Design of Reinforced Concrete Structures. Volume 2

327 Pages·20.048 MB·English

by  Ghoneim Mashhour, El-Mihilmy Mahmoud.

RIC F.rames
DESIGN OF REINFORCED
CONCRETE STRUCTURES
Volume 2
MashhourAhmed Ghoneim
Professor of Concrete Structures
Cairo University
Mahmoud Tharwat EI-Mihilmy
Associate Professor of Concrete Structures
Cairo University
Second Ec:Jition
·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 understanding 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.
ill 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 honomble 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 contains the following chapters
• Solid slabs
• Hollow block slabs
• Paneled beams
• Flat slabs
• Reinforced concrete stairs
• Short columns
• Eccentric sections
• Slender columns
• Reinforced concrete Frames
It also includes appendices containing design aids.
TABLE OF CONTENTS
1. SOLID SLABS
1.1 Introduction ............................................................................................ '" ........ 1
1.2 One-Way Solid Slabs ............................................................................ ·. ............ 2
1.2.1 Definition .. ;. ............................. ~ ................................................................ 2
1.2.2 Structural Behavior. ................................................................................... 3
1.2.3 Effective Span ........................................................................................... 4
1.2.4 Minimum Thickness .................................................................................. 5
1.2.5 Bending moments ...................................................................................... 6
Example 1.1 ....................................................................................................... 8
1.3 Two-Way Slabs ................... ,. ............................................................................ 13
1.3.1 Definition .................................................................................................. 13
1.3.2 Elastic Analysis of Plates .......................................................................... 13
1.3.3 Load Distribution Factors According to ECP 203 ..................................... 16
1.3.4 Minimum Thickness .................................................................................. 18
1.3.5 Related Code Provisions ............................................................................ 19
1.3.6 Comer Reinforcement ............................................................................... 21
Example 1.2 ....................................................................................................... 22
2. HOLLOW BLOCK SLABS
2.1 Introduction ................................................................. ~ ............................................ 29
2.2 One-Way Hollow Block Slabs .................................................................................. 31
2.2.1 GeneraL .................................................................................................... 31
2.2.2 Arrangement of blocks .............................................................................. 32
2.2.3 Code Provisions ........................................................................................ 35
2.2.4 Design of One-way Hollow Block Slabs ................................................... 36
2.2.4.1 Design of Ribs ................... ·. ............................................................ 36
2.2.4.2 Design of Hidden Beams ............................................................... 38
Example 2.1 ....................................................................................................... 40
2.3 Two-Way Hollow Block Slabs ............................................................................ :. ... 51
2.3.1 Method of Analysis ................................................................................... 53
2.3.2 Design oftwo-way hollow slabs with projected beams ............................. 53
2.3.2.1 Design of ribs .............................................· . .................................. 53
2.3.2.2 Design of Projected beams ............................................................. 54
Example 2.2 ....................................................................................................... 58
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3. PANELED BEAMS
5. REINFORCED CONCRETE STAIRS
3.1 Introduction .............................................................................................................. 70
5.1 Introduction .............................................................................................................. 174
:C .......................................
3.2 Load Distribution ............................................................ 72 5.2 Structural Systems of Stairs ...................................................................................... 177
3.3 Code Provisions .................................................................................................· . ...... 75 5.2 Cantilever Type ........................................................................................................ 178
304 Simplified Design Method ........................................................................................ 76 Example 5.1 ....................................................................................................... 181
3.5 Design of Skew Paneled Beams ................................................................................ 81 5.3 Slab Type .....................................................................~ ........................................ 194
Example 3.1 ....................................................................................................... 82 Example 5.2 ....................................................................................................... 198
Example 5.3 ....................................................................................................... 207
4. FLAT SLABS
6. SHORT COLUMNS SUBJECTED TO CONCENTRIC
4.1 Introduction .............................................................................................................. 102
4.2 Statical Equilibrium of Flat Slabs ............................................................................. 104 COMPRESSION
4.3 Minimum Dimensions According to ECP 203 .......................................................... 105
6.1 Introduction .............................................................................................................. 223
404 Analysis of Flat Slabs ............................................................................................... 108
6.2 Axially Loaded Tied Columns .................................................................................. 224
4.5 Direct Design Method ............................................................................................... 108
6.2.1 Behavior and Strength ........................................... · .. · ............. ·· .. ·· .. · .......... 224
4.5.1 Limitation ofthe direct method ................................................................. 108
6.2.2 Code Provisions for Tied Columns ........................................................... 226
4.5.2 Definition of colunm strip and field strip .................................................. 108
6.2.3 Splicing of Vertical Reinforcement .......................... ··· .... ··· .. ··· .. ····· .. ··· ...... 229
4.5.3 Calculation of slab load ............................................................................. 108
Example 6.1 .................................................................. · .. ···· .. · ........................... 232
4.504 Statical Moment Mo .................................................................................. 11 0
Example 6.2 .................................................................. · .. · .. ·· .. · .... ·· .................... 234
4.5.5 Distribution of the Statical Moment .....•.................................................... 111
6.3 Axially Loaded Spiral Colun1ns ................................................................................ 235
4.5.6 Moment Correction ................................................................................... 114
6.3.1 Behavior and Strength ............................................ ····.· .. ··· .... · .. ·· ............... 235
4.5.7 Provision for Pattern Loading .................................................................... 115
6.3.2 Minimum Spiral Reinforcement .............................. · .. ············· .. ·· .............. 237
4.5.8 Design Steps According to the Direct Design Method .............................. 115
6.3.3 Code Provisions for Spiral Columns ......................................................... 239
4.6 Reinforcement of Flat Slabs ...................................................................................... 116
Example 6.3 ....................................................................................................... 241
4.6.1 General. ..................................................................................................... 116
Example 604 ....................................................................................................... 243
4.6.2 Column Head Reinforcement ....................................... ~ ............................ 120 604 Design of Composite Columns ........................................................: .. ;. .................... 245
4.6.3 Reinforcement at Openings in Flat Slabs .................................................. 121
604.1 Design Guidelines ..... , ............................................................................... 245
4.7 Punching Shear Strength of Flat Slabs ...................................................................... 122
Example 6.5 ....................................................................................................... 252
4.7.1 General. ........................................................................... ;. ........................ 122
Example 6.6 ....................................................................................................... 254
4.7.2 Critical Sections ........................................................................................ 123
Example 6.7 ....................................................................................................... 257
4.7.3 Concrete Punching Shear Strength ............................................................ 125
6.5 Calculation of Axial Loads on Columns ................................................................... 259
4.704 Detailed Analysis ...................................................................................... 126
6.5.1 Area Method ............................................................................................. 259
4.704.1 Introduction ................................................................................... 126
6.5.2 Reaction Method ............................................ ··· .. ·· .. ··· .. ·· .... · ...................... 261
4.704.2 Calculations ofthe Punching Stresses ............................................ 126
4.7.5 Simplified Method .................................................................................... 131
4.8 One-Way Shear Strength .......................................................................................... 133
7. DESIGN OF SECTIONS SUBJECTED TO ECCENTRIC
Example 4.1 ....................................................................................................... 134
Example 4.2 ....................................................................................................... 147 FORCES
Example 4.3 ................................ , ................ ~ ..................................................... 162
Example 4.4 ....................................................................................................... 163 7.1 Introduction .............................................................................................................. 262
4.9 The Equivalent Frame Method ........................................................................· . ......... 165 7.2 Interaction Diagrams ..................................................... ··· .. ·· .. ·· ................................. 264
. 4.9.1 Introduction ...............................•............................................................... 165 7.2.1 Definition ................................................................................................... 264
4.9.2 Structural.Analysis .................................................................................... 165 7.2.2 Modes of Failure ........................... : ........................................................... 265
Example 4.5 ;. ..................................................................................................... 170 7.2.3 Development of the Interaction Diagram ................................................... 267
4.10 Computer Model of Flat Slabs ........... ; .................................................................... 172
iv
iii
7.2.4 Plastic Centroid ......................................................................................... 270 8. SLENDER COLUMNS
Example 7.1 ............................ '. ................................................... :. ..................... 271
Example 7. 2 ...................................................................................................... 273 8.1 Definition of Slender Colurrms ................................................................................. 369
Example 7.3 ....................................................................................................... 274 82 Classification of Buildings ................................ ····· .. ······ ........................................... 372
7.3 Sections SubjecttoEccentric Compression Forces ..........................................•........ 281 8:3 Braced and Unbraced Colurrms ..................................... ··········· ................................. 375
7.3.1 Design Ul!ing mteraction Diagrams ............................................... : ........... 282 8.4 Slenderness Considerations in the Egyptian Code ............................. ·:··················· ... 376
Example 7.4 ........................................................ , .............................................. 286 8.4.1 Code Definition of Slender Colurrms ............. ; .......................................... 376
7 .3.2Design Using MUS Approach ................................................................... 288 8.4.2 Unsupported Height ofa Compression Member (Ho) ............................... 377
Example 7.5 ....................................................................................................... 292 8.4.3 Effective Height ofa Compression Member (He) ..................................... 378
7.3.3 Design Curves For Eccentric Sections ....................................................... 294 8.5 Design Moments in Slender Braced Colurrms .................... ;. .......... ················ ........... 383
Example 7.6 ....................................................................................................... 296 8.5.1 Calculation ofthe Additional Moments ..................................... ·········· ...... 383
7.4 Sections Subjected to Eccentric Tension Forces ....................................................... 299 8.5.2 Design Moments ....................................................................................... 384
7.4.1 Sections Subject to Small Eccentric Tension Forces ..................... ;. .......... 300 8.6 Design Moments in Unbraced Slender Colurrms ...................................... ·········· ....... 387
Example 7.7 ....................................................................................................... 301 8.6.1 Additional moment ...... , ........... : ................................................................ 387
7.4.2 Sections Subjected to Big Eccentric TensionForces ................................. 303 8.6.2 Design moments ........................................................................................ 387
Example 7.8 .......................................................................... ~ ........................... 304
!:l \\\:
7.5 T-Sections Subjected To Eccentric Forces ................................................................ 305 §i~ ~l
Example 7.9 ....................................................................................................... 306
Example 7.10 ..................................................................................................... 308
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Example 7.11 .................................. ~ ................................................................... 310 H:
7.6 Analysis of Irregular Sections ................................................................................... 312
7.6.1 General. ..................................................................................................... 312
7.Q.2 Strength of Shear Walls ............................................................................. 313 9. REINFORCED CONCRETE FRAMES
Example 7.12 ..................................................................................................... 315
7.7 mteraction Diagrams For Circular Colurrms ............................................................. 320 9.1 Introduction .............................................................................................................. 419
Example 7.13 .................................................................................................•... 323 9.2 Definition of the Frame ............................................................................................. 420
Example 7.14 ..................................................................................................... 325 9.3 The Choice of the Type ofthe Frame .......................................... ······· ...................... .422
Example 7.15 ..................................................................................................... 327 9.4 Lay~ut of a Hall Supported by RIC Frames ............................................................. .425
7.8 mteraction Diagrams For Box Sections .................................................................... 329 9.5 Reinforcement Detailing of Rigid Frames ..................................... ············ ............... .427
Example 7.16 ..................................................................................................... 331 9.6 HinE:'T:TI::::::::::::::::::::::::::::::::::::::::::'::.::':::::.::::::::~i
7.9 Colurrms Subjected to Biaxial Bending ..................................................................... 334
7.9.1 General ...................................................................................................... 334
7.9.2 Exact Analysis of Biaxial Bending ............................................................ 335
7.9.3 Minimum Eccentricity for Biaxially Loaded Columns .............................. 343 APPENDICES
Example 7.17 ..................................................................................................... 344
7.9.4 Biaxial mteraction Diagrams ..................................................................... 345 Appendix A Design Charts for Sections Subjected to Flexure ...................................... .465
7.9.5 The use of Biaxial Interaction Diagrams ................................................... 345 Appendix B mteraction Diagrams Top and bottom steel ...................................... ···· .. ··.47 3
Example 7.18 ..................................................................................................... 347 Appendix C mteraction Diagrams Uniform steeL ................. : ............................. · ........ 522
7.9.6 ECP-203 Design Procedure for Biaxial Bending ....................................... 349 Appendix D Design Charts for Sections Subjected to EccentrIC Forces ......................... 535
Example 7.19 ..................................................................................................... 353 Appendix E Interaction Diagrams for Circular S.ections ...... : .................................... :. ... 560
7.9.7 Biaxial Bending in Unsymmetrically Reinforced Sections ........................ 355 Appendix F Interaction Diagrams for Hollow ~lrcular SectlOns ................................... 573
Example 7.20 ...................................................................................................... 359 .A ppendix G Interaction Diagrams for Box SectlOns ..............: ....................................... 581
7.9.8 Circular Colurrms under Biaxial Bending .................................................. 362 Appendix H Interaction Diagrams for Biaxially Loaded SectlOns ................................. 586
Example 7.21 ..................................................................................................... 363 Appendix I Interaction Diagrams for L-Sections ............................... ············· .............. 615
7.9.9 mteraction Diagrams for L-Sections .......................................................... 365
v vi
1
SOLID SLABS
Photo 1.1 Burj Dubai during construction (2007)~ ______
1.1 Introduction
Reinforced concrete solid slabs are used in floors, roofs and as decks of bridges as
shown in Photo 1.1. Slabs may span in one direction or in two directions depending on
the slab dimensions and the· surrounding supporting elements. Slabs spanning in one
direction are referred to as one-way slabs while those spanning in two directions are
referred to as two-way slabs.
1.2.2 Structural Behavior
1.2 One-Way Solid Slabs
The direction in which the slab bends is called the main direction as shown in Fig 1.1.
1.2.1 Definition The main reinforcement is placed in this direction as illustrated in Fig. 1.2.
For a one-way slab supported on four beams like the one shown in Fig. 1.2, the strip
One-way solid slab~ are extensively used in buildings, especially for spans less than 4
near the middle acts as a one-way slab. However, at the slab parts near the edges,
meters. To be classified as a one-way slab, the ratio of the long side to the short side
some of the load is transferred in the longitudinal direction producing a two-way slab
of the slab panel must exceed 2. They are referred to as one-way slabs because the
action. Thus, top reinforcement should be added on each side of the girder to account
bending is mainly in the short direction. Typically, a 1m wide strip of the slab is
for this action. If this reinforcement is ignored, wide cracks may develop on the top of
analyzed and the reinforcement required for this strip is used in all parts ofthe slab.
the slab along edges (A-B) and (A'-B')
cantilever slabs main direction
r
7 Secondary reinforcement
Main reinforcement direction
direction
/ I "
~
I I !
-I .-._._. --I-
---------------1
I I
iiiI ~S&1<>:. ' '9E8.<.:. t '!Iii. .'E5" ·'g<<~8>: t IIii A
I i i
i ! --- i
! I I beams
i
I
i i
<=
i .S .g I
iI 'E" '<~8> t iI
i I Fig. 1.2 Structural action of one-way slabs
.. ! I
... ... --- -_.
... main direction I ~
I !
i .. I
main i i <= i
direction i i ... .5·g i The load transferred to the perpendicular direction is almost equal to zero except near
'" <>
I I secondary E ~ t I the edge beams (Beams AB and A'Bl Thus, a secondary mesh is required in this
i I - '8 I
direction direction (as shown in Figs. 1.2 and 1.3) to carry this small portion and to keep the
~~. ·1 ~
main reinforcement in place. Also, the secondary reinforcement is place.d to control
cracks produced by shrinkage or temperature changes and to help in distribl,lting
I I
concentrated loads transversely.
Fig. 1.1 One-way slabs
3
2
1.2.4 Minimum Thickness
The depth of solid slabs is usually controlled by deflection rather than flexural
strength requirements. The ECP-203 gives the minimum thickness for one-way slabs
reinforced with high grade steel in which the deflection calculations can be ignored as
listed in Table 1.1.
Table 1.1 (Loft)< ratios for members spanning less than 10 meters or cantilevers
spanning less. than 2m ({y=400 N/mm2). (Deflection calculations can be ignored)
a-Simply supported b-Coutiuuous
Simply One end Two ends Cantilever
Element
Fig. 1.3 One-way slabs supported on two sides supported continuous continuous
Solid slabs 25 30 36 10
It should be noted that if a slab panel is supported only on two sides, it would act as
one-way slab regardless of the ratio Of the long side to the short side. Figures 1.3.a and Hidden Beams
1.3.b show examples of slabs act as one way because of having supporting beams on 20 25 28 8
and hollow blocks
two sides only.
.* Lo is the clear span.
1.2.3 Effective Span
The values listed in Table (1.1) are valid when using high grade steel 400/600. In the
The effective span (Lef!) for solid slabs is given by the follOwing equation
case of using other types of reinforcing steel, the values mentioned in Table 1.1 should
be divided by factor S, given by:
Lelet" +t
max of s
Lef! = min of. {1.05xLc/",,, for simple or continuous slabs ...................... (1.1) {;o ................................. ;.. ....................
{ CLto CL (L) 4 = 0.40 + (1.2)
Where.!;, is the yield strength of reinforcing steel in Nlrnm2•
L . {Lei"'"
eff = mIll 0i f edge +tot sC L (L) c~.o r canb'1 ever s Ia b s .............................................. (1.2) The code also provides an absolute minimum thickness for one-way slabs
L 130 simple span
tmin = L /35 continuous from one end ......................... (1.3)
~r.-.- -----L-cle-~----trl---.~ 1
L 140 continuous from two ends
where L is the effective span
In addition, the absolute minimum thickness should not be less than 80 mm for slabs
i I
i L i L subjected to static loads and 120 mm for slabs subjected to dynamic loads. The
i • I aforementioned thickness can be reduced in case of prefabricated slabs. To satisfY
serviceability requirements for corrosion and fire protection, the concrete cover should
Continuous span Cantilever span not be less than 20mm.
Fig. 1.4 Effective spans for solid slabs
5
4