Civil Engineering
Reinforced Cement Concrete & Pre-stressed Concrete Comprehensive Theory with Solved Examples and Practice Questions
Publications
Publications
MADE EASY Publications Corporate Office: 44-A/4, Kalu Sarai (Near Hauz Khas Metro Station), New Delhi-110016 E-mail:
[email protected] Contact: 011-45124660, 8860378007 Visit us at: www.madeeasypublications.org
Reinforced Cement Concrete & Pre-stressed Concrete © Copyright, by MADE EASY Publications. All rights are reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted in any form or by any means (electronic, mechanical, photo-copying, recording or otherwise), without the prior written permission of the above mentioned publisher of this book.
First Edition: 2014 Reprint: 2015 Second Edition (Revised and Updated): 2016
© All rights reserved by MADE EASY PUBLICATIONS. No part of this book may be reproduced or utilized in any form without the written permission from the publisher.
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
(iv)
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
(v)
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
(vi)
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
(vii)
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
nnnn
(viii)
