Features • Reflects the very latest Egyptian Code provisions (ECP 203 -2007) and includes all major changes and additions. • Numerous illustrations and figures for each topic. • Good theoretical background for each topic with code provisions. • Extensive examples in each chapter utilizing SI units. • All examples are worked out step by step ranging from simple to advanced. • Full reinforcement details for every example. • Numerous design charts for sections subjected to flexure. This volume covers the following topics: • Reinforced Concrete Fundamentals • Design of Singly Reinforced Sections • Design of Doubly Reinforced Sections • Design of T-Beams • Bond and Development Length • Design for Shear • Design of Simple and Continuous Beams • Design for Torsion • Design for Combined Shear and Torsion • Truss Models for RIC Beams DESIGN OF REINFORCED CONCRETE STRUCTURES Volume 1 Mashhour Ahmed Ghoneim Professor of Concrete Structures Cairo University Mahmoud Tharwat EI-Mihilmy Associate Professor of Concrete Structures Cairo University Second Edition 2008 PREFACE Teaching reinforced concrete design, carrying out research relevant to the behavior of reinforced concrete members, as well as designing concrete structures motivated the preparation of this book. The basic objective of this book is to furnish the reader with the basic upderstanding of the mechanics and design of reinforced concrete. The contents of the book conform to the latest edition of the Egyptian Code for the Design and Construction of Concrete Structures ECP-203. The authors strongly recommend that the Code be utilized as a companion publication to this book. The book is aimed at two different groups. First, by treating the material in a logical and unified form, it is hoped that it can serve as a useful text for undergraduate and graduate student courses on reinforced concrete. Secondly, as a result of the continuing activity in the design and construction of reinforced concrete structures, it will be of value to practicing structural engineers. Numerous illustrative examples are given, the solution of which has been supplied so as to supplement the theoretical background and to familiarize the reader with the steps involved in actual design problem solving. In writing the book, the authors are conscious of a debt to many sources, to friends, colleagues, and co-workers in the field. Finally, this is as good a place as any for the authors to express their indebtedness to their honorable professors of Egypt, Canada and the U.S.A. Their contributions in introducing the authors to the field will always. be remembered with the deepest gratitude. This volume covers the following topics • Reinforced Concrete Fundamentals .• Design of Singly Reinforced Sections • Design of Doutily Reinforced Sections • Design of T -Beams • Design for Shear • Bond and Development length • Design of Simple and Continuous Beams • Truss Models for the Behavior of RIC Beams • Design for Torsion It also includes appendices containing design aids. TABLE OF CONTENTS 1. REINFORCED CONCRETE FUNDAMENTALS 1.1 Introduction ........................................................................... " .......................... 1 1.2 Reinforced Concrete Members ....................... , ................................................... 3 1.3 Reinforced Concrete .......................................................................................... 5 1.4 Reinforced Concrete Behavior ........................................................................... 5 1.5. Mechanical Properties of Concrete .................................................................... 7 1.5.1 Compressive Strength ................................................................................ 7 1.5.2 Tensile strength ......................................................................................... 11 1.5.3 Modulus of Elasticity ................................................................... ;. ........... 13 1.5.4 Strength of Concrete Under Biaxial Loading ............................................. 14 1.5.5 Shrinkage .................................................................................................. 16 1.5.6 Creep ......................................................................................................... 17 1.6 Reinforcing Steel ............................................................................................... 18 1.7 Limit States Design Method ............................................................................... 20 1.8 Strength Reduction Factors ................................................................................ 20 1.9 Classification of Loads ....................................................................................... 23 1.10 Load Combinations ............................................................................................ 25 Example 1.1 ....................................................................................................... 28 2. DESIGN OF SINGLY REINFORCED SECTIONS 2.1 Introduction ....................................................................................................... 31 2.2 Reinforced Concrete Beam Behavior ... :. ............................................................ 32 2.3 Flexure Theory of Reinforced Concrete ............................................................. ~4 2.3.1 Basic Assumptions of the Flexure Theory ................................................. 34 2.3.2 Stress-Strain 'Relationships .......................................... , ............................. 35 2.3.2.1 Concrete in Compression ........................................... ;. .............................. 35 2.3.2.2 Reinforcing Steel ....................................................................................... 36 2.3.3 The Equivalent Rectangular Stress Block .................... ,. ............................ 37 2.4 Analysis of Singly Reinforced Sections .............................................................. 39 2.5 Maximum Area of Steel of a Singly Reinforced Section ................................... .42 2.6 Balanced, Under, and Over Reinforced Sections ............................................... .47 2.7 Minimum Area of Steel. ..................................................................................... 48 2.8 Factors Affecting Ultimate Strength .................................................................. 49. Example 2.1 ..................................• ,. .......................................................... 52 Example 2.2 ............................................................................................... 54 Example ·2.3 ............................................................................................... 56 Example 2.4 .................................................................. ~ ............................ 58 ii Example 2.5 ............................................................................................... 60 3.2.7 Design of T-sections Using Curves .......................................................... 139 Example 2.6 ................................................................................................ 62 3.2.7.1 Development of the Curves ...................................................... ; ................ 139 Example 2.7 ............................................................................................... 65 3.2.7.2 Using the Design Aids (charts C1-J and RT-J) .......................................... 142 Example 2.8. .................................................................................. , ............ 67 Example 3.17 (a<ts) .................................................................................. 143 2.9 Design of Singly Reinforced Sections by First Principles .................................. 69 Example 3.18 (a>ts) .................................................................................. 145 Example 2.9 ................................................................................................ 70 3.3 Design ofL-Sections .......................................................................................... 147 Exalnple 2.10 ............................................................................................. 73 Example 3.19 ............................................................................................. 149 2.10 Design of Singly Reinforced Sections Using Curves .. ; ........................................... 75 Example 3.20. ............................................................................................ 151 2.10.1 Design Charts (R-J..l) ............................................................................................. 75 2.10.2 Design Chart (R-ro) ............................................................................................. 77 4. SHEAR IN RIC BEAMS Example 2.11 ............................................................................................. 80 Example 2.12 ............................................................................................. 81 4.1 Introduction ....................................................................................................... 153 Example 2.13 ............................................................................................. 83 4.2 Shear stresses in Elastic Beams ........................................................... ; .............. 154 Example 2.14 .............................................................................................. 84 4.3 Shear Stresses in Cracked RIC Beams ............................................................... 158 Example 2.15 .................................................................. , .......................... 85 4.4 Behavior of Slender Beams Failing in Shear ...................................................... 159 4.4.1 Inclined Cracking ...................................................................................... 159 3. DOUBLY REINFORCED BEAMS AND T-BEAMS 4.4.2 Internal Forces in Beams without stirrups ................................................. 160 3.1 Doubly Reinforced Sections .............................................................................. 86 4.4.3 Behavior of Slender Beams with Stirrups ..................................... : ............ 162 3.1.1 Introduction ....................................................................................................... 86 4.5 Egyptian Code's Procedure for Shear Design .................................................... 164 3.1.2 Analysis of Doubly Reinforced Sections ................................................... 88 4.5.1 Critical Sections for Shear ......................................................................... 164 4.5.2 Upper limit of Design Shear Stress ............................................................ 166 3.1.3 Maximum Area of Steel for Doubly Reinforced Sections .......................... 92 4.5.3 Shear Strength Provided by Concrete ........................................................ 166 Example 3. 1( compression steel yields) ...................................................... 95 4.5.4 Shear Strength Provided by Shear Reinforcement.. ................................... 167 Example 3.2 ............................................................................................... 97 4.5.5 Code Requirements for Shear Reinforcement.. .......................................... 170 Example 3.3 (compression steel does not yield) ........................................ 98 Example 4.1 ............................................................................................... 172 3.1.4 Design of Doubly Reinforced Sections Using First Principles ........................... 100 Example 4.2 ............................................................................................... 176 Example 3.4 ................................................................................................ 101 Example 4.3 ............................................................................................... 180 Example 3.5 ............................................................................................... 103 Example 4.4 ............................................................................................... 183 Example 3.6 ............................................................................................... 105 Example 3.7 ................................................................................................ 107 3.1.5 Design of Doubly Reinforced Sections Using Curves ........................................ 108 5 BOND, DEVELOPMENT LENGTH AND SPLICING OF Example 3.8 ............................................................................................... 111 REINFORCEMENT Example 3.9 ...................................................................... ; ........................ 112 5.1 Introduction ....................................................................................................... 186 Example 3.10. ............................................................................................. 113 5. 2 Average Bond Stresses in a Beam. ..................................................................... 187 3.2 T-Bearns ............................................................................................................ 115 5.3 True Bond Stresses in a Beam. ................................. :. ........................................ 189 3.2.1 Application ofT-Beams ............................................................................ 115 5.4 Development Length ............................................................. ;. ........................... 190 3.2.2 Effective Flange Width .............................................................................. 115 5.4.1 Theoretical Considerations ........................................................................ 190 3.2.3 Analysis ofT-Beams ........................................... :. ..................................... 119 5.4.2 Development Length According to ECP 203 ............................................. 192 3.2.4 Minimum Area of Steel for T -sections ...................................................... 122 5.5 Bar Cutoffs in Flexural Menibers ....................................................................... 196 3.2.5 Maximum Area of Steel for T -sections ...................................................... 123 5.5.1 The Moment of Resistance ofa RIC Beam. ............................................... 196 3.2.6 Design ofT-sections Using First Principles ............................................... 126 5.5.2 Curtailment of Bars in Beams .................................................................... 198 Example 3.11 .............................................................................................. 127 5.5.3 Egyptian Code's Requirements for Curtailment .. ; ..................................... 200 Example 3.12 .............................................................................................. 129 5.6 Beams with Bent-up Bars .................................... : .............................................. 203 Example 3.13 T Sections (a<ts) ................................................................. 131 5.7 Anchorage of Web Reinforcement ..................................................................... 203 Example 3.14 (a>ts) .................................................................................. 133 5:8 Splicing of Reinforcement ................................................................................. 204 Example 3.15 ..................................................................... ·. ........................ 135 5.8.1 Lap splices ................................................................................................. 204 Example 3.16 ........ ~ .................................................................................... 137 5.8.2 Welded and Mechanical Connections ........................................................ 206 iii iv 6 REINFORCED CONCRETE BEAMS 8 DESIGN FOR TORSION 6.1 Introduction ....................................................................................................... 207 6.1 Statical Systems of RiC Beams .......................................................................... 208 8.1 Introduction ....................................................................................................... 326 6.2 The effective span .............................................................................................. 209 8.2 Equilibrium Torsion and Compatibility Torsion ................................................. 327 6.3 Loads Acting on Beams ..................................................................................... 210 8.2.1 General ...................................................................................................... 327 6.3.1 Own weight of beams ................................................................................ 210 8.2.2 Equilibrium Torsion .................................................................................. 327 6.3.2 Slab loads .................................................................................................. 211 8.2.3 Compatibility Torsion ............................................................................... 329 6.3.3 Wall loads ................................................................................................. 216 8.3 Principal Stresses due to Torsion ....................................................................... 330 6.4 Slenderness limits for beams .............................................................................. 219 8.4 Thin-Walled Tube in Torsion .......................................................... , .................. 331 6.5 Linear Elastic Analysis of Continuous Beams ................................................... 220 8.5 Space-Truss Model for Torsion ................................................ ·. ......................... 333 6.6 Reinforcement Detailing in'RiC Beams ............................................................. 221 8.5.1 Components of the Space Truss ................................................................. 333 6.6.2 Bar Spacing ............................................................................... ,. .............. 222 8.5.2 Diagonal Compressive Stresses ................................................................. 335 6.6.3 Egyptian Code Recommendations ............................................................. 223 8.5.3 Forces in Stirrups ...................................................................................... 337 Example 6.1 ............................................................................................... 224 8.5.4 Longitudinal Force .................................................................................... 337 Example 6.2 ............................................................................................... 231 8.6 The Design for Torsion in the Egyptian Code ............................................ : ....... 339 Example 6.3 ............................................................................................... 235 8.6.1 General ...................................................................................................... 339 Example 6.4 ............................................................................................... 241 8.6.2 Calculation of the Shear Stress due to Torsion .......................................... 339 Example 6.5 ............................................................................................... 245 8.6.3 Consideration of Torsion ........................................................................... 341 Example 6.6. .............................................................................................. 254 8.6.4 Adequacy ofthe Concrete CrOss-Section .................................................. 341 Example 6.7 ............................................................................................... 266 8.6.5 Design of Torsional Reinforcement.. ......................................................... 341 Example 6.8 .................................................................. _.. .......................... 273 8.6.5.1 Closed Stirrups ................................................. : ........................................ 341 Example 6.9 ............................................................................................... 283 8.6.5.2 Longitudinal Reinforcement. ................................................................. 342 8.6.6 Code Requirements for Reinforcement Arrangement ................................ 342 7 TRUSS MODEL FOR BEAMS FAILING IN SHEAR 8.6.7 Summary of Torsion Design According to ECP 203 .~ ............................... 345 Example 8.1 ............................................................................................... 347 7.1 Introduction ....................................................................................................... 290 Example 8.2 ............................................................................................... 351 7.2 Background ........................................................................................................ 291 Example 8.3 ............................................................................................... 355 7.2.1 Slender Beams Versus Deep Beams .......................................................... 291 8.7 Combined Shear and Torsion ............................................................................. 359 7.2.2 Analysis of Forces in RiC Slender Beams ................................................. 293 8.8 The Design for Shear and Torsion inECP 203 .................................................. 359 7.2.2.1 Sectional Analysis ................................................................................. 294 8.8.1 Consideration of Torsion ............ : .........................................................., ... 359 7.2.2.2 Mechanical-Mathematical Models ...................................................... 295 8.8.2 Adequacy of the Concrete Cross-Section .................................................. 360 7.3 Truss Model for Slender Beams ......................................................................... 296 8.8.3 Design of Transverse Reinforcement.. ..................................· . .... : ............... 361 7.4 Traditional 45-Degree Truss Model ................................................................... 297 8.8.4 Design of Longitudinal Reinforcement. ..................................................... 361 7.4.1 Formation ofthe45-Degree Truss ............................................................. 297 8.8.5 Summary of the Design for Shear and Torsion .......................................... 362 7.4.2 Evaluation of the Forces in the Stirrups ..................................................... 298 8.9 Compatibility Torsion ............................................................ :. .......................... 365 7.4.3 The Compression Force in the Diagonals .................................................. 299 8.10 Torsional Rigidity ............................................................................................... 365 7.4.4 The Axial (Longitudinal) Force Due to Shear ........................................... 302 Example 8.5 ............................................................................................... 372 7.4.5 Comments on the 45-Degree Truss-Model ................................................ 303 Example ·8.6 ................................................................................................ 376 7.4.6 Comparison of the Truss Model and ECP 203 ........................................... 303 Example 8.7 ............................................................................................... 382 Example 7.1 ............................................................................................... 304 Exalnple 7.2. ........................................ ; ..................................................... 310 APPENDIX A: DESIGN AIDS ......................................................................... 391 7.6 The Variable-Angle Truss ModeL. .................................................................... 316 7.6.1 General ........................................................................ c. ............................. 316 REFERENCES ........................................................................................................ 409 7.6.2 Analysis of the Variable Angle Truss ModeL .......................................... 317 Example 7.3 ............................................................................................... 320 v vi 1 REINFORCED CONCRETE FUNDAMENTALS Photo 1.1 Nile City Towers, Cairo-Egypt. 1.1 Introduction Reinforced concrete is one of the most important available materials for construction in Egypt and all over the world. It is used in almost all structures including; buildings, bridges, retaining walls, tunnels, tanks, shells and even ships. Concrete is a mixture of sand and gravel held together with a paste of cement and water. Sometimes one or more admixture is added to change certain 1.2 Reinforced Concrete Members characteristic of the concrete such as its workability, durability, and time of hardening. Concrete has a high compressive strength and a very low tensile Reinforced concrete structures consist of a series of members. The first and the strength. second floors of the building shown in Fig. 1.1 have a slab-and-beam system, in which the slab spans between beams, which in tum apply loads to the columns. Reinforced concrete is a combination of concrete and steel wherein the steel Again, the columns' loads are applied to footings, which distribute the load over reinforcement provides the tensile strength lacking in the concrete. Steel a sufficient area of soil. reinforcement is also capable of resisting. compression forces and is used in columns as well as in other situations to be described later. The structure shown in Fig 1.2 is a typical framed structure. The slab carries its own weight, flooring and live loads. The load is then transferred to secondary The tremendous success of reinforced concrete can be understood if its beams. The reactions of the secondary beams are transferred to the girders, numerous advantages are considered. These include the following: which in tum are supported by the columns. Finally, the columns' loads are applied to the footings, which distribute the load to the soil. • It is a low maintenance material. • It has great resistance to the action of fire provided that there is adequate cover over the reinforcing steel. • A special nature of concrete is its ability to be cast in to a variety of shapes from simple slabs, beams, and columns to great arches and shells. • A lower grade of skilled labor is required for erection as compared to other materials such as structural steel. • In. most areas, concrete takes advantage of inexpensive local materials (sand, gravel, and water) and requires a relatively small amount of cement and reinforcing steel. To use concrete successfully, the designer must be completely familiar with its weak points and its strong ones. Among its disadvantages are the following: • Concrete has a very low tensile strength, requiring the use of tensile reinforcing. • Forms are required to hold the concrete In place until it hardens sufficiently. Formwork could be expensive. • The properties of concrete could vary widely due to variations in its proportioning and mixing. Furthermore, the placing and curing of concrete is not as carefully controlled, as is the production of other materials such as structural steel. • In general, reinforced concrete members are relatively large, as compared Photo 1.2 Reinforcement placement during construction to structural members, an important consideration for tall buildings and long span bridges. 3 2 1.3 Reinforced Concrete R.C. Beam It is a well-known fact that plain concrete is strong in compression and very weak in tension. The tensile strength of concrete is about one-tenth its compressive strength. As a result, a plain concrete beam fails suddenly as soon as the tension cracks start to develop. Therefore, reinforcing steel is added in the tension zone to carry all the developed tensile stresses; this is called a reinforced concrete beam. . Concrete and steel work together beautifully ·in reinforced concrete structures. The advantages of each material seem to compensate for the disadvantages of the other. The great shortcoming oflow concrete tensile strength is compensated for by the high tensile strength of the steel. The tensile strength of the steel is approximately equal to 100-140 times the tensile strength of the usual concrete mix. Also, the two materials bond together very well with no slippage, and thus act together as one unit in resisting the applied loads. The disadvantage of steel is corrosion, but the concrete surrounding the reinforcement provides an excellent protection. Moreover, the strength of the exposed steel subjected to fire is close to .zero, but again the enclosure of .the Fig. 1.1 Slab and beam system in a building reinforcement in the concrete produces very satisfactory fire protection. Finally, concrete and steel work very well together in temperature changes because their coefficients of thermal expansion are almost the same. The coefficient of thermal expansion for steel is 6.5xlO·6, while that for the concrete is about Loads 5.5xlO-6. 1.4 Reinforced Concrete Behavior The addition of steel reinforcement that bonds strongly to concrete produces· a Secondary beam relatively ductile material capable of transmitting tension and suitable for any structural elements, e.g., slabs, beam, columns. Reinforcement should be placed in the locations of anticipated tensile stresses and cracking areas as shown in Fig Column 1.3. For example, the main reinforcement in a simple beam is placed at the bottom fibers where the tensile stresses develop (Fig. 1.3A). However, for a cantilever, the main reinforcement is at the top of the beam at the location of the maximum negative moment (Fig.l.3B). Finally for a continuous beam; a part of the main reinforcement should be placed near the bottom fibers where the positive moments exist and the other part is placed at the top fibers where the Footing negative moments exist (Fig. 1.3C). Fig. 1.2 Typical reinforced concrete structural framing system 4 5