Design of Reinforced Concrete Structures. Volume 1

219 Pages·12.983 MB·English

by  Ghoneim Mashhour, El-Mihilmy Mahmoud.

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
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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
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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
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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
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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
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