- - —- ■ —. —X -------------------------------------- - • \ I | ’ # i^?.y \ 4 i«e v fl I J ; SbJ? ,rJ j^-p .. C2222JI-• pB^x i JJ-zixjJ kJ J J (IS : 456-2000) 2nd Edition • • N. KRISHNA RAJU Preface The extensive use of reinforced concrete for a variety of structural members has necessitated a proper understanding of the design in structural concrete members by the structural engineers. The wide spread use of reinforced con crete is the natural outcome of the rapid development in the theory and design procedures with the introduction of the philosophy of limit state design. The book presents the design of a variety of reinforced concrete structures like Continuous beams, Portal frames, Silos, Bunkers, Chimneys, Shells Overhead Water tanks, Virendeel girders, Trusses, Deep beams, Box culverts, Folded plates, Hyperbolic cooling towers, Curved girders, Poles, Pipes and Bridge deek systems. The design of these advanced reinforced concrete struc tures conform to the revised Indian Standard Code IS :456-1978 and S.I. units have been adopted for all the design examples. The topics covered are intended to meet the requirements of graduate and post graduate curicula of most of the engineering institutions in India. The book is primarily design oriented with more emphasis on types of design with minimum extent of theory, presented wherever required for application in design. The various design steps are identified and provided in a logical sequence. The book is extensively illustrated with working drawings showing the reinforcement details. The examples for practice provided at the end of each chapter is intended to help the students preparing for university examinations. The references provided at the end of the book have been extensively used in the preparation of the text and are gratefully acknowledged. The author is grateful to his wife, Pramila and daughters Sarvamangala and Amrutha for extending their fullest co-operation in the preparation of the type script. Finally the author welcomes .constructive criticisms and suggestions which will immensely help in updating the contents of the book. Bangalore N. KRISHNA RAJU January, 1986 © N. KRISHNA RAJU First Published ; 1986 First Reprint : 1988 All rights reserved. No part of this book may be reproduced or transmitted without the prior and written permission from the author and the publisher. Distributors: College Book Store 1701-2, Nai Sarak, Delhi-110006 Published by Satish Kumar Jain for CBS Publishers & Distributors 485, Jain Bhawan, Bhola Nath Nagar, Shahdra, Delhi-110032 Printed at Nazia Printers, Lal Kuan, Delhi-110006. Contents Preface v List of symbols xiii 1. Continuous Beams I 1.1 Introduction 1 1.2 Effective span 1 1.3 Span/depth ratio 2 1.4 Bending moments and shear forces 2 1.5 Design Example 4 1.6 Design Example 6 1.7 Examples for Practice 9 ’ 2. Bunkers and Silos 11 2.1 Introduction 11 2.2 Difference between bunker and silo. 11 2.3 Design of square or rectangular bunkers 13 2.4 Design of circular bunkers 17 2.5 Design Example 17 2.6 Design Example 21 2.7 Design of battery of bunkers 26 2.8 Design of silos 27 2.9 Silos for storage of cement 33 2.10 Design Example 35 2.11 Design Example 39 2.12 Design Example 40 2.13 Examples for Practice 42 3. Chimneys 44 3.1 General 44 3.2 Parts of Chimney 44 3.3 Design Factors 45 3.4 Stresses in R.C. Shafts due to self weight and wind loads 46 viii Contents 3.5 Stresses in Horizontal Reinforcement due to shear force 49 3.6 Stresses due to Temperature difference 50 3.7 Design Example 57 3.8 Design Example 57 3.9 Design Example 64 3.10 Design of Reinforcements in Chimneys using Charts 66 3.11 Analysis and design of R.C. Chimneys subjected to Dynamic loads 67 3.12 Examples for Practice 67 4. Curved Beams 69 4.1 General 69 4.2 Analysis of Bending and Torsional moments in circular beams 69 4.3 Moments in semicircular beams supported on thr columns 71 4.4 Design Example 72 4.5 Design Example 74 4.6 Examples for Practice 78 5. Towers 79 5.1 General 79 5.2 Design Principles 79 5.3 Computation of moments due to wind loads 80 5.4 Wind load Analysis of a Tower with circular group of columns 85 5.5 Design Example 87 5.6 Design Example 90 5.7 Examples for Practice 93 6. Elevated Water Tanks 95 6.1 Types of overhead water tanks 95 6.2 Intz type tank 95 6.3 Design example of Intz type water tank 101 6.4 Conical or Funnel shaped tank 115 6.5 Design Example of Funnel shaped over head Tank 117 6.6 Examples for Practice 128 7. Box—Culverts 131 7.1 General Aspects 131 7.2 Design Loads 131 7.3 Design of Critical sections 133 7.4 Design Example 134 7.5 Examples for Practice 40 8. Portal Frames 141 8.1 Introduction 141 8.2 Analysis and Design of Portal Frames 141 8.3 Design Example 143 8.4 Design Example 149 8.5 Examples for Practice 157 9. Multistorey Building Frames 158 9.1 Analysis of Multistorey Frames 158 9.2 Method of substitute Frames 158 Contents ix 9.3 Design Example 160 9.4 Bending moments in columns 168 9.5 Analysis of Multistorey frames subjected to Horizontal forces 169 9.6 Design Example 173 9.7 Examples for Practice 175 10. Shells 176 10.1 Introduction 176 10.2 Shell Terminology 176 10.3 Classification of shells 181 10.4 General specification of shells 181 10.5 Analysis of shells 184 10.6 Examples for Practice 203 11. Hyperbolic Paraboloid Shells 205 11.1 General Features 205 11.2 Geometry of Hyper shell 205 11.3 Analysis of Membrane forces 206 11.4 Inverted Umbrell roof 207 11.5 Design Example 208 11.6 Design Example 210 11.7 Types of hyperbolic Paraboloid Roofs 214 11.8 Examples for Practice 215 12. Hyperbolic Cooling Towers 217 12.1 General Aspects 217 12.2 Hyperboloid of Revolution 217 12.3 Analysis of Membrane forces 218 12.4 Design Example 222 12.5 Analysis of Hyperbolic Cooling Towers for wind load 225 12.6 Design Example 229 12.7 Examples for Practice 230 13. Folded Plates 231 13.1 General Features 231 13.2 Analysis of Folded plates 231 13.3 Structural behaviour of Folded plates 233 13.4 Whituey’s Method 235 13.5 Simpson’s Method 235 13.6 Iteration Method 236 13.7 Beam Method 237 13.8 Winter and Pei’s Method 237 13.9 Equation of three shears 237 13.10 Design Example 239 13.11 Stress Conditions in Hipped plates 240 13.12 Design Example 241 13.13 Design Example 245 13.14 Design Example 253 13.15 Examples for Practice 256 '14. Grid or Coffered Floors 258 14.1 General Features 258 x Contents 14. 2 Analysis of Grid Floors 258 14. 3 Design Example 262 14. 4 Examples for Practice 269 IS. Virendeel Girders 271 15.1 General Features 271 15.2 Analysis of Virendeel Girdders 271 15.3 Design Example 273 15.4 Design Example 275 15.5 Design of Members of Virendeel Girder 275 15.6 Design Example 277 15.7 Examples for Practice 280 16. Trusses 281 16.1 General Features 281 16.2 Dimensions of Trusses 281 16.3 Material Requirements 282 16.4 Constructional Features 283 16.5 Analysis of Trusses 284 16.6 Design Example 285 16.7 Examples for Practice 291 17. Poles 292 17.1 General Features 292 17.2 Classification of Poles 293 17.3 Design Features 293 17.4 Design Example 294 17.5 Examples for practice 297 18. Deep Beams 299 18.1 General Features 299 18.2 Parameters Influencing design 299 18.3 Flexural Bending Stresses 300 18.4 Shear Stresses in Deep Beams 306 18.5 I.S. Code Provisions 306 18.6 Design Example 308 18.7 Design Example 311 18.8 Design Example 312 18.9 Examples for Practice 313 19. Pipes 314 19.1 General Aspects 314 19.2 Classification of R.C.C. Pipes 314 19.3 Design Principles 314 19.4 Reinforcements in Pipes 316 19.5 Tests on Pipes 316 19.6 Design Example 317 19.7 Design of Non Pressure R.C.C. Pipes for Culverts 318 19.8 Design Example 321 19.9 Examples for Practice 324 Contents xi 20. Bridge Deck Systems 325 20.1 General Types 325 20.2 Analysis and Design of slab Decks 325 20.3 Analysis and Design of Tee beam and slab decks 334 20.4 Design Example 335 20.5 Design Example 339 20.9 Examples for Practice 351 Appendix 1 355 Appendix 2 356 References 357