximum shear strength,
helps interested readers to pursue topics further.
minimum and maximum shear reinforcement, critical section for
• Last but not the least, this book provides the most updated
shear as well as design and detailing of various types of shear
information in this subject covering the state-of-the-art trends
reinforcement based on different theories are discussed. Details
and developments.
on shear in beams with high-strength concrete and steel and shear
strength of members with axial force are also included.
USING THE BOOK
Chapter 7 discusses the bond between steel reinforcement
The text is divided into 20 chapters and completely covers the and concrete as it is necessary for the composite action of RC
undergraduate curriculum of most universities and the postgraduate members. Local and anchorage bonds are distinguished and
(PG) course of several universities. The teacher adopting this book development length provisions for various types of bars are
is requested to exercise discretion in selecting portions of the text discussed. Anchoring rebars with hooks/bends and headed bars
to be presented for a particular course. It is suggested that portions are explained and discussions on splicing and curtailment of
of Chapters 6–8, 11, 13, 16, and 18–20 may be taught at PG level reinforcement are included.
and Chapters 1–4 may be left for self-study.
Although relevant information from the Indian Standard code IS 456 considers the design of torsion approximately as additional
of practice has been included in the text, readers are advised bending moment and shear force. The plastic space truss model
to refer to the latest codes published by the Bureau of Indian considered in ACI and other codes is fully explained. The design
Standards, New Delhi—IS 456:2000, codes on design loads method based on this model and graphical methods for torsion
(IS 875 and IS 1893), design aids to IS 456 (SP 16:1980), are discussed in Chapter 8. Detailing for torsion is also explained.
handbook on concrete reinforcement and detailing (SP 34:1987),
Chapters 9–11 deal with the design of one-way, two-way, and
explanatory handbook on IS 456:1978 (SP 24:1980), and code on
fl at slabs/fl at plates respectively. In each of these chapters, the
ductile detailing of RC structures (IS 13920:1993).
behaviour of these slabs is explained and considerations for the
design are discussed. The design for concentrated load is considered
CONTENTS AND COVERAGE and design procedures as well as design using charts are explained.
Topics such as non-rectangular slabs, opening in slabs, ribbed or
The book comprises 20 chapters and fi ve appendices.
voided slabs, slabs on grade, waffl e slabs, hollow-core slabs, and
Chapter1 provides information about the historical devel opments, yield-line analysis are also covered. Flat plates are susceptible to
advantages, ingredients, and proportioning of concrete mixes. It failure in punching shear. Hence, greater emphasis has been given
also covers types of concrete and reinforcing bars and properties of to the design and detailing to prevent punching shear.
fresh and hardened concrete, since a designer should have a sound
Serviceability checks for defl ection and cracking at working
knowledge of the material that is used for designing.
loads are important for the proper functioning of structural
Chapter 2 discusses the various RC elements and possible elements during their design life. This aspect is covered in
structural forms to resist gravity as well as lateral loads and a Chapter 12, with a comparison of the provisions found in other
brief discussion on formwork. This information will be useful in codes. Vibration and fatigue control are also briefl y discussed.
practice to select the structural form.
The design of short and slender columns subjected to axial load
Many failures are attributed to the lack of determination of the as well as combined axial load and bending moment is covered
actual loads acting on structures. Hence the various loads and in Chapters 13 and 14. Different classifi cations of columns are
their combinations to be considered in the analysis are provided provided and the determination of effective length of columns is
inChapter3. explained. The design methods as well as the use of design aids
are illustrated with examples. Biaxially loaded columns as well as
Chapter 4 introduces the design considerations and the role of the
L-, T-, and +-shaped columns are also discussed.
structural designer in the complete design process. Various design
philosophies are explained with their advantages and drawbacks. Chapter 15 deals with the design of different types of footings,
Sampling and acceptance criteria are also discussed. An introduction piles, and pile caps. Soil as well as structural design and detailing
to the evolving performance-based design is also provided. are explained.
Thefl exural analysis and design of beams is discussed in Chapter Chapter16 discusses the design of load-bearing walls, retaining
5. This chapter deals with the analysis and design of singly and walls, and shear walls. Behaviour of these walls is discussed
doubly reinforced rectangular beams, fl anged beams, deep, wide and theories of earth pressures provided. Practical topics such as
and hidden beams, and lintel and plinth beams. Limits on minimum opening in walls, construction joints, drainage and compaction of
and maximum reinforcement, slenderness limits, and design using backfi ll are also included.
Preface ix
The design of different types of staircases is provided in Chapter Shaw of UK; Architects Jesse Reiser and Chad Oppenheim;
17 and design of tension members are covered in Chapter18. The Prof. Mir M. Ali of University of Illinois at Urbana-Champaign;
design of beam-column joints, and beam-t o-beam joints are provided Prof. K.S. Moon of Yale University; Prof. C.V.R. Murty
inChapter19. This chapter also discusses the design of corbels and of IIT, Madras; Prof. Mete Sozen of Purdue University;
anchors and detailing of obtuse- and acute-angled corners. M/s Tata Steel Ltd; Taylor & Francis; William Palmer
Jr (Editor-in-Chief, Concrete Construction); Er Hanns U.
As RC designs are carried out in design offi ces using standard
Baumann of BauTech, California; Mr Stefan Sommerand
computer programs, a typical analysis and design of a multi-
of Cobiax, Switzerland; Mr Kate Stevenson of Max Frank
storey building is carried out using the STAAD.Pro software in
Ltd, UK; C.M. Dordi of M/s Ambuja Cements Ltd; Ar. Jan
Chapter 20. This chapter gives the students an exposure to how
Lorant of Gabor Lorant Architets, Inc., Phoenix, Arizona;
designs are handled in practice and also guide them to use such
Mr Casper Ålander of Celsa Steel Service, Finland;
software packages.
Ms Sabrina Bénéteau of Compagnie Eiffage du Viaduc de
Appendices A–E provide some useful information such as Millau, France; Er S.A. Reddi, former Deputy Managing
properties of soils, strut-and-tie method of design, design aids, Director of Gammon India Ltd; Dr V.S. Parameswaran,
conversion factors, and some rules of thumb and practical tips. Former Director of SERC; Kenaidan Contracting Ltd,
Ontario, Canada; Mr Cary Kopczynski of Cary Kopczynski &
Though care has been taken to present error-free material, some
Company, Bellevue, Washington; Insul-Deck, LLC, Villa Rica,
errors might have crept in inadvertently. I would highly appreciate
Georgia; Er Cliff Schwinger, Vice-President of The Harman
if these errors are brought to the attention of publishers. Any
Group, Inc.; and Er N. Prabhakar, Mumbai and several others
suggestions for improvement are also welcome.
for giving me permission to use photos and fi gures originated
by them (they are acknowledged below the fi gures). My special
ACKNOWLEDGEMENTS
thanks go to Mrs Anuthama Srisailam for her help in getting
Sir Isaac Newton once said, ‘If I have seen farther than others, it photos of high-rise buildings in Chicago.
is because I have stood on the shoulders of giants.’ In the same I am privileged and grateful to Prof. B. Vijaya Rangan,
way, I have been greatly infl uenced in the preparation of this Emeritus Professor of Civil Engineering, Curtin University of
book by the books, papers, and lectures of great professors and Technology, Perth, Australia, for his encouraging words and for
designers. I would like to apologize for any phrase or illustrations writing the foreword to this book.
used in this book inadvertently without acknowledgement. I also thank all those who assisted me in the preparation of
I am grateful to my teachers (late) Prof. P. Purushothaman this book. First and foremost, I thank Er Yogesh Pisal, Senior
of College of Engineering, Guindy (now belonging to Anna Engineer (Civil), Aker Powergas Private Ltd, Mumbai for
University), and Prof. P. Sabapathy of Thiagarajar College of writing Chapter 20 on Design of Multi-storey Buildings.
Engineering, Madurai, who cultivated great interest in me about My sincere thanks are due to Prof. P. Suryanarayana, retired
designing RC structures. My understanding of this subject was Professor and former Dean (planning and development) of
greatly infl uenced by the books and publications of several Maulana Azad National Institute of Technology, Bhopal (MP),
authors listed in the Bibliography section at the end of the book. for going through all the chapters patiently and offering useful
I have also learnt a lot from the discussions I had on several comments; Er R.K. Desai, Former Chief Engineer (Civil), ITI
occasions with Prof. A.R. Santhakumar (former Dean of Anna Ltd, Bangalore for providing many tables of Appendix C; Er V.M.
University and Professor at IIT Madras). Rajan, Superintending Engineer (Civil) TANGEDCO, Chennai
I thank the following organizations/publishers for permitting for providing many tables of Appendix D; Er Rahul Leslie for
me to reproduce material from their publications: American his help in providing computer solutions to some problems;
Concrete Institute (ACI), Farmington Hills, Michigan; American Er Naseef Ummer of IIT Delhi and Er Hemal Mistry for their
Society of Civil Engineers (ASCE), Reston, Virginia; Mr Toru help in locating the literature; and Er Pankaj Gupta of Roark
Kawai, Executive Director of Japan Concrete Institute (JCI); Consulting, Noida, UP, for sharing Australian and New Zealand
Structural Engineers Association of California (SEAOC), The codes. I also thank my several friends at www.sefi ndia.org (in
Indian Concrete Journal, Mumbai; Indian Concrete Institute, particular, Er T. Rangarajan, Er Vikramjeet, Er P.K.Mallick,
Chennai; NBM & CW, New Delhi; Elsevier Ltd; Oxford, UK; Er Vivek Abhyankar, and Er E.S. Jayakumar) for sharing their
Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany; knowledge, and Er Siddique and Er Ganesh of Nagpur for their
NISEE-PEER Library, University of California, Berkeley; encouragement.
Prof. Durgesh Rai, Coordinator, NICEE, IIT Kanpur; and I will be failing in my duty if I do not acknowledge the help
Ar. Daniel Safarik, Editor, Council on Tall Buildings and and wonderful assistance I received from Ms S. Chithra at all the
Urban Habitat(CTBUH), Chicago. I also thank Concrete stages of this book. Lastly, I acknowledge the excellent support
Reinforcing Steel Institute (CRSI), Schaumburg, Illinois; and coordination provided by the editorial team of Oxford
Portland Cement Association (PCA), Skokie, Illinois; Mr Chris University Press, India.
Dr N. Subramanian
Gaithersburg, Maryland, USA
FOREWORD
The global use of concrete is second only to water. We have been designing, constructing, using, and maintaining numerous concrete
structures in the past century to fulfi l our infrastructure demands. All this professional experience, along with extensive research, has
guided us to understand the construction and behaviour of concrete structures. This vast knowledge is transferred through books and
research publications.
This book on concrete structures is outstanding in every way; congratulations to Dr Subramanian for writing such a marvellous
and useful book! Dr Subramanian has an extensive professional and research experience. He has been involved in the design and
construction of over 650 projects, and published several books and over 200 research papers. He has received many awards and
prizes for his contributions, including the Scientist of the Year Award from the Tamil Nadu Government in India. He has used his vast
professional experience, in-depth knowledge, and r esearch outputs to produce this outstanding book.
This book is unique in many aspects. It contains extensive information on design and construction of concrete structures. The
following are some of the highlights of this book:
• Numerous photographs and well-labelled illustrations
• Clear numerical examples that are helpful to both young readers and professional engineers
• Case studies that clearly illustrate the topic discussed
• Subject matter in each chapter is extensively covered with useful information
• Review questions and exercises at the end of each chapter, which are again useful to students and refreshing for professional
engineers
• Extensive list of references at the end of each chapter for further reading
This book will be highly cherished by the budding and professional engineers alike. Dr Subramanian has performed a great service
to concrete construction by writing this book. I am privileged and honoured to write this Foreword. Congratulations once again to Dr
Subramanian, and wish this book a great success!
Dr B. Vijaya Rangan
Emeritus Professor of Civil Engineering
Curtin University
Perth, Australia
BRIEF CONTENTS
Features of the Book iv
Foreword vi
Preface vii
Detailed Contents xi
List of Symbols xvii
1. Introduction to Reinforced Concrete 1
2. Structural Forms 45
3. Loads and Load Combinations 70
4. Basis of Structural Design 102
5. Flexural Analysis and Design of Beams 142
6. Design for Shear 214
7. Design for Effective Bond between Concrete and Steel 262
8. Design for Torsion 306
9. Design of One-way Slabs 334
10. Design of Two-way Slabs 362
11. Design of Flat Plates and Flat Slabs 415
12. Serviceability Limit States: Defl ection and Crack Control 467
13. Design of Axially Loaded Short Columns 506
14. Design of Columns with Moments 546
15. Design of Footings and Pile Caps 585
16. Design of RC Walls and Structural Walls 644
17. Design of Staircases 702
18. Design of Tension Members 726
19. Design of Joints 743
20. Design of Multi-storey Buildings 790
Appendix A: Properties of Soils 809
AppendixB: Design Using Strut-and-tie Model 813
Appendix C: Analysis and Design Aids 822
Appendix D: Practical Tips and Some Rules of Thumb 839
Appendix E: Conversion Factors 850
Bibliography 853
Index 854
DETAILED CONTENTS
Features of the Book iv
Foreword vi
Preface vii
Brief Contents x
List of Symbols xvii
1. Introduction to Reinforced Concrete 1 2.3.2 One-way and Two-way Slab Systems 52
2.3.3 T wo-way Flat Plates and Flat Slabs 54
1.1 I ntroduction 1
2.3.4 Grid Floors 56
1.1.1 Brief History 2
2.3.5 Composite Floors 56
1.1.2 Advantages and Disadvantages of Concrete 3
2.4 Precast and Prestressed Concrete Buildings 56
1.2 C oncrete-making Materials 4
2.5 Lateral Load Resisting Systems 57
1.2.1 Cement (Portland Cement and Other Cements) 4
2.5.1 Rigid or Moment-resisting Frames 58
1.2.2 Aggregates 8
2.5.2 Shear-walled Frame Systems 58
1.2.3 Water 10
2.5.3 Outrigger and Belt Truss Systems 59
1.2.4 Admixtures 11
2.5.4 Framed-tube Systems 60
1.3 Proportioning of Concrete Mixes 13
2.5.5 Braced-tube Systems 60
1.4 Hydration of Cement 16
2.5.6 Tube-in-tube and Bundled-tube Systems 61
1.5 Types of Concrete 17
2.5.7 Diagrid Systems 62
1.5.1 Ready-mixed Concrete 17
2.5.8 Other Systems 62
1.5.2 High-performance Concrete 18
2.5.9 Transfer Girders 62
1.5.3 Structural Lightweight Concrete 20
2.6 Structural Integrity 64
1.5.4 Fibre-reinforced Concrete 21
2.7 Slip-form and Jump-form Constructions 66
1.5.5 Ductile Fibre-reinforced Cementitious Composites 21
2.7.1 Slip-form Construction 66
1.5.6 Ferrocement 23
2.7.2 Jump-form Construction 66
1.6 Reinforcing Steel 24
1.6.1 Corrosion of Rebars 26
1.7 Concrete Mixing, Placing, Compacting, and Curing 27 3. Loads and Load Combinations 70
1.8 Properties of Fresh and Hardened Concrete 29
3.1 Introduction 70
1.8.1 Workability of Concrete 29
3.2 Characteristic Actions (Loads) 70
1.8.2 Compressive Strength 29
3.3 Dead Loads 72
1.8.3 Stress–Strain Characteristics 32
3.4 Imposed Loads 72
1.8.4 Tensile Strength 33
3.4.1 Consideration of Slab Loads on Beams 73
1.8.5 Bearing Strength 33
3.4.2 Consideration of Wall Loads on Beams 74
1.8.6 Modulus of Elasticity and Poisson’s Ratio 33
3.5 Impact Loads 75
1.8.7 Strength under Combined Stresses 35
3.6 Snow and Ice Loads 75
1.8.8 Shrinkage and Temperature Effects 35
3.7 Wind Loads 75
1.8.9 Creep of Concrete 36
3.7.1 Vortex Shedding 77
1.8.10 Non-destructive Testing 36
3.7.2 Dynamic Effects 78
1.9 Durability of Concrete 36
3.7.3 Wind Effects on Tall Buildings 79
3.8 Earthquake Loads 80
3.8.1 Natural Frequencies 82
2. Structural Forms 45
3.8.2 Equivalent Static Method 83
2.1 Introduction 45 3.8.3 Rules to be Followed for Buildings in Seismic
2.2 Basic Structural Elements 46 Areas 84
2.2.1 Footings 47 3.8.4 Devices to Reduce Earthquake Effects 85
2.2.2 Columns 47 3.9 Other Loads and Effects 86
2.2.3 Beams 48 3.9.1 Foundation Movements 87
2.2.4 Slabs 48 3.9.2 Thermal and Shrinkage Effects 87
2.2.5 Walls 48 3.9.3 Soil and Hydrostatic Pressure 88
2.2.6 Trusses 49 3.9.4 Erection and Construction Loads 89
2.3 Floor and Roof Systems 51 3.9.5 Flood Loads 89
2.3.1 Bearing Wall Systems 51 3.9.6 Axial Shortening of Columns 89
xii Detailed Contents
3.10 Pattern Loading 90 5.5.6 Slenderness Limits for Rectangular Beams 157
3.11 Load Combinations 90 5.5.7 Guidelines for Choosing Dimensions and Reinforcement
of Beams 158
5.5.8 Procedure for Proportioning Sections for
4. Basis of Structural Design 102 Given Loads 160
5.5.9 Design of Over-reinforced Sections 162
4.1 Introduction 102
5.5.10 Design Using Charts and Design Aids 162
4.2 Steps Involved in Construction 102
5.6 Doubly Reinforced Rectangular Beams 162
4.3 Roles and Responsibilities of Designers 103
5.6.1 Behaviour of Doubly Reinforced Beams 164
4.4 Design Considerations 105
5.6.2 Analysis of Doubly Reinforced Rectangular
4.4.1 Safety 105
Beams 165
4.4.2 Stability 108
5.6.3 Limiting Moment of Resistance and Compression
4.4.3 Serviceability 109
Steel 166
4.4.4 Economy 109
5.6.4 Design of Doubly Reinforced Rectangular Beams 166
4.4.5 Durability 109
5.6.5 Design Using Charts and Design Aids 168
4.4.6 Aesthetics 116
5.7 Flanged Beams 168
4.4.7 Environment Friendliness 116
5.7.1 Effective Width of Flange 169
4.4.8 Functional Requirements 118
5.7.2 Behaviour of Flanged Beams 170
4.4.9 Ductility 120
5.7.3 Analysis of Flanged Beams 171
4.5 Analysis and Design 121
5.7.4 Minimum and Maximum Steel 174
4.5.1 Relative Stiffness 122
5.7.5 Doubly Reinforced Flanged Beams 176
4.5.2 Redistribution of Moments 124
5.7.6 Design of Flanged Beams 178
4.6 Codes and Specifi cations 125
5.7.7 Design of Flanged Beams Using Charts
4.7 Design Philosophies 126
and Design Aids 179
4.7.1 Working Stress Method 127
5.7.8 Design of L-beams 180
4.7.2 Ultimate Load Design 129
5.8 Minimum Flexural Ductility 180
4.7.3 Principles of Limit States Design 129
5.9 Deep Beams 181
4.7.4 Sampling and Acceptance Criteria 131
5.10 Wide Shallow Beams 185
4.8 Limit States Method 132
5.11 Hidden Beams 185
4.8.1 Limit States of Strength 133
5.12 Lintel and Plinth Beams 186
4.8.2 Serviceability Limit States 135
5.13 High-strength Steel and High-strength Concrete 187
4.9 Design by Using Model and Load Tests 136
5.14 Fatigue Behaviour of Beams 188
4.10 Strut-and-tie Model 136
4.11 Performance-based Design 136
6. Design for Shear 214
5. Flexural Analysis and Design of Beams 142
6.1 Introduction 214
5.1 Introduction 142 6.2 Behaviour of Reinforced Concrete Beams under Shear 215
5.2 Behaviour of Reinforced Concrete Beams in Bending 143 6.2.1 Behaviour of Uncracked Beams 215
5.2.1 Uncracked Section 143 6.2.2 Behaviour of Beams without Shear
5.2.2 Cracking Moment 145 Reinforcement 218
5.2.3 Cracked Section 145 6.2.3 Types of Shear or Web Reinforcements 220
5.2.4 Yielding of Tension Reinforcement and Collapse 146 6.2.4 Behaviour of Beams with Shear/Web
5.3 Analysis of and Design for Flexure 146 Reinforcements 227
5.3.1 Effective Span 146 6.3 Factors Affecting Shear Strength of Concrete 229
5.4 Analysis of Singly Reinforced Rectangular Sections 146 6.4 Design Shear Strength of Concrete in Beams 231
5.4.1 Assumptions Made to Calculate Ultimate 6.4.1 Maximum Shear Stress 233
Moment of Resistance 146 6.4.2 Effects Due to Loading Condition 234
5.4.2 Design Bending Moment Capacity of 6.5 Critical Section for Shear 234
Rectangular Section 149 6.6 Minimum and Maximum Shear Reinforcement 236
5.4.3 Balanced, Under-reinforced, and Over-reinforced 6.6.1 Maximum Spacing 236
Sections 150 6.6.2 Upper Limit on Area of Shear Reinforcement 237
5.4.4 Depth of Neutral Axis 151 6.7 Design of Shear Reinforcement 237
5.4.5 Resisting Moment Strength for Balanced 6.7.1 The Ritter–Mörsch Truss Model 238
Sections 152 6.7.2 Modifi ed Compression Field Theory 240
5.5 Design of Singly Reinforced Rectangular 6.7.3 Design Procedure for Shear Reinforcement 241
Sections 153 6.7.4 Transverse Spacing of Stirrups in Wide Beams 242
5.5.1 Minimum Depth for Given M 153 6.7.5 Design Aids 242
u
5.5.2 Limiting Percentage of Steel 153 6.7.6 Anchoring of Shear Stirrups 242
5.5.3 Factors Affecting Ultimate Moment Capacity 154 6.8 Shear Design of Flanged Beams 243
5.5.4 Minimum Tension Reinforcement 154 6.9 Shear Design of Beams with Varying Depth 243
5.5.5 Maximum Flexural Steel 156 6.10 Shear Design of Beams Located in Earthquake Zones 244