SP 17 ACI DESIGN HANDBOOK

AC1 34OR-97

AC1
DESIGN
HANDBOOK
?

international

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

PUBLICATION
SP-17(97)

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

Design of
Structural Reinforced Concrete Elements
in Accordance with the
Strength Design Method of AC1 318-95


THIS DOCUMENT I
S PROTECTED BY THE LAWS OF COPYRIGHT

If additional copies are needed, in whole or in part, contact the Member Services Department of

the American Concrete Institute:
P.O. Box 9094
Farmington Hills, Michigan
48333-9094
TEL: 248-848-3800
FAX: 248-848-3801

SIXTH EDITION

Copyright 1997
American Concrete Institute
P.O. Box 9094
Farmington Hilis, MI 48333-9094

Third Printing, July 2001

All rights reserved including rights of reproduction and use in any form or by any means, including the making of copies
by any photo process, or by any electronic or mechanical device, printed or written or oral, or recording for sound or
visual reproduction or for use in any knowledge or retrieval system or device, unless permission in writing is obtained
from the copyright proprietors.
Printed in the United States of America

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

The Institute is not responsible for the statements or opinions expressed in its publicaîiwis. Institute publications are not able
to, nor intended to, supplant individualtraining, responsibilityor judgement of the user, or the supplier, of the information presented.

international

ISBN 0-087031-045-3

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT


AC1 340R-97

AC1 Design Handbook
Design of Structural Reinforced Concrete Elements
in Accordance with the Strength Design Method of AC1 318-95
Reported by AC1 Committee 340
Mohsen A. Issa. Chairman
Husam A. Omar, Secretary
Richard Furlong'
Moussa A. Issa
James S. Lai
Douglas O. Lee
S. Ali Mirra

Edward G. Nawy
William E. Rushing, Jr
Charles G. Salmon
Murat Saatcioglu
Sudhakar P. Vema

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

Param D. Bhat
William W. Bintzer
Patrick J. Creegan
Om P. Dixit
Noel J. Everard

'Consulting Member
The AC1 Design Handbook is intendedfor use by individuals having a general familiarity with the strength
design method and with "Building Code Requirements for ReinforcedConcrete (AC1 31&95)." This
publication provides information for the engineering design and analysis of beams, one-way slabs, brackets,
footings, pile caps, columns. two-way slabs, and seismic design.
Informationis presented on three sections: Design Aids. Design Examples, and Commentary on Design
Aids. The Design Examples illustrate the use of the Design Aids, which are tables and graphs intended to
eliminate routine and repetitiouscalculations. The Commentary explains the analytical basis for the Design
Aids.
Keywords: anchorage (stnidural); axial loads; bars; beams (supports); bending; bending moments; biaxial loads;
brackets; buckling; columns (supports); concrete construction; concrete piles; concrete slabs; connections:
cracking (fracturing); deflection; flanges; flexural strength; footings; frames; load factors; loads (forces); long
columns; moments of inertia; pile caps; reinforced concrete; reinforcing steels; shear strength; clendemess ratio;
spiral columns; splicing; stiffness; strength analysis; structural analysis; structural design; T-beams; tension;
torsion.

AC1 Committee Repons. Guides. Standard Practices, and Commentariesare intended for guidance in planning, designing. executing
and inspecting consmiction. This document is intended for the use of individuals who are competent to evaluate the significanceand
limitations of i n content and recommendationsand who will accept responsibility for the application of the material it contains. The
Amaican Concrete Instimte disclaims any and all responsibility for the stated piinciples. The InStiNte shall not be liable for any loss
or damage arising therefrom.
Reference to this document shall not be made in conuact documents. If items found in this document axe desired by the

ArchitectlEngineer to be a part of the c o n m t documents. they shall be restated in mandatory language for incorporation by the
Architecfigineer.
I

I

internationaì-

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

AMERICAN CONCRETE INSTITUTE
P.O.Box 9094
Fannington Hills. MI 48331-9094
Phone: 2481848-3700 Fax: 2481848-3701

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT


TABLE OF CONTENTS
AC1 3 18-95 Strength Reduction Factors ..........................................
Xiv
FOREWORD ............................................................... xv
NOTATION ...............................................................
xvii

DESIGN AIDS

FLEXURE 1Reinforcement ratios and a,,for quick approximatedesign of
rectangular beams with no compression reinforcement ..........................
5
FLEXURE 2-Nominal strength coefficients for design of rectangular beams
with tension reinforcement only
FLEXURE 2 . 1 4 ' 3000 psi ............................................. 6
FLEXURE 2.2-f,'
4000 psi .............................................
7
FLEXURE 2 . 3 4 ' 5000 psi ............................................- 8
FLEXURE 2 - 4 4 ' 6000 psi ............................................
-9
FLEXURE 3-Nominal strength coefficients for rectangular beams with compression
reinforcement in whichf, ' =fy and for flanged sectionswith hl< a
10
FLEXURE 3 . 1 4 ' 3000 psi & 4000 psi ...................................
-11
FLEXURE 3 . 2 4 . 5000 psi & 6000 psi ..................................
FLEXURE 3.3-Coefficient I& for use in computingA, for flange Section with &FLEXURE 4-Nominal strength Md for compression reinforcement in whichf, . =fy ....... 13
FLEXURE Moefficient F for use in calculating nominal strengths M , MnI.
and M, .....-14
FLEXURE &Nominal strength M, for slab sections 12 . wide
3000 psi. fy 40. O00 psi (graph) .......................
15
FLEXURE 6.1.1-f,'
FLEXURE 6.1.2-f,'
3000 psi. fy 40. O00 psi (table) ........................
16
FLEXURE 6.2.1-4'

3000 psi. fy 60.O00 psi (graph) .......................
17
FLEXURE 6.2.2-4'
3000 psi. fy 60.O00 psi (table) .......................
-18
FLEXURE6.3.1-f,'=4000psi, fy=40.OOOpsi(graph) ...................... - 1 9
FLEXURE 6 . 3 . 2 4 ' 4000 psi. fy 40.O00 psi (table) ........................
20
FLEXURE 6.4.1-f,'
4000 psi. fy 60.O00 psi (graph) ...................... -21
4000 psi. fy 60.O00 psi (table) ........................
22
FLEXURE 6.4.2-4'
FLEXURE6.5.1-f,'=5000psi, fy=40.OOOpsi(graph) ......................
-23
FLEXURE 6.5.2--'
5000 psi. fy 40.O00 psi (table) .......................- 2 4
5000 psi. fy 60.O00 psi (graph) ......................
-25
FLEXURE 6.6.1--'
5000 psi. fy 60.O00 psi (table) .......................
-26
FLEXURE 6.6.2-A'
6000
psi.
fy
40.
O00
psi
(graph)

......................
-27
FLEXURE 6.7.1-f,'
28
6000 psi. fy 40.O00 psi (table) ........................
FLEXURE 6.7.2--'
6000 psi. fy 60.O00 psi (graph) .......................
29
FLEXURE 6.8.1-f,'
30
6000 psi. fy 60.O00 psi (table) ........................
FLEXURE 6.8.2-L'

.
.
.
.
.
.

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

.
.
.
.
.
.
.
.

.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.

.
.
.

REINFORCEMENT I-Nominal cross section area,weight, and nominal
-33
diameter of ASTM standard reinforcing bars ................................
REINFORCEMENT 2 - 0 0 , s section areas for vanous combination of bars .............. 34
REINFORCEMENT 3-Properties of bundled bars .................................. 36
REINFORCEMENT 4-Sectional propehes and areas of plain and deformed welded
Copyright American Concrete Institute

Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

iii
Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT


wirereinforcement ...................................................... 37
REINFORCEMENT 5-Spec~cations and properties of wire and welded reinforcement
REINFORCEMENT 5.1-Specifications covering welded wire reinforcement ...... - 3 8
REINFORCEMENT 5.2-Minimum requirements of steel wires in welded wire
reinforcement ..........................................................
38
REINFORCEMENT 6-Common styles of welded wire reinforcement .................- 3 9
REINFORCEMENT 7-Typical development and splice length for welded wire reinforcement
REINFORCEMENT 7.1.1-Plain wire reinforcement; fy = 60,O00 psi f,‘ = 3000 psi . . 40
REINFORCEMENT 7.1.2-Plain wire reinforcement; fy = 60,O00 psi f,. = 4000 psi . . 4 1
REINFORCEMENT 7.2.1-Deformed wire reinforcement;
fy = 60,O00 psi, f,. = 3000 psi............................................. - 4 2
REINFORCEMENT 7.2.2-Deformed wire reinforcement,
fy = 60,O00 psi, f,. = 4000 psi .............................................
-43
REINFORCEMENT P r a c k control in beams and slabs
REINFORCEMENT 8.1-Maximum A values per bar ......................... -44
REINFORCEMENT 8.2-Beam web size and reinforcement required ............ - 4 5
REINFORCEMENT %Minimm beam web widths required for two or more
bars in one layer for cast-in-place nonprestressed concrete ....................... 46
REINFORCEMENT IO-Minimum beam web widths for various bar combinations
(interior exposure) .....................................................

-47
REINFORCEMENT 11Maximum web width b, per bar for single bars used
as flexural tension reinforcement in beam webs and slabs, as required for crack
controlprovisions ............................................................. 48
REINFORCEMENT 12-Minimum beam web widths b, for various bar combinations of
-49
bundled bars (iterior exposure) ..........................................
REINFORCEMENT 13-Maximum web width b, per bundle, as required for crack control
provisions for bars of one s k in one layer ..................................
-50
-51
REINFORCEMENT 1 A B a r selection table for beams ..............................
REINFORCEMENT 15-Areas of bars in a section 1 ft. wide .........................
-56
REINFORCEMENT 16-Maximum bar spacing for single bars
in one row for one-way slabs .............................................
-57
REINFORCEMENT 17-Basic development length ratios of bars in tension .............. 58
REINFORCEMENT 18.1-Basic development length,Z of standard hooks in tension . . . . . - 6 0
REINFORCEMENT 18.2-MinimUm embedment lengths to provide 2 in.
cover to tail of standard 18O-degree end hook .................................
61
REINFORCEMENT 19-Maximum size of positive reinforcement bars satisP, = ( M f l J + Pa, IEq. (12.2) of AC1 318-951 for various span lengths .............. - 6 2
REINFORCEMENT 19.1-6 = 40,O00 psi ..................................
-62
RENFORCEMENT 19.2-f, = 60,O00 psi ..................................
-63
REINFORCEMENT 20-Maximum allowable pitch s, in,
REINFORCEMENT 20.1-For circular viral columns......................... -64
RENFORCEMENT 20.2-For square coiumns................................65

RENFORCEMENT 20.3-Recommended minimum number of spacers wiîh
various spirai sizes x.2 column sizes ....................................... - 6 6
REINFORCEMEN” 21-”4inimum face dimension b, in., of rectangular tied columns
accommodating various numbers of bars n per face ...........................
-67
--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

iv

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT


REINFORCEMENT 22-Maximum number of bars n, that can be accommodated
in square columns having bars equally distributed on four faces
REINFORCEMENT 22.1.1-22.1.4-Using bearing splices ................... 68-71
REINFORCEMENT 22.2.1 -22.2.4-Using normal lap splices ................. 72-75
REINFORCEMENT 22.3.1 -22.3.4-Using tangential lap splices .............. 76-79
REINFORCEMENT 23A“aximum number of bars n, that can be accommodated
in columns having bars arranged in a circle
REINFORCEMENT 23.1.1.23.1 .&Using bearing splices ................... 80-83
REINFORCEMENT 23.2.1-23.2.4-Using normal lap splices ................. 84-87
RENORCEMENT 23.3.1-23.3.4-Using
tangential lap splices .............. 88-91
SHEAR l-stirrup design requirements for nonprestressed beams with vertical Stirnips and
normal-weight concrete subjected to flexure and shear only ..................... - 9 4

SHEAR 2-Diagram for selecting spacing of stinups .................................
95
SHEAR 3-Mi.nimum beam height to provide embedment required for #6, #7, and #8 vertical
96
stirrups wi&fy = 60,O00 psi ...............................................
SHEAR &Design shear strength V, for U-stirmps
SHEAR 4.1-f, = 40 ksi.................................................. 97
SHEAR4.2-f, =60ksi..................................................
98
SHEAR %Effective depth of footings and slabs requiredto provide perimeter shear strength
SHEAR 5.1-Interior rectangular column (q= 40) for which ß, = wb s 2. . . . . . . . . .99
SHEAR 5.2-hterior circular column (as= 40) ..............................
100
SHEAR &Maximum nominal torsional moment T,that may be neglected
(AC13 18-95 Section 11.6.1) and maximum nominal torsional moment T,required for
statically indeterminate torsion (AC1 3 18-95 Section 11-62) ....................
101
SHEAR 7.1-Values of
win.)And & (kips)
SHEAR 7.1.1--’ = 3,O00 psi ............................................
102
SHEAR 7 . 1 2 4 ’ = 4,o00 psi ............................................
102
SHEAR 7.1.3-f,‘ = 5,O00 psi ............................................
103
SHEAR 7.1.44’ = 6,O00 psi ............................................
103
SHEAR 7.2-Val~e~of K, (fi-k)
SHEAR 72.1-f,’ = 3,000 psi ............................................
104

SHEAR 7.2.2-f,’ = 4,000 psi ............................................
104
SHEAR 7.2.3-3’ = 5,O00 psi .............................................
105
SHEAR 7.2.4-f,’ = 6,O00 psi ............................................
105
SHEAR 7.3-values of K, (fi-kh.)
S H E A R 7.3.1-fp: = 40,O00 psi ...........................................
106
SHEAR 7.3.2-3,
= 60,O00 psi ...........................................
106
SHEAR 7.4-Values of KI (fi-k)
S H E A R 7.4.1--’ = 3,O00 psi ............................................
107
SHEAR 7.4.24’ = 4,O00 psi ............................................
107
SHEAR 7 . 4 . 3 4 ’ = 5,O00 psi ............................................ 108
SHEAR7.4.4-i’=6,OOOpsi ............................................ 108
DEFLECTION l-lrackuig moment M,
DEFLECTION 1.1-For rectangular sections ................................ 110
DEFLECTION 1.2-For T or L sections with tension at the bottom
’

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

V

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT


--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

(positive moment) .....................................................
111
DEFLECTION 1.3-For T or L sections with tension at the top (negative moment)
and 0.2 .............................
112
DEFLECTION ~ 3 . 1 - =
ß 0.1,0.15,
~
113
DEFLECTION 1.3.2-ßh=0.25, 0.30, and0.40 ...........................
DEFLECTION 2-Cracked section moment of inertia I, for rectangular sections
with tension reinforcement only .......................................... 114
DEFLECTION 3-0s
moment of inertia for Ig of T-section ........................ 115
DEFLECTION 4-Cracked section moment of inertia I, for rectangular
sections with compression steel, or T-sections(values of Ki2)
116
DEFLECTION 4.1-For ß, from 0.1 through 0.9 .............................
DEFLECTION 4.2-For ßc h m 1.0 through 5.0 ............................. 117
DEFECTION %Effective moment of inertia I,
DEFLECTION 5.1-(value~of k;)........................................
118

DEFLECTION 5.2-For rectangular sections with tension reinforcement only
(values of KJ .........................................................
119
DEFLECTION 6.1-Coefficient & and typical M,formdas for calculating
immediate deflection of flexural members ..................................
120
DEFLECTION 6.2-Coefficient & for calculating immediate deflection
o f f l e d m e m b e r s ...................................................
-121
DEFLECTION 7-Values of lu, and òcfor use in a, = (Kdô, )(w/b)
(immediate deflection by the approximate method) ...........................
122
DEFLECTION 8-Creep and shrinkage deflection (additional long-time deflection)
due to sustained loads ........... i ......................................
123
DEFLECTION 9-Modulus of elasticity E, for various concrete strenghs................ 124
COLUMNS 1-Slenàemess ratios kur and k¿Jhbelow which effects of slenderness may be
126
neglected for columns braced against sidesway ...............................
COLUMNS 2-Effective length fáctor k for columns in braced and nonbraced frames ...... 127
COLUMNS 3F'actored K, and K,for cornpuhg flexural stiffness term (*EI)
COLUMNS 3.1-For rectangular tied columns with steel on four faces .......... -128
COLUMNS 3.2-For rectangular tied columns with steel on two end faces ....... -129
130
COLUMNS 3.>For circular spiral columns ................................
131
COLUMNS 3.4-For square spirai columns .................................
COLUMNS 4-Values of E(EJJ2.51 x lo-' for computing flexural stiffness EI of
cracked sectionsof rectangular and circular columns
132

COLUMNS 4.i--' = 3 ksi ..............................................
133
COLUMNS 4.2--' = 4 ksi ..............................................
COLUMNS 4 . 3 4 = 5 ksi............................................... 134
C O L C ? S4 . 4 4 ' = 6 ksi..............................................
-135
COLUMNS 4.5----' = 9 ksi ..............................................136
COLUMNS 4.&-' = i 2 ksi ............................................. 137
COLUMNS 5- Moment mamiifier term C, for columns
COLUMNS 5.1-For rectangular tied columns and square columns with
steel arranged in a circle-- . = 3 ksi .......................................
138
COLUMNS 5.2-For rectangular tied columns and square columns with

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

vi

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT


.

steel arranged in a circle--’ 4 ksi .......................................
138
COLUMNS 5.3-For rectangular tied columns and square coliimns with
steel arranged in a circle--. 5 ksi....................................... -139

COLUMNS 5.4-For rectangular tied columns and square columns with
steel arranged In a circle--. 6 ksi ....................................... 139
COLUMNS 5.5-For rectangular tied columns and square columns with
steel arranged in a circle-- . 9 ksi .......................................
140
COLUMNS 5.6-For rectaugular tied columns and square columns with
steel arranged in a circle-f,. 12 ksi ......................................
140
COLUMNS 5.7-For circular columns-f,
. = 3 ksi ........................... 141
141
COLUMNS 5.8-For circular columns-L’ 4 ksi ...........................
...........................
142
COLUMNS 5.9-For circular c01iunns-f’ 5 ksi
COLUMNS 5.10-For circular columns--- . 6 ksi ..........................
142
COLUMNS 5.1 1-For circular columns-- . = 9 ksi ..........................
143
COLUMNS 5.12-For circular columns--- . 12 ksi .........................
143
COLUMNS /:Values of y for column cross sections
144
COLUMNS 6.1-For #3 and #4 ties or spirais................................
COLUMNS 6.2-For #5 ties and spirals ....................................
145
COLUMNS 7 - N o d load-moment strength interaction diagram
COLUMNS 7.1.1-R3-60.6
.............................................
146

COLUMNS 7.1.2-R3-60.7
.............................................
147
COLUMNS 7.1.3-R3-60.8
............................................. 148
COLUMNS 7.1.4-R3-60.9
..............................................
149
150
COLUMNS 7.2.1R4-60-6 .............................................
COLUMNS 7.2.2-R4-60.7
.............................................
151
............................................. 152
COLUMNS 7.2.3-R4-60.8
.............................................
153
COLUMNS 7.2.4-R4-60.9
.............................................
154
COLUMNS 7.3.1-DC-60.6
............................................. 155
COLUMNS 7.3.2-R5-60.7
COLUMNS 7.3.3R5-60.8 .............................................
156
157
COLUMNS 7.3.4-R5-60.9 .............................................
COLUMNS 7.4.1R6-60.6 ............................................
-158
COLUMNS 7.4.2-R6-60.7

.............................................
159
COLUMNS 7.4.3-R6-60.8
.............................................
160
COLUMNS 7.4.4-R6-60.9 .............................................
161
COLUMNS 7.5.1-0-75.6
.............................................
162
COLUMNS 7.5.2-R9-75.7
.............................................
163
.............................................
164
COLUMNS 7.5.3-DO-75-8
165
COLUMNS 7.5.4429-75.9 .............................................
COLUMNS 7.6.1R12-75.6 ............................................
166
COLUMNS 7.6.2-R12-75.7
...................................... ...... 167
COLUMNS 7.6.3R12-75.8 ............................................
168
COLUMNS 7.6.kR12-75.9 ............................................
169
170
COLUMNS 7.7.1L3-60-6 ..............................................
171
COLUMNS 7.7.2-L3-60-7 ..............................................

COLUMNS 7.7.3-L3-60-8 ..............................................
172
’

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

.
.


--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

COLUMNS 7.7.6L3-60.9 ..............................................
173
174
COLUMNS 7.8.1L4-60.6 ..............................................
-175
COLUMNS 7.8.2-L4-60.7 .............................................
176
COLUMNS 7.8.3-L4-60.8 ..............................................
COLUMNS 7.8.6L4-60.9 .............................................. 177
178
COLUMNS 7.9.1-L5-60.6 ..............................................

COLUMNS 7.9.2-L5-60.7 .............................................. 179
1??I
COLUMNS 7.9.3L5-60.8 ..............................................
COLUMNS 7.9.6L5.60.9 .............................................. 16 .
COLUMNS 7.10.1-L6-60.6 .............................................
182
183
COLUMNS 7.10.2-L6-60.7 .............................................
COLUMNS 7.10.3L6-60.8 ............................................. 184
COLUMNS 7.10.GL6-60.9 .............................................
185
COLUMNS 7.1 1.1L9-75.6 ............................................. 186
187
COLUMNS 7.1 1.2T9-75.7 .............................................
188
COLUMNS 7.1 1.3-L9-75.8 .............................................
189
COLUMNS 7.1 1.GL9.7 5.9 .............................................
190
COLUMNS 7.12.1L12-75.6 ............................................
COLUMNS 7.12.2712-75.7 ............................................
191
192
COLUMNS 7.12.3-L 12-75.8 ............................................
COLUMNS 7.12.4-L12-75.9 ............................................
19:
194
COLUMNS 7.13.1-43-60.6 ............................................
COLUMNS 7.13.243-60.7 ............................................ 195
196

COLUMNS 7.13.343-60.8 ............................................
COLUMNS 7.13. A 3 . 6 0.9 ............................................. 197
COLUMNS 7.14.1-CM0.6 ............................................
198
199
COLUMNS 7.14.244-60.7 ............................................
-200
COLUMNS 7.14.3-CM0.8 ...........................................
COLUMNS 7.14.Are60.9 ...........................................
201
202
COLUMNS 7.15.145-60.6. ...........................................
203
COLUMNS 7.15.245-60.7 ............................................
-204
COLUMNS 7.15.345-60.8 ...........................................
-205
COLUMNS 7.15.4-C5-60.9 ...........................................
-206
COLUMNS 7.16.146-60.6 ...........................................
COLUMNS 7.16.246-60.7 ...........................................
-207
-208
COLUMNS 7.16.3-C6-60.8 ...........................................
209
COLUMNS 7.16.AG60.9 ............................................
-210
COLUMNS 7.1 7.149-75.6 ...........................................
211
COLUMNS 7.17.2-49-75.7 ............................................

-212
COLUMNS 7.17.349-75.8 ...........................................
-213
COLUMNS 7.17.4-c9-75.9 ...........................................
COLUMNS 7.18.1412-75.6 ..........................................
-214
COLUMNS 7.18.2412-75.7 .......................................... -215
COLUMNS 7.18.3412-75-8. .......................................... 216
COLUMNS 7.18.4-cl2-75.9 .......................................... -217

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

viii

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT


COLUMNS 7.19.1-S3-60.6
............................................
218
........................................... -219
COLUMNS 7.19.2-S3-60.7
COLUMNS 7.19.3-43-60.8 ............................................
220
COLUMNS 7.19.AS3-60.9 ............................................. 221
COLUMNS 7.20.1-s4-60.6
...........................................

-222
............................................ 223
COLUMNS 7.20.2-S4-60.7
COLUMNS 7.20.3-S4-60.8
............................................ 224
COLUMNS 7.20.6S4-60.9 ........................................... -225
............................................ 226
COLUMNS 7.21.1-C5-60.6
COLUMNS 7.21.2-S5-60.7
........................................... -227
............................................ 228
COLUMNS 7.21.3-S5-60.8
229
COLUMNS 7.21.AS5-60.9 ............................................
COLUMNS 7.22.1-S6-60.6
........................................... -230
COLUMNS 7.22.2-S6-60.7
........................................... -231
COLUMNS 7.22.3-S6-60.8
........................................... -232
............................................ 233
COLUMNS 7.22.4-S6-60.9
COLUMNS 7.23.1-S9-75.6
...........................................
-234
........................................... -235
COLUMNS 7.23.2-S9-75.7
COLUMNS 7.23.3-S9-75.8
........................................... -236
COLUMNS 7.23.4-49-75.9 ............................................

237
COLUMNS 7.24.1-S12-75.6
..........................................
-238
.......................................... -239
COLUMNS 7.24.2-S12-75.7
COLUMNS 7.24.3-S 12-75.8 ..... .....................................
-240
241
COLUMNS 7.24.AS12-75.9 ...........................................
COLUMNS &-Solution to reciprocal load equation for biaxial bendingP,,
;/A, as a function of PJA,
Pv /A, and Po /A, .............................
242
COLUMNS 9-Solution to reciprocal load equation for biaxial bendingP,,/Poas a function of P,/P,, and PV /Po .................................. -243
COLUMNS 10-Biaxial bending design constant ß-For rectangular columns
244
COLUMNS 10.1-Witb two bars on each of four .faces ........................
-244
COLUMNS 10.2-With three bars on each of four faces .....................
COLUMNS 10.3-With four or more bars on each of four faces ................ -245
COLUMNS 10.4-With three,four, or five bars on each of two opposite faces ..... 245
-246
COLUMNS 11-Biaxial moment relationship ....................................
’

SLABS 1 ” B i n i m m slab thickness
SLABS 1.1-Minimum thickness of slab without intdor beams................ -248
SLABS 1.2-Minimm slab thiclmess for deflection of slabs on beams,
drop panels or bands

SLABS 1.2.13, 40,000 psi ........................................
-249
60,O00 psi ........................................
-250
SLABS 1.2.2-SLABS 2-Factor ?for calculating a ........................................... 251
252
SLABS 3.1-Factor klfor perimeter shear-Interior column ....................
SLABS 3.2-Factors k,’and k; for perimeter shear-Square interior column. . . . . . . 253

.
.

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

ix

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT


SLABS 3.3-Factors k2 and k3 (corrected fiom ki and k;) for perimeter shearNon-squarerectangular column ...........................................

TWO-WAY ACTION REINFORCEMENT 1-Maximrrm spacing of main reinforcement
for two-way action slabs and plates for crack control .........................
-263
TWO-WAY ACTION RENFORCEMENT2-Maximum tolerable crack widths

(recommended by AC1 Committee 224, Cracking. but not required by AC1 3 18.95) . . 264
TWO-WAY ACTION REINFORCEMENT 3-Crack widths as a function of grid index MI
in slabs and plates for any exposure condition (recommenáed by
AC1 Committee 224. Cracking. but not required by AC1 318-95) ................ 265
SEISMIC 1-bobable moment strengths for beams ...............................
-268
SEISMIC 2-Seismic design shear force, V, for beams and columns .................. -269
SEISMIC 3-Details of traosversereinforcement for beams and columns ................ 270
SEISMIC AVoiumetric ratio of spiral reinforcement p, for concrete confinement ........ 271
SEISMIC %Area ratio of rectilinear hoop reinforcement p, for concrete confinement ..... 272
SEISMIC &Joint shear .= in an interior beam-column joint ........................
273
SEISMIC 7-Joint shear .= in an exterior beam-column joint .......................
-274

GENERAL I.¡-Moments
in beams with fixed ends. fi-kips ........................
GENERAL 1.2-Moments in beams with fixed ends, fi-kips ........................
GENERAL 2.l-propertie~ of SeCti01ls ..........................................
GENERAL 2.2-prOperties of SeCti01ls ..........................................
CONVERSION FACTORS ....................................................

-276
-277
-278
-279
280

DESIGN EXAMPLES

Flexure Design Examples
I-Determination of tension reinforcement area for rectanguiar beam subject to
simple bending; no compression reinforcement .............................-284
2-Design of rectangular beam subject to simple bending; no compression reinforcement ... 285
3-Selection of slab thickness and tension reinforcement for slab subject to
Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

X
Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

254
SLABS 3.4-Factor k, for perimeter shear-Edge column .....................
-255
SLABS 3.5-Factors kj’ and k; for perimeter shear-Square edge column ........ 256
SLABS 3.ó-Factor k; (corrected fiom ki ) for perimeter shear-Non-square
rectangular edge column.................................................
257
SLABS 3-7-Factor k3 (CO&
fiomk; ) for perimeter shear-Non-square
rectangular edge column ...............................................
-258
SLABS 3.8-Factor k, for perimeter Shear-Corner column .................... 259
SLABS 3.9-Factors k2) and k; for perimeter shear-Square comer column....... -260
SLABS 3.1 &Factors k2 and k3 (corrected fiom k2)and ki) for perimeter shearNon-square rectangular comer column ..................................... 261
SLABS 3.1 I-Correction factor kato be applied to effective slab depth for column

(or capital) aspect ratios greater than 2.0 .................................... 262


Reinforcement Design Examples
1-For rectangular beam subject to benping, selection of reinforcement saliseing
bar spacing and cover requirements and crack control provisions
(using REINFORCEMENT 8.1,8.2, or 11) ................................
.296
2-For a one-way slab, verification íhat reinforcement satisfies spacing and cover
requirements and crack control provisions (using REINFORCEMENT 16). ....... .298
3-For rectangular beam subject to simple bending, selection of reinforcement
(found to require two layers) SatisQing bar spacing and cover requirements
and crack control provisions (verified using REMFORCEMENT 8.1) ........... -299
&For recâangular beam subject to simple bending, selection of reinforcement satisbar spacing and cover requirements and crack control provisions
(verified using REINFORCEMENT 11) ...................................
.301
I-DetWmination of maximumwidth of a beam reinforced with bundled bars satiscrack control provisions ................................................
-302
&Determination of development length required for positive-momentreidorcemmt in a
continuousbeam ......................................................
303
7-Detembation of development length required for positive-moment reinforcement
confined by stirrups ...................................................
-304
&Determination of development length required for negative-moment reinforcement .... -305
9-Determination of splice length required for dowels in tension in the stem
ofaretainingwall .....................................................
306
1Determination of development length required for bar endhg in
astandard90deghook .................................................

307

Shear Design Examples
1-Design of beam for shear strength by method of AC1 318-95, Section 11.3.1 ......... -310
2-Dete1mhation of shear strength of concrete in beam by more detaiied method
ofSection11.3.2 ......................................................
312
3-Determhíion of shear strength of concrete in beam by method of AC1 3 18-95,
-313
Section 11.3.1, and more detailed method of Section 11.3.2 ....................
4-Selection of size and spacing of vertical stirrups (minimum Stirnips required) ........ - 314
%Design of vertical stirrups for beam for which shear diagram is triangular. ...........-316
&Design of vertical stirnips for beam for which shear diagram is
trapezoidaland triangular ................................................
319
7-Design of inclined stirrups for beam for which shear diagram is triangular ........... .321
%-Determination
of thickness of slab (or footing) required to provide perimeter
shearstrength(square) ..................................................
~ 2 3
9-Determination of thickness of slab (or footing) required to provide perimeter
Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

xi

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

simple bending; no compression reinforcement .............................
.287
4-Selection of slab thickness and tension reinforcement for slab subject to simple bending;
no compression reinforcement; given p = OSp, or slab thickness ................ .289
5-Selection of slab thickness (for deflection control) and tension reidorcement for slab
subject to simple bending; no compression reinforcement ..................... . 2 91
6-Detennination of tension and compression reinforcement areas for rectangular beam
subject to simple bending; compression reinforcement is found not to yield ....... .293


shear strength (circular) ................................................
-324
1&Design of T-section for torsion ............................................ -325
11-Design of spandrel beam for torsion ......................................... 326
12-Design of T-section for torsion and flexural shear reinforcement ................... 327
1%Design of bracket in which provision is made to prevent development of horizontal
330
tensile force (N, = O) ...................................................
14-Design of bracket in which there is a horizontal tensile force N , ................. -332
1%Design for shear and equilibrium torsion .....................................
-334
16-Design for shear and equilibrium torsion ......................................
336
-338
17-Design for shear and compatibility torsion ...................................
1&-Design for shear and compatibility torsion ....................................
340

Footing Design Examples
1-Design of a continuous (wall) footing .........................................
2-Design of a square spread footing ...........................................
%Design of a rectangular spread footing .......................................
+Design of a pile cap ......................................................

344
-346
-349
-352

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

Deflection Design Examples
1-Effective moment of inertia for a rectangular section with tension reinforcement ....... 356
2-Deflection of a simple span, rectangular beam with tension re~orcement........... -357
3-Moment of inertia of a cracked T-section with tension reinforcement ............... -358
&Moment of inertia of a cracked &on with tension and compression reidorcement ... -359
%Live load deflection of a continuous beam .....................................
360
6-Simplified method for approximak calculation of deflection .......................
362
7-Effective moment of inertia of a rectangular beam with tension reinforcement .........363
8-Cracking moment for T - d o n ............................................. -364

Column Design Examples
1-Required area of steel for a rectangular tied column with bars on four faces
(slenderness ratio found to be below critical value) ..........................
-366
2-For a specified reinforcement d o . selection of a column section size for a

-368
rectangular tied column with bars on end faces only ..........................
3-Selection of reidorcement for a square spiral column with reverse curvature
(slenderness ratio found to be below critical value) ...........................
369
&Design of square column section subject to biaxial bending using resultant moment ... -371
%Design of circular spiral column section subject to very small design moment .........373
6-Selection of reinforcement for a rectaqph tied column with bars on four faces
(slenderness ratio found to be above critical value) ............................
375
7-Selection of reinforcement for a square spiral column with single curvature
(slenderness ratio found to be above critical value) ........................... -379
, for each column and
&Determination of moment magnification factors 6
6, for each level and required reinforcement ratio pgfor columns in the hrst
two stones of an unbraced íÌame ......................................... -382
%Determination of adequacy of square tied column section to biaxial bending,
using reciprocal load method with UPn,equation ............................. 391
Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

xii

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT


1 0 - D e t e e t i o n of adequacy of square tied column section subject to biaxial bending.
using load contour method and COLUMNS 10 and 11 .........................

393

Two-way Slab Design Examples
1-Two-way slab without beams. designed according to Direct Design Method ........... 396
2-Reinforcement spacing for crack control in panel of uniformly loaded two-way
slab for severe environment ..............................................
417

Seismic Design Examples
1-Adequacy of beam flexural design for seismic requirements ......................
-420
2-Design of transverse reinforcement for potential hinge regions of i111
earhquake resistant beam ............................................... 421
-423
3-Design of an earthquake resistant column .....................................
&Shear strength of a monolithic beam-column joint ............................... 426

COMMENTARY
Commentary on Design Aids for Strength of Members in Flexure ......................
430
Commentary on Resorcement Design Aids ......................................
438
Commentary on Design Aids for Shear Strength of Beams and Slabs .................. -453
-458
Commentary on Design Aids for Columns .......................................
Commentary on Design Aids for Deflection Control ............................... -470
-476
Commentary on Slab Design Aids ..............................................
Commentary on Two-way Action Reinforcement .................................

-479
-481
Commentary on Seismic Design Aids ...........................................

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

xiii

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT


AC1 318-95
Strength Reduction Factors*

I

FLEXURE. WITHOUT AXIAL LOAD
AXIAL TENSION O R AXIAL
TENSION WITH FLEXURE
~

Members with spiral reinforcement
conforminrr to Section 20.9.3
~~~

0.75"

Other reinforced members

O. 70"

Members in high seismic zones with
factored axial compressive forces
exceeding (A,f;/ZO) if transverse
reinforcement does not conform to
Section 21.4.4

0.50

0.8.5

SHEAR A N D TORSION

SHEAR A N D TORSION
(in regions of high seismic risk)

0.90

0.60
Nominal shear strength of the
member is less than the nominal shear
corresponding to the development of
the nominal flexural strength of the
member

Shear in joints of buildings

O.85

BEARING O N CONCRETE"'

O. 70

FLEXURE IN PLAIN CONCRETE

0.65

*

**
***

Design strength provided by a member shall be taken as the nominal strength, calculated
from the design aids given in this handbook, multiplied by the appropriate strength reduction
factor 4. Alternate strength reduction 4 factors for tise with ASCE 7 load factors are
included in ACi 318-95, Appendix C.
See AC1 318-95 Section 9.3.2.2 or Appendix B for adjustment to these 4 values for low
levels of axial compression.
Also see ACI 318-95 Section 28.13.

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

xiv

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

AXIAL COMPRESSION O R
AXIAL COMPRESSION WITH
FLEXURE

I

0.90


The AC1 Design Handbook is intended for use by
persons having a general familiarity with the strength
design method and with “Building Code Requirements
for Structural Concrete (AC1 3 18-95).”
This volume presents information for the engineering
design and analysis of beams, slabs, brackets, footings,
pile caps, columns, two-way slabs, and seismic design.

to bring it into accordance with that code. The resulting
second edition of Volume 1, which incorporated some
material on columns, was issued in 1973 and a second,
corrected printing was published in 1974.
The August 1977 AC1 Journal carried “Step-by-step
Design Procedures in Accordance with the Strength
Design Method of AC1 3 18-7 1 ,”subsequently published

as AC1 Committee Report 340.3R-77.
While AC1 3 18-77 was being prepared for publication
in the fall of 1977. Committee 340 was revising the
handbook volumes accordingly. The resulting new
edition of Volume 2 on columns was published in May
1978. In late 1978, a supplement to the Strength Design
Handbook dealing with two-way-action slabs and entitled
Slab Design in Accordance with ACI 318-77 was
published.
The third edition of Volume 1, published in 1981,
contained two divisions: Division I dealt with beams,
one-way slabs, brackets, footings, and pile caps and
incorporated the Step-by-step Design Procedures-all
material being updated to AC1 318-77. Division II
consisted of the two-way slab design supplement.
The fourth edition of Volume 1 was published in 1984.
It was the revised edition of the third edition to conform
to AC1 3 18-83, including new flow charts for design of
members in flexure. Design of Two-way Slabs was
published as a supplement to Volume 1 in 1985.
The fifth edition of Volume 1 was formatted in the same
manner as the fourth edition. Design of Two-way Slabs
(Supplement to Volume I) was made a separate volume,
Volume 3 of the AC1 Design Handbook.
This edition is developed in accordance with AC1 3 1895. This version of the code was prepared in a format to
correspond to a strength reduction factor of 1.0. This
format was used in order to make the handbook more
usefil for international use.

SECTIONS

Design Aids are tables and graphs intended to save the
designer the effort of repeatedly performing routine
calculations. All Design Aids apply to concrete having f:
ranging between 3 and 12 ksi with Grade 40,60, and 75
steel reinforcement depending on the type of the
structural member. A note at the bottom of each Design
Aid indicates which Design Example illustrates the use of
the table or graph.
Design Examples illustrate the use of the Design Aids
(but are not intendeil to show how to design a structure).
Commentary on Design Aids gives the basis for the
Design Aids.
Forjudiciousapplication and optimum efficiency, users
of this handbook should first acquaint themselves with
the Commentary. Design Examples will help veri@
procedures and results. It is not, however, the objective
of the handbook to teach the novice how to design in
reinforced concrete. Readers are expected to be
competent in design before attempting to use this
handbook.

AC1 COMMIITEE 340 AND ITS WORK
HANDBOOK USER’S COMMENTS

AC1 Committee 340, Design Aids for Building Codes,
was organized in 1958 for the purpose of preparing a
handbook that would simpliQ the design of reinforced
concrete structural elements using the strength design
method in accordance with the AC1 Building Code. The
handbook was prepared in two volumes: Volume 1

covering beams, one-way-action-slabs, footings, and
other members except columns; and Volume 2 treating
columns only. Volume 1 was issued in 1967; Volume 2
was ready first and published in 1964. Both volumes
were in accordance with the 1963 version of the AC1
Building Code.
In 1971 when AC1 3 18-7 1 was issued, Committee 340
was charged with revising the existing handbook material

AC1 Committee 340 welcomes suggestionsfrom users
of this handbook on how to make future printings more
useful. Comments should be directed to AC1 Committee
340, American Concrete Institute, P.O. Box 9094,
Farmington Hills, Michigan 48333.

ACKTWOWLEDGMENTS
Many individuals and organizations have contributed to
the preparation of this book, giving their time and effort
to the preparation of charts, tables, examples, and

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

xv

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

computer programs, as well as undertaking critical
review of the manuscript. Although it is practical to
acknowledge individually all of these contributions, they
are nonetheless greatly appreciated,for such efforts have
contributed materially to the quality of this handbook.
The leadership and work of the committee chairman,
Mdisen A. Issa, are greatly appreciated for which a large
portion of the handbook development process is
attributed to. The work of every committee member
involved in the development of the New Design
Handbook is appreciated. Also appreciated are the
efforts of Dr. Issa’s graduate students, Alfred A. Yousif
and Stanislav Dekic.
Grateful acknowledgment is made of computer time
contributed by the University of Illinois at Chicago.

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

xvi

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT

NOTATION

=
=

This notation section defmes symbols used in this
volume covering beams, one-way slabs, footings, pile
caps, columns, two-way slabs, and their reinforcement.
Words in parentheses such as "(Flexure)" or "(Shear)"
indicate portions of this handbook in which symbol
is used.
depth of equivalent rectangular stress block,
in. (Flexure)
length for column section considered rigid
(one half slab thickness) or length of rigid
column section at beam end (square column
with boxed capital), in. (Two-way slabs)
factor for computing K,, in-'
depth of equivalent rectangular stress block
for balanced conditions, in. (Flexure)
immediate deflection at midspan, in.
(Deflection)
immediate deflection due to dead load, in.
immediate deflection due to dead load
and live load, in.
immediate deflection due to live load, in.
f , (1 0.590) / 12000, ft-kip / in', a coeffcient for computing reinforcement area A,y.
(Flexure)
f , ( i - d'/d) i 12000, fi-kip í in', a coefficient for computing reinforcement area A :s
(Flexure)

-

aiooo
l,ooo(

1

-:)( 1-5)--c( ):1

'

a coefficient for computing reinforcement
area A', when compression reinforcement
does not yield. (Flexure)
f , (1 - hf i 2 4 I 12000, fi-kip i in', a coefficient for evaluating flange effects on moment in T-beams (Flexure)
any area, in2
b t / n = effective tension area of concrete
for crack control, in2 per bar (Reinforcement)
b t / n' = effective tension area of concrete
for crack control in case bundled bars are
used, in2,per bar bundle (Reinforcement)
loaded area, in2
the area of the lowest base of the largest
úustum of pyramid, cone, or tapered wedge
contained wholly within the support and
having for its upper base the loaded area,
and having side slopes of 1 vertical to 2
horizontal, in2
area of individual bar, in2. (Reinforcement)

area of concrete at cross section considered,
in2(Flexure)
area of critical shear section = bod (Twoway slabs)

=
=

=

=
=
=
=

=
=
=

area of core of spirally reinforced column
measured to outside diameter of spiral
area enclosed by outside perimeter of concrete cross section
gross area enclosed by shear flow path, in2
minimum area of tension reinforcementA ,
to keep neutral axis low enough for
compression reinforcement to reach yield
strain under factored load conditions, in2
(Flexure)
area of reinforcement in brackets or corbel
resisting
factored

moment
[ K, a + NI,, (h-41, in2
gross section area of column cross section,
in2 (Shear)
area of shear reinforcement parallel to
flexural tension reinforcement, in2(Shear)
area of tension reinforcement to resist force
N,, on brackets, in2(Shear)
area enclosed by centerline of the outermost
closed transverse torsional reinforcement,
in2
area of non-prestressed tension reinforcement, in2(Shear, Two-way slabs)
area of compression reinforcement, in2
(Flexure )
minimum amount of flexural reinforcement,
in2

= area of tension reinforcement in tension

zone required to counterbalance compressive force in overhanging portion of flanges
in flanged section, in2(Flexure)
= area of bar or wire from which spiral is
formed, in2(Columns)
= total area of longitudinal reinforcement in
cross section, in2
= area of tension reinforcement required to
counterbalancecompressive force in web or
steam of flanged section, or in concrete
alone in beams reinforced in compression,
in2(Flexure)

= area of larger bars in a bundle, in' (Reinforcement)
= area of tension reinforcement required
under factored load conditions for a rectangular beam with tension reinforcement
only, in2(Flexure)
= area of steel per ft of slab width, in2 (Twoway slabs)
= area of smaller bars in the bundle, in2
(Reinforcement)
= area of tension reinforcement required
under factored load conditions to counterbalance compressive force contributed by
compressive reinforcement, in2(Flexure)
= maximum area of tension reinforcement at
which depth of stress block a will be equal
to or smaller then flange thickness h,
(Flexure)

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT


C,,,= 0.6 + 0 . 4 ( h f 1/M,) but not less than
0.4. For all other cases, C,,,shall be taken as

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

area of one leg of a closed stirrup resisting
torsion, within a distance s, in2(Shear)
total cross section area of all transverse
reinforcement which is within the spacing s
and which crosses the potential plane of
splitting through the reinforcement being
developed, in2
total area of web reinforcement in tension
within distance s. measured in direction
parallel to longitudinal reinforcement, in2
(Shear)
area of shear friction reinforcement, in2
width of compression face of member, in.
(Flexure)
overall cross section dimension of rectangular column, in. (Columns)
capital depth measured from lower surface
of slab (Two-way slabs)
perimeter of critical section for two-way
shear, in.
width of the critical section defined in
1 1.12.1.2(a) measured in the direction of
the span for which moments are
determined, in.
width of the critical section defined in
11.12.1.2(a) measured in the direction
perpendicular to b,
ratio of long side to short side of concentrated load or reaction area
width of column transverse to direction of
applied moment (= c2 when there is no
capital), in.

size of square drop panel, fi (Two-way
slabs)
web width, in.
width of beam stem, in. (Two-way slabs)
nominal bearing strength of loaded area
spacing or cover dimension, in.
distance from extreme compression fiber to
neutral axis
size of rectangular or equivalent rectangular
column, capital, or bracket measured in the
direction of the span for which moments are
being determined, in.
size of rectangular or equivalent rectangular
column, capital, or bracket measured transverse to the direction of the span for which
moments are being determined, in.
clear concrete cover to surface of outer
layer of reinforcement, in. (Two-way
slabs)
compression force, kips (Flexure)
torsion constant, see Eq. (13-7) (Two-way

1.O.)
compression force in reinforcement, kips
(Flexure)
= distance from the extreme compression
fiber to centroid of tension reinforcement,
in. (Flexure, Two-way slabs)
= distance from the extreme compression
fiber to centroid of compression reinforcement, in. (Flexure)
= nominal diameter of bar, in. (Reinforcement)

= equivalent diameter for bundled bars, in.
(Reinforcement)
= diameter of a reinforcing bar closest to
concrete extreme tensile surface, in. (Twoway slabs)
= diameters of bars in bundles with two different sizes, in. (Reinforcement)
= distance from extreme tensile surface to
center of closest tensile reinforcing bar, in.
(Reinforcement, Two-way slabs)
= distance from extreme tensile fiber to center
of gravity of closest bundle or layer of
bundles, in. (Reinforcement)
= distance from extreme compression fiber to
centroid of tension reinforcement of drop
panel, in.
= nominal diameter of stirrups, in. (Shear,
Columns)
= distance from extreme tensile fiber to
centroid of tension reinforcement = t/2, in.
(Reinforcement)
= dead loads, or their relative internai moments and forces
= eccentricity of axial load at end of beam,
measured from centerline of beam, in.
(Flexure)
= eccentricity of axial load at end of member,
measured from centroid of the tension
reinforcement, calculated by conventional
methods of frame analysis, in. (Flexure)
= eccentricity along x-axis, in. (Columns)
= eccentricity along y-axis, in. (Columns)
= modulus

of elasticity of concrete

=

=0.033~

Ecb
Ecc
Ecs

slabs)
compression force in concrete, kips (Flex-

Es

Ure)
factor relating actual moment diagram to an
equivalent uniform moment diagram (For
members braced against sidesway and
without transverse loads between supports,
Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

EI

xviii

\llel ,ksi

modulus of elasticity of beam concrete, ksi
(Two-way slabs)
= modulus of elasticity of column concrete,
ksi (Two-way slabs)
= modulus of elasticity of slab concrete, ksi
(Two-way slabs)
= modulus of elasticity of steel reinforcement
(29000 ksi) (Flexure)
= flexural stimiess of cross section for frame
analysis, k-inz (Flexure)

=

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT


=
=
=

=

=

f

.%

fy

=

=

=
=

F

=

h

=

=

h"
hC

=
=

=

=
=
=
=

=

=
=
=

=
=

flexural stiffness of compression member,
k-in2 (Flexure)
specified compressive strength of concrete,
psi
average tensile splitting strength of light
weight aggregate concrete,.psi
7 . 5 c

=

=
=

, modulus of rupture of con-

crete, psi
calculated tension stress in reinforcement at
service loads, ksi (Reinforcement, Two-way
slabs)
calculated stress in reinforcement in compression, E,vE) if,.,psi (Flexure)
specified yield strength of nonprestressed

reinforcement, psi (Flexure, Two-way
slabs)
yield strength of closed transverse torsional
reinforcement
yield strength of longitudinal torsional
reinforcement
bd2
I2000

JC

=

=

k

=
=

flexural coefficient = - or M /KI,

=

II

(Flexure)
overall thickness of section or thickness of
member (Beams, One-way slabs, Two-way
slabs)

diameter of round column or side of a
rectangular column, in (Columns)
diameter of round column, in.
pier or column dimension parallel to
investigated direction (= cl when there is no
capital, for Two-way slabs), in. (Two-way
slabs)
core diameter of spiral column = outside
column dimension minus cover, in. (Columns)
total thickness of drop panel (slab thickness plus drop), in. (Two-way slabs)
effective thickness of a column for slenderness considerations, in.
flange thickness, in. (Flexure, Deflection)
thickness of slab, in. (Two-way slabs)
minimum thickness of slab, governed by
deflection requirements, in. (Two-way
slabs)
minimum thickness of slab, governed by
shear requirements, in. (Two-way slabs)
moment of inertia of section resisting externally applied loads, in4(Shear)
moment of inertia of gross section of column, in4(Columns)
moment of inertia of cracked section transformed to concrete, in4(Deflection)
moment of inertia about centroidal axis of
gross section of beam (including part of
adjacent slab section as defined in ACI 3 1895, Section 13.2.4), in4(Two-way slabs)

=

=

=

=
=

=
=

=

K

=

=

=
=
=

Kcn

-

moment of inertia of gross concrete section
about the centroidal axis, neglecting reinforcement, in4(Deflection)
gross moment of inertia of T-section, in4
(Deflection)
moment of inertia of reinforcement about
centroidal axis of member cross section, in.
(Columns)
property of assumed critical section analogous to polar moment of inertia (Two-way

slabs)
(d - 0.5 4) / d, ratio of lever arm between
flange centroid and centroid of tension
reinforcement to effective depth d of a
section (Flexure)
(d - 0.5 a) / d, ratio of lever arm between
centroid of compression rectangular stress
block and tension reinforcement to effective
depth d of a rectangular section (Flexure)
moment coefficient for flexural members
(Flexure)
steel strength factor used in evaluation of
h,y(4(Two-way slabs)
effective length factor for compression
members (Columns)
column stiffness coefficient (Two-way
slabs)
flexural stiffhess coefficient (Two-way
slabs)
perimeter shear stress factor, in" (Two-way
slabs)
moment-shear transfer stress factor, in-* ft'
(Two-way slabs)
moment-shear transfer stress factor, in" ft'
(Two-way slabs)
moment-shear transfer stress factor for
square column or capital, in-2fi-' (Two-way
slabs)
moment-shear transfer stress factor for
square column or capital, in-2ft-' (Two-way

slabs)
fracture coefficient used in crack width
determination to obtain maximum allowable spacing of reinforcement in two way
slabs and plates (Two-way slabs)
a constant relating to EI and having the
same units as EI
I728 t2/ 4 8 4 = coefficient for immediate
deflection of beam (Deflection)
u,b / ó, w = coefficient for approximate
immediate deflection of beam (Deflection)
coefficient relating moment at midspan to
deflection at midspan (Deflection)
-x-

4

12000

cracking moment of T-section (Deflection)

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

, coefficient for computing
6

Licensee=Bechtel Corp/9999056100

Not for Resale, 05/04/2005 04:29:24 MDT


@, =

length of slab span transverse to P I , measured center-to-center supports (Two-way
slabs)
= width of interior design frame (transverse to
PI), measured from center line to center line
of adjacent slab panels (AC1 3 18-95, Section 13.6.2.3) (Two-way slabs)
= width of exterior design frame ,measured
from center line to center line of adjacent
slab panels (AC1 3 18-95, Section 13.6.2.3)
(Two-way slabs)
0,
= embedment length at support or at point of
inflection, in. (Reinforcement)
= average of P, or P, (Two-way slabs)
Pc
= length of compression member in a frame,
measured from center to center of joints in
the frame
= vertical distance between supports, in.
= height of column
c
= development length, in. (Reinforcement)
@d1
= usable (available) anchorage length, in.
(Reinforcement)
e&

= basic development length of straight bars,
in as specified in Sections 12.2.2 and 12.3.2
of AC1 3 18-95 (Reinforcement)
P&
= development length of hooked bars, to
exterior face of bar at the bend, in. (Reinforcement)
e,,
= basic development length of standard hook
in tension, in. (Reinforcement)
= longer of P, or width of design frame e2
et
Pl,
= clear span measured face to face of supports
(Reinforcement)
= clear span measured face to face of supports
or face to face of beams in slabs with beams
(Two-way slabs)
= shorter of e, or width of design frame P2
4
4,
= unsupported height of column (Two-way
slabs)
= length of shearhead arm from centroid of
concentrated load or reaction, in. (Shear)
L
= live loads, or their related internal moments
and forces (Two-way slabs)
= magnified factored moment to be used for
design of column (Columns)
m

= distance from exterior face of edge panel to
center of exterior column (Two-way slabs)
M
= fixed-end moment coefficient (Two-way
slabs)
M,
= smaller
factored end moment on
compression member, positive if member is
bent in single curvature, negative if bent in
double curvature, kip-fî (Columns)
M,n,v = factored end moment on compression member at the end at which M, acts, due to loads
that cause no appreciable side sway, calculated using a fust order elastic frame analysis

I , / bd 3, coefficient for moment of inertia
of cracked rectangular sections with tension
reinforcement only (Deflection)
Icr / bd 3, coefficient for moment of inertia
of cracked rectangular sections with compression reinforcement, or T-beams (Deflection)
I, / 4, coefficient for effective moment of
inertia (Deflection)
I, / (b, h / I 2 ) , coefficient for gross moment of inertia of T-beams (Deflections)
12000 M,, / b d 2 = f'! O ( 1 - 0.59 O),
strength coefficient of resistance, psi (Flexure)

Ki,

=

Ki,

=

Ki,

=

Ki,

=

K,,

=

Kllr

=

K,

=

puting reinforcement area A,, psi (Flexure)
torsional stiffness of transverse torsional
member; moment per unit of rotation =

K,

=

transverse

EX[
0 - 11
12000 b"

A,

, coefficient for com-

reinforcement

index

=

f,

1500 s n

-

(bw- 3.5)(h - 3.5)
12

KI,

=

K,

=

Kd

=
=

KvJ

=

ZK

=

P

=

=
=

=

P, to P5

=

4

=

a, , coefficient for

design of torsion reinforcement (Shear)
strength coefficient for resistance =
MJF= 12,000 M,, / ( b d )=X.'O( 1 - 0.590)
p, divided by the reinforcement ratio for
shear friction reinforcement perpendicular
to shear plane (Shear)
Av&, shear coefficient for stirrups (Shear)
[6.5 - 5.1 (N, / V,)'"][1+(64 + 160 (Nut /
Vu)'" p] 0.5 (Shear)
2.0 - a / d (Shear)
Combined flexural stiffhess of slab and
column (Two-way slabs)
span length, ft or in. (Reinforcement,Shear)
span length of beam, center-to-center of
supports (Two-way slabs)
width of slab strip used to calculate a
(Two-way slabs)
span length of beam or slab, as defined in
AC1 3 18-95, Section 8.7, in. (Columns)
minimum spans required for bar development depending on type of span and support and percentage of bars extended into
support, ft and in. (Reinforcement)
length of slab span in the direction in which
moments are being determined, measured
center-to-center supports (Two-way slabs)

PV

xx
Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT


=

=

=
=
=
=

=

=

=
=

=
=
=
=

=
=
=
=
=
=
=

=
=

=

unbalanced moment at support, in direction
of span for which moments are being determined (Two-way slabs)
factored end moment on compression member at the end at which M, acts, due to
loads that cause appreciable side sway,
calculated using a first order elastic frame
analysis
larger factored end moment on compression
member, always positive (Columns)
unbalanced moment perpendicular to M l
(Two-way slabs)
minimum value of M2
factored end moment on compression member at the end at which M2 acts, due to loads

that cause no appreciable side sway, calculated using a first order elastic frame analysis
factored end moment on Compression member at the end at which M, acts, due to loads
that cause appreciable side sway, calculated
using a first order elastic frame analysis
factored negative moment at interior column (except first interior column), kip-ft
(Two-way slabs)
factored positive moment at interior span ,
kip-ft (Two-way slabs)
factored negative moment at exterior support, kip-ft (Two-way slabs)
factored negative moment at first interior
support, kip-ft (Two-way slabs)
factored positive moment at midspan of
exterior span, kip-ft (Two-way slabs)
maximum moment in member at stage for
which deflection is being computed, in-lb
moment at center of beam or a moment
value related to the deflection, kip-ft (Deflection)
cracking moment of gross concrete section
= ZJ /y,, in-ft (Deflection)
moment due to dead load, kip-ft (Deflection)
moment due to dead and live load, kip-ft
(Deflection)
moment due to live load, kip-ft (Deflection)
reinforcing spacing grid index for crack
control (Two-way slabs)
nominal moment strength of section, kip-ft
(Flexure)
nominal moment strength of section with
compression and tension reinforcement,
kip-ft (Flexure)

nominal moment strength of overhanging
flanges of T-beam, kip-ft (Flexure)
nominal moment strength of rectangular
beam (or web of T-beam) when reinforced
for tension only, kip-ft (Flexure)
nominal moment strength of a cross section
before compression reinforcementand extra

=

=
=
=
=
=
=
=

=
=
=
=
=

=

=
=

=

=
=
=
=

=

=

=

=
=
=

=
=
=

tension reinforcement are added = MI,- Mta,
k i p 4 (Flexure)
that portion of MI,assigned to compression
reinforcement or flange regions of I and
T-sections, kip-ft (Flexure)
total factored static moment (Flexure)
moment at point of zero shear (Shear)
moment due to loads causing appreciable
sway
moment at left support, for deflection,

kip-ft (Deflection)
moment at right support, for deflection,
kip-ft (Deflection)
applied factored moment at section, kip-ft
(Flexure, Two-way slabs)
factored moment acting on section if axial
force N, is considered to act at centroid of
tension reinforcement, kip-ft (Flexure)
nominal moment strength about x-axis
(Columns)
nominal moment strength about y-axis
(Columns)
equivalent uniaxial moment strength about
x-axis (Columns)
equivalent uniaxial moment strength about
y-axis (Columns)
factored moment about x-axis (Columns)
factored moment about y-axis (Columns)
service wind load moment, kip-ft (Columns)
modular ratio = E, / E, (Deflection)
equivalent number of bars = tensile reinforcement area over largest bar area, for
crack control (Reinforcement)
number of longitudinaltorsion bars (Shear)
number of bar diameters between center
and perimeter of bend (Reinforcement)
number of bars in flexural tension reinforcement (Reinforcement)
equivalent number of bar bundles = projected surface of bundle over actual surface
of bundle (Reinforcement)
compressive force on reinforcement in a
cross section, kipft (Flexure)

factored axial load normal to cross section
occurring simultaneously with V , - to be
taken as positive for compression, negative
for tension, and to include effects of tension
due to shrinkage and creep, kips (Shear)
factored tensile force on bracket or corbel
acting simultaneouslywith Vu,kips (Shear)
service concentrated load on beam, kips
(Deflection)
nominal axial load strength (balanced strain
conditions), kips (Columns)
critical axial load, kips (Columns)
service axial dead load, kips (Columns)
service axial live load, kips (Columns)
nominal axial load strength at given eccentricity, kips (Columns)

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT


=

Plu.*

=

Ply*

=

P"

=

PI,

=

PI,,.

=

P
I
I
X

=

ply

=

PCP

Ph

=
=

9s
r

=
=

S

=
=

=
SI

=

si,st

=

si

=

=

S2

Sby

S

S,

=
=
=

t

=

T

=
=

=

T,

=

T.

=

approximation of nominal axial load
strength at eccentricities e, and e,, , kips
(Columns)
nominal axial load strength for eccentricity
e,, along x axis only, x-axis being axis of
bending, kips (Columns)
nominal axial load strength for eccentricity
e,. along y axis only, y-axis being axis of
bending, kips (Columns)
nominal axial load strength at zero eccentricity, kips (Columns)
factored axial load at given eccentricity,
kips (Columns)
factored axial load for eccentricity er along
y-axis only, kips (Flexure)
factored axial load for eccentricity e,, along
x-axis only s @PIiy,kips (Flexure)
factored axial load for eccentricity e,,, along
y-axis only s @i',,
kips (Flexure)
outside perimeter of cross-section A,,, in.
perimeter of center line of outermost closed
transverse torsional reinforcement, in.
stability index for story
radius of gyration of cross section of compressive member
center to center spacing of bars, in.
center to center spacing of web reinforcement, in. (Shear)
maximum spacing of transverse reinforcement within Pd center to center, in.

required stirrup distance, ft (Shear)
center to center spacing of reinforcement in
either direction "1" or "2",in. (Shear)
reinforcement spacing measured in direction of span for which moments and crack
control are being analyzed, in. (Two-way
slabs)
reinforcement spacing measured perpendicular to spanwise direction of span for which
moments and crack control are being analyzed, in. (Two-way slabs)
clear spacing between bars or bundles of
bars, in. (Reinforcement)
elastic section modulus of section, in'
pitch of spiral, center to center of bar (Columns)
thickness of tension area for crack control,
in. (Reinforcement)
thickness of wall of hollow section, in.
load caused by the cumulative effect of
temperature, creep, shrinkage, differential
settlement, and temperature
tension force on reinforcement, kips
(Flexure)
nominal torsional moment strength provided
by
torsion
reinforcement
(Reinforcement)
factored torsional moment at section
(Shear)

Copyright American Concrete Institute
Provided by IHS under license with ACI

No reproduction or networking permitted without license from IHS

U

=

=
=

=
=
=
=
=
=
=
=
=
Y

=

W

=
=

WC

Wd

=
=

=
=

wmech

=
=

=
=
X

=
=

X

=

=
=
=
=

xxii

beam width factor in ratio u / h,,, used in
calculation of u& u = b for interior beam;
u = 2b for edge beam (Two-way slabs)
(V, / b J ) , nominal shear stress carried by
concrete, psi (Shear)
shear stress at diagonal cracking due to all
factored loads, when such cracking is result
of excessive principal tensile stresses in
web, psi (Shear)
(V,Jb,&, nominal shear stress, psi (Shear)
(V,, / bd), nominal shear stress, psi (Twoway slabs)
(V, / b,ú), nominal shear stress carried by
reinforcement, psi (Shear)
nominal shear strength attributable to concrete, kips (Shear, Two-way slabs)
nominal shear strength attributable to shear
reinforcement, kips (Shear)
nominal shear strength at section, kips
(Shear)
factored shear force, kips (Shear)
factored horizontal shear in story
factored perimeter shear force on critical
shear section (Two-way slabs)
factored shear force caused by wall supported slab (Two-way slabs)
crack width, in. (Reinforcement, Two-way
slabs)
pattern loading unit load, psf (Two-way
slabs)
unit weight of concrete, pcf
uniformly distributed factored dead load,
kips per ft (Two-way slabs), or kips per in

uniformly distributed factored live load,
kips per ft (Two-way slabs), or kips per in
maximum tolerable crack width for type of
exposure, in. (Two-way slabs)
mechanical load per unit area, psf (Twoway slabs)
superimposed dead load, psf (total dead
load not including self weight of slab, Twoway slabs)
factored load per unit length of beam
(Flexure)
factored load per unit area, psf; = (typically) 1.4 wJ+ 1.7 w,(Two-way slabs)
variable distance
shorter overall dimension of rectangular
part of section, in. (Two-way Slabs)
distance between centroid of column and
centroid of shear section, in. (Two-way
slabs)
minimum clear spacing between bundled
bars, in. (Reinforcement)
distance from extreme tensile fiber to neutral axis, in. (Deflection)
variable distance
longer overall dimension of rectangular part
of section, in. (Shear, Two-way slabs)

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

Pl,¡

centroidal distance from bottom of bundled
bars, in. (Reinforcement)
= distance from centroidal axis of gross
section, neglecting reinforcement, to extreme fiber in tension, in.
= quantity limiting distribution of flexural
reinforcement (Reinforcement)
= angle between shear reinforcement and
longitudinal axis of member, degrees
(Shear)
= bar location factor
= relative beam stiffness; ratio of flexural
stiffness of beam section to flexural stiffness of a width of slab bounded laterally by
center lines of adjacent panels (if any) on
each side of beam = (E,&) i
(Twoway slabs)
= a in direction el
= a in direction e,
= b/b,(Deflection)
= constant used to compute V , in nonprestressed slabs
= average value of a for all beams on edges
of slab panel (Two-way slabs)
= ratio of distance between extreme tensile
fiber and neutral axis to distance between
neutral axis and centroid of tensile
reinforcement ,x, i x, (Reinforcement)
= coating factor
= ratio of long to short clear spans (P.) of a
slab panel (Two-way slabs)
= biaxial bending design constant = constant

portion of uniaxial factored moment
strengths M,, and M,w,,,which may be permitted to act simultaneously on the column
cross section (Columns)
= a coefficient relating depth of equivalent
rectangular stress block to depth from
compression face to neutral axis = 0.85 for
fc' s 4.0 ksi and 0.85 - O.O5Y, ' - 4.0) for
fi'> 4.0 ksi, (PI 2 0.65), (Flexure)
= ratio of dead load per unit area to live load
per unit area (in each case without load
factors) (Two-way slabs)
= design coefficient for deflection = mp'/ n
p; = (n-l)p'/np ;= (616, - i)h,/dnp (Deflection)
= ratio of long side to short side of concentrated load or reaction area (Shear, Twoway slabs)
= ratio of maximum factored axial dead load
to maximum total factored axial load,
where the load is due to gravity effects
only in the calculation for P, in Eq. (1 0.7),
or ratio of the maximum factored sustained
lateral load to the maximum total factored
lateral load in the story in the calculation
for P, in Eq. (1 0.8) (Columns)
= ratio between long and short center-tocenter spans (e, / e,) (Two-way slabs)
=

YI

Z

a

ß

ß*

ß.
P E

ßd

ßh
ß,

ß,,
ßy

Y

=
=

=
=
=

=

=

y,

=

YP

=

Y"

=

6

=

6h

=

6s

=

E

=

E,

=

€3

=

E',

=

EU

=

8

=

A

=

=

=

Am

:
€

=
=

=
=

h,/ h (Deflection)
ratio of torsional stiffness of edge beam to
flexural stifkess of a width of slab equal to
span length of beam, center-to-center of
supports = (Ec&') i (EJJ (Two-way slabs)
ratio of c to d (Flexure)
sin a + cos a for inclined stirrups (Shear)
bar size factor
factor in calculating slab thickness required
by deflection; = the value of the denominator of Eq. (9- 1i), or (9- 13) divided by 1O00
(Two-way slabs)
ratio of distance between centroid of outer
rows of bars and thickness of cross section,
in the direction of bending (Columns)
hction of unbalanced moment transferred
to column by flexure, Eq. (13-1) (Two-way
slabs)
moment at point of zero shear to simple
span maximum moment (Shear)
hction of unbalanced moment transferred
by eccentricity of shear at slab-column
connection; = 1 - y,(Two-way slabs)
coefficient depending on type of span and
degree of reinforcement (Deflection)

moment magnification factor for columns
braced against sidesway (Columns)
moment magnification factor for frames not
braced against sidesway, to reflect lateral
drift resulting fiom lateral and gravity loads
(Columns)
unit strain, in. i in. (Flexure)
unit strain in concrete (Flexure)
unit strain in tension reinforcement (FlexUre)
unit strain in compression reinforcement
(Flexure)
fy 1 E, nominal yield strain of reinforcement
(Flexure)
angle of compression diagonals in truss
analogy for torsion
lightweight aggregate concrete factor.
When lightweight concrete is used
fCltl(6.72fc3. When normal weight concrete
is used 1.O (Shear)
ratio of M, with compression reinforcement
to M, without compression reinforcement
(Columns)
multiplier for additional long-time deflection, equals to ratio of creep and shrinkage
deflection to immediate deflection due to
sustained loads (Deflection)
a coefficient relating development lengîh to
minimum required span length
coefficient of fiction
time-dependent factor for sustained load
(Deflection)

dimensionless constant used in computing
lgand Zw (Columns)

--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

Copyright American Concrete Institute
Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT


P
P‘
Pb
--`,``,,,,``,,`,,`,,`,,````,`-`-`,,`,,`,`,,`---

p),c

PK

p,

active steel ratio = A ,s, / (24d c ) (Two-way
slabs)
= reinforcement ratio for shear friction reinforcement (Shear)
4
= strength reduction factor as defmed in
Section 9.3 of AC1 3 18-95

pe,pie,pm= factors used in distribution of moment in an
exterior span (Two-way slabs)
o
= coefficient indicating relative strength of
reinforcement and concrete in member
= pf, lfE’ (Flexure, Two-way slabs)
= ratio of sum of stifìñess Z ( I / e,) of com$
pression members in a plane at one end of
a compression member

tension reinforcement ratio = A,y/ bd (Flexure)
= compression reinforcement ratio= A:, / bd
(Flexure)
= reinforcement ratio producing balanced
conditions (Flexure)
= balanced percentage of reinforcement for a
section with compression reinforcement
(Flexure)
= A,,, / A, = ratio of total reinforcement area to
cross-sectional area of column (Columns)
= A,$/ bJ(Flexure)
=

Pit

’‘

Fig. 1-Notation

Copyright American Concrete Institute

Provided by IHS under license with ACI
No reproduction or networking permitted without license from IHS

=

xxiv

for slabs

Licensee=Bechtel Corp/9999056100
Not for Resale, 05/04/2005 04:29:24 MDT