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Reinforced Cement Concrete & Pre-stressed Concrete Comprehensive Theory with Solved Examples and Practice Questions

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First Edition: 2014 Reprint: 2015 Second Edition (Revised and Updated): 2016

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Preface This book was motivated by the desire to further the evolution of a concise book on RCC and Pre-stressed Concrete. Keeping in focus the importance of this subject in GATE and ESE, we have done a proper study and thereafter developed the content of the book accordingly. This edition has an expanded discussion of all relevant topics in the subject. Initially, we compiled the perceptions of our students on their problems in GATE and ESE while dealing with the questions from this subject. We identified their various problems like- lack of fundamentals of the subject, difficulty in solving simple solutions, shortage of a complete study package, etc. These strengthened our determination to present a complete edition of RCC and Pre-stressed Concrete textbook. The book addresses all the requirements of the students, i.e. comprehensive coverage of theory, fundamental concepts, objective type problems and conventional problems, articulated in a lucid language. The concise presentation will help the readers grasp the concepts with clarity and apply them with ease to solve problems quickly. The books not only covers the entire syllabus of GATE and ESE, but also addresses the need of many other competitive examinations. Topics like ‘Basic Design Concepts, Working Stress Method (WSM) of Design, Analysis and Design by LSM, Doubly Reinforced Beam Design by LSM, Design for Shear in Reinforced Concrete, Design for Bond Reinforced Concrete, Design for Torsion in Reinforced Concrete, Analysis and Design of Flanged Beams by LSM, Limit State of Serviceability, Two Way Slab Design, Design of Compression Members and Columns, Design of Reinforced Concrete Shallow Foundation, Prestressed Concrete, Masonry Design working stress methods and limit state methods, pre-stress concrete’, are given full coverage in line with our research on their importance in competitive examinations. We have put in our sincere efforts to present elaborate solutions for various problems, different problem solving methodology, some useful quick techniques to save time while attempting MCQs without compromising the accuracy of answers. A summary of important points to remember is added at the end of each topic. For the convenience of readers, points to remember are specifically highlighted in the form of a note- both in theory as well as solved examples. At the end of each chapter, sets of practice question are given with their keys, that will allow the readers to evaluate their understanding of the topics and sharpen their problem solving skills. Our team has made their best efforts to remove all possible errors of any kind. Nonetheless, we would highly appreciate and acknowledge if you find and share with us any printing, calculation and conceptual error. It is impossible to thank all the individuals who helped us, but we would like to sincerely thank all the co-authors, editors and reviewers for putting in their efforts to publish this book. We also express our thanks to MADE EASY publications for completing and publishing the book on time. With Best Wishes B. Singh CMD, MADE EASY

Contents

Reinforced Cement Concrete & Pre-stressed Concrete

Chapter 1 Introduction��������������������������������������������������������� 1



2.4

Tests on Cement.............................................................14



1.1

Introduction....................................................................... 1



2.5

Methods to Increase the Durability of Concrete



1.2

Types of Concrete............................................................ 1



1.3 Importance of Design Codes in the Design of

against Chemical Attack..............................................15

2.6

Concrete Structures......................................................15

Structures........................................................................... 2

1.4

Characteristic Strength of Concrete.......................... 3



1.5

Grade of Concrete............................................................ 4



1.6

Concrete Mix Design...................................................... 4



1.7

Steps Involved in Mix Design of Concrete as per IS

1.8



1.10 Modulus of Elasticity and Poisson’s Ratio of

Behaviour of Concrete in Tension.............................. 9

1.11 Effect of Duration of Loading on Stress Strain Curve..................................................................................11



1.12 Creep of Concrete..........................................................11



1.13 Compressive Strength of Concrete in the Design



2.8

IS 456: 2000 Recommendations for .......................19



2.9

Various types of Young’s Modulus of Elasticity of

2.10 Properties of Reinforcement and its use in



2.11 Cover Requirements as per IS 456: 2000.................... 25



2.12 Spacing of Reinforcement..........................................25



2.13 Other Important Considerations in Reinforced Concrete............................................................................25

Concrete............................................................................10

Load and Resistance Factor Design........................18

Reinforced Concrete Structures...............................23

Compression...................................................................... 8 1.9

2.7



Behaviour of Concrete under Uniaxial





Concrete (Ec)....................................................................22

Recommendation............................................................ 5

Design Philosophies for the Design of Reinforced



2.14 Major Reasons of Structure Failure..........................27



2.15 List of Major Indian Standard (IS) Codes Relating to Reinforced Concrete................................................27



2.16 Major Challenges for a Structural Designer......................28



Objective Brain Teasers..................................................28

of Structures....................................................................12

Chapter 3

Chapter 2

Working Stress Method of Design���������� 30

Basic Design Concepts�����������������������������������13



3.1

Introduction.....................................................................30



2.1

Introduction.....................................................................13



3.2

Proceeding from Bending Moments to Flexural



2.2

Necessity of Designing Reinforced Concrete

Stresses..............................................................................30

Structures.........................................................................13

2.3



Hydraulic and Non-Hydraulic Cements...................... 14

3.3

Analysis of Composite/Non-homogeneous Sections.............................................................................30

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3.4

Stress-strain Distribution............................................30





3.5

Transformed Section....................................................31



Objective Brain Teasers............................................... 105



3.6

Modular Ratio..................................................................32



Conventional Practice Questions............................. 108



3.7

Transformed Area of Reinforcement-

4.12 Transverse Moments in One Way Slabs...................... 96



Tension Steel...................................................................33

Chapter 5



Transformed Area of Reinforcement-Compression

Design of Doubly Reinforced Beam by Limit State Method������������������������������������� 109

3.8

Steel....................................................................................33

3.9

Cracking Moment..........................................................33



3.10 Behaviour of Reinforced Concrete in Flexure...........................33



3.11 Location of Reinforcing Bars in Beam Section....35



3.12 Usefulness of Concrete in Tension Side....................... 35



3.13 Permissible Stresses in Concrete and Steel..........35



3.14 Assumptions in the analysis of beams by working stress method (at service loads)...............................36



3.15 Design of Reinforced Concrete Structures .......................37



3.16 Singly Reinforced Sections.........................................37



3.17 Doubly Reinforced Beam Section............................40



3.18 Singly Reinforced Flanged Section..........................42



3.19 Doubly Reinforced Flanged Section.......................43



3.20 Limitations of WSM of Design...................................43



Objective Brain Teasers..................................................55



Conventional Practice Questions................................56

Introduction.....................................................................57



4.2

Analysis of Beams by LSM...........................................57



4.3

Assumptions in the Analysis Design by LSM.......57



4.4

Analysis of Singly Reinforced Sections..................60



4.5

Requirements of Flexural Design.............................74



4.6

Deflection Control by Limiting the



Span/Depth Ratio..........................................................77



4.7

Selection of Member Sizes.........................................78



4.8

Design of Reinforced Concrete Rectangular

4.9



4.11 Slabs as Rectangular Beams.......................................96

Doubly Reinforced Beam Section......................... 109



5.3

Hanger Bars v/s Compression Reinforcement.......109



5.4

Analysis of Doubly Reinforced Rectangular



Beam Sections............................................................. 110



5.5

Limiting Moment of Resistance............................. 111



5.6

Balanced Doubly Reinforced Sections......................111



5.7

Design of Doubly Reinforced Rectangular



Beam Section............................................................... 112



5.8

Design Steps for a Given Factored Moment (Mu)......114



5.9

Deflection Control in Doubly Reinforced Beams.......114



Objective Brain Teasers............................................... 124



Conventional Practice Questions............................. 125



6.1

Introduction.................................................................. 126



6.2

Shear in Reinforced Concrete................................. 126



6.3

Shear Stress Distribution in Rectangular

6.4

Combined Effect of Bending Stress and



Shear Stress in a Beam.............................................. 130



6.5

Shear Transfer Mechanism...................................... 131



6.6

Nominal Shear Stress................................................. 132



6.7

Critical Sections for Shear........................................ 133



6.8

Design Shear Strength of Concrete without



Shear Reinforcement................................................. 134



Shear Strength of Concrete with Shear

6.9

Reinforcement............................................................. 135

Types of Beams...............................................................82

4.10 Comparison between WSM and LSM of Design..... 84

5.2



Reinforcement Arrangement in Different





Homogeneous Section............................................. 127

Beams.................................................................................79

Introduction  ............................................................. 109

Design for Shear in Reinforced Concrete��126

Analysis and Design by Limit State Method (LSM)����������������������������������������������������57 4.1

5.1

Chapter 6

Chapter 4





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6.10 Minimum Shear Reinforcement............................ 138



6.11 Maximum Spacing of Shear Reinforcement..... 139



6.12 Steps for Shear Reinforcement Design.....................139



6.13 Shear Connectors in Members Subjected



8.9

Design for Torsion as per Working Stress Method.....171

8.10 Design for Torsion as per Limit State Method........173



to Flexure....................................................................... 139





Objective Brain Teasers............................................... 151



Objective Brain Teasers............................................... 184



Conventional Practice Questions............................. 153



Conventional Practice Questions............................. 185

Chapter 7

Chapter 9

Design for Bond in Reinforced Concrete����154

7.1

Introduction.................................................................. 154

Analysis and Design of Flanged Beams by LSM����������������������������� 186



7.2

Bond in Reinforced Concrete.................................. 154



9.1

Introduction.................................................................. 186



7.3

Mechanism of Force Transfer.................................. 154



9.2

Flanged Beams............................................................ 186



7.4

Bond Stress................................................................... 155



9.3

Effective Width of Flange......................................... 187



7.5

Various Types of Bond............................................... 155



9.4

Compressive Stress Distribution in the Flange......188



7.6

Flexural Bond............................................................... 155



9.5

Analysis of Flanged Beams Sections (by Limit



7.7

Anchorage/Development Bond............................ 156



7.8

Development Length................................................ 157



9.6

Derivation of the Expression to Determine ‘yf’.......195



7.9

Mechanisms of Bond Failure................................... 159



9.7

Types of Analysis Problems..................................... 195



7.10 Factors affecting the Bond Strength.................... 159



9.8

Integral Action of Slab and Beam......................... 195



7.11 Bends, Hooks and Mech. Anchorages.......................159



9.9

Design of Flanged Beam Sections (by Limit State



7.12 Anchoring Bars in Tension....................................... 160



7.13 Anchoring Bars in Compression............................ 160



Objective Brain Teasers............................................... 203



7.14 Mechanical Devices for Anchorages.................... 160



Conventional Practice Questions............................. 204



7.15 Anchoring Shear Reinforcement........................... 160



7.16 Reinforcement Splicing............................................ 161



Objective Brain Teasers............................................... 162



Conventional Practice Questions............................. 164

State Method).............................................................. 188

Method).......................................................................... 196

Chapter 10 Limit State of Serviceability-Deflection and Cracking�������������������������������������������������� 205

Chapter 8



10.1 Introduction.................................................................. 205



10.2 The Limit States of Serviceability-Deflection

Design for Torsion in Reinforced Concrete������������������������������������165



10.3 Limit State of Serviceability: Deflection...........................206



8.1

Introduction.................................................................. 165



10.4 Limit State of Serviceability: Cracking.......................212



8.2

Design for Torsion....................................................... 165



10.5 Other Limit States of Serviceability...................... 213



8.3

Mechanism of Torsion in Reinforced



and Cracking................................................................ 205

Objective Brain Teasers............................................... 214



Concrete Structures................................................... 165



8.4

Plain Concrete Subjected to Torsion.................... 167

Chapter 11



8.5

Torsionally Reinforced Concrete Subjected

Two Way Slab Design���������������������������������� 215



to Torsion....................................................................... 168



8.6

Analysis for Torsion..................................................... 169



8.7

Torsional Reinforcement.......................................... 169



8.8

IS 456: 2000 Provisions for the Design of Reinforcement in Members Subjected to Torsion.....170



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11.1 Introduction.................................................................. 215



11.2 One Way v/s Two Way Slabs.................................... 215



11.3 Dealing with Torsion in Two Way Slabs.....................217



11.4 Wall-Supported and Column/Beam Supported Slabs ......................................................... 218



11.5 Design of Wall-supported (or Rigid Beam



12.20 Limitations of Design Charts of SP-16.....................264

Supported) Two-Way Slabs..................................... 218



Objective Brain Teasers............................................. 269



11.6 Thickness of Slabs  .................................................. 218



Conventional Practice Questions.......................... 271



11.7 Analysis of Two Way Slabs....................................... 219



11.8 Shear in Two Way Uniformly Loaded Slabs........ 224



Objective Brain Teasers............................................... 235



Conventional Practice Questions............................. 236

Chapter 13 Design of Reinforced Concrete Shallow Foundations��������������������������������� 272

13.1

Introduction............................................................... 272



13.2

Footings....................................................................... 272

Design of Compression Members/Columns���������������������������������������237



13.3

Footing as a Structural Element.......................... 272



13.4

Types of Footings...................................................... 273



12.1 Introduction.................................................................. 237



13.5

Distribution of Soil Pressure under Isolated



12.2 Compression Member/Column in a Structure......237



12.3 Classification of Columns......................................... 237



12.4 Shear Consideration in Columns........................... 240



12.5 IS 456: 2000 Recommendations for the

Chapter 12



Footings....................................................................... 277

Footing Design: General Requirements and Codal (IS 456 : 2000) Provisions........................... 280

Design of Columns..................................................... 240

12.6 Design of Short Columns under Axial Compression................................................................. 243



13.6

12.7 Design of short columns with Axial Load and



13.7

Plain Concrete Footings......................................... 286



13.8

Design of Rectangular Isolated Footing.......................288



13.9

Design of Sloped Isolated Footing..................... 291



13.10 Design of Circular Isolated Footing of



Uniform Thickness.................................................... 292

Uniaxial Bending......................................................... 250



13.11 Design of Wall............................................................ 293



12.8 Failure Modes in Eccentric Compression..................251



13.12 Design of Combined Footings............................. 311



12.9

Design Strength of Axially Loaded Short



13.13 Soil Pressure Distribution in Combined Footing.....311

Columns with Uniaxial Bending.......................... 252



13.14 Geometric Design of Combined Footings....... 311



12.10 Interaction Charts as Analysis Aids.................... 253



13.15 Design Aspects of Two Column Combined



12.11 Design Aids as Non-dimensional Interaction

Footing......................................................................... 311

Diagrams...................................................................... 254



13.16 Combined Footing of Beam-Slab....................... 311



12.12 Design Charts of SP-16........................................... 254



Objective Brain Teasers............................................. 318



12.13 Design of Short Columns under Axial



Conventional Practice Questions.......................... 320

Compression and Biaxial Bending...................... 255

12.14 Interaction Surface................................................... 255

Chapter 14



12.15 IS 456: 2000 Procedure for the Design of

Prestressed Concrete��������������������������������� 321



Columns with Axial Load and Bi-axial Bending..256

12.16 Design Steps for the Design of Column with Axial Load and Bi-axial Bending.......................... 256



12.17 Design of Long/Slender Columns....................... 260



12.18 Analysis of Slender/Long Columns.................... 261



12.19 Provisions for the Design of Slender





14.1 Introduction................................................................ 321



14.2 Need of High Strength Concrete in



Prestressing................................................................. 321



14.3 Need of High Tensile Steel in Prestressing....... 322



14.4 Relative Comparison of Prestressed and Reinforced Concrete Beam.................................... 322

Columns as per IS 456: 2000................................. 261



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14.5 Terminologies............................................................. 322



14.6 Advantages of Prestressed Concrete........................324



14.21 Tendon Stresses: Effect of Loading on



14.7 Design of High Strength Concrete Mixes.....................325





14.8 High Tensile Steel...................................................... 326





14.9 Cover Requirements in Prestressed Concrete



Tensile Stresses in Tendons.................................... 347

14.22 Stresses in Beam at Different Stages of Loading......................................................................... 349

Members...................................................................... 327



14.23 Prestress Losses3....................................................... 350



14.10 Protection of Prestressing Steel........................... 327



14.24 Cracking Moment..................................................... 358



14.11 Prestressing System.................................................. 327



14.25 Design of Prestressed Concrete Beam



14.12 Tensioning Devices................................................... 327



Members...................................................................... 360



14.13 Pre-tensioning and Post-tensioning Systems......328



Objective Brain Teasers............................................. 377



14.14 Assumptions in the Analysis and Design of



Appendix-A.............................................................................. 380

Prestressed Concrete Members........................... 330



Masonry Design



14.15 Analysis of Prestress................................................. 331



Introduction................................................................... 380



14.16 Prestress Pressure Distribution in Beams......................336



Masonry Reinforcement............................................ 383



14.17 Effect of Loading on Stresses in Tendons......... 337



Effective Height of Walls............................................ 384



14.18 Prestressed Beam with Parabolic



Effective Length of Walls............................................ 385



Tendon Profile............................................................ 338



14.19 P-line or Pressure Line............................................. 339



14.20 The Concept of Load Balancing........................... 344



Appendix-B..............................................................386

Objective Brain Teasers................................................ 386

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