Aci Design Handbook

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THIS DOCUMENT 1s PROTECTED BY THE LAWS OF COPYRIGHT

ff additional copies are needed, in whole or in part, contact the Member Services Department of the American Concrete lnstitute:

P.O.Box 9094 Farmington Hills, Michigan 48333-9094 TEL: 248-848-3800 FAX: 248-848-3801 SIXTH EDITION Copyright 1997 American Concrete lnstitute P.O. Box 9094 Farmington Hiils, MI 48333-9094 Second Printing, November 1998 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 u s e 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 publications. lnstitute publications are not able to, nor intended to, supplant individual training, responsibility or judgement of the user, or the supplier, of the inforrnation presented.

ACI 340R-97

ACI Design Handbook Design of Structural Reinforced Concrete Elements in Accordance with the Strength Design Method of ACI 318-95 Reported by ACi Committee 340 Mohsen A. Issa, Chairman

Husam A. O m a r , Secretary P a r a m D. Bhat William W. Bintzer Patrick J. C r e e g a n Om P. Dixit Noel J. Everard

Richard Furlong* M o u s s a A. lssa James S. Lai Douglas D. Lee S. Ali Mirza

Edward G. Nawy Wlliiam E. Rushing, Jr. Charles G. S a l m o n Murat Saatcioglu S u d h a k a r P. V e r m a

'Consulting Member

The AC1 Design Handbook is intended for u s e by individuals having a general famiiianty with the strength design method and with "Building Code Requirements for Reinforced Concrete (ACI 318-95)."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. Information is presented on three sections: Design Aids, Design Examples, and Commentafy on Design Aids. The Design Examples illustrate the use of the Design Aids, which are tables and graphs intended to eliminate routine and repetitious calculations. The Commentary explains the analytical basis for the Design Aids. Keywords: anchorage (structural); 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; slenderness ratio; spiral columns; splicing; stiiness; strength analysis; structural analysis; structural design; T-beams; tension; torsion.

ACI Cornminee Repom. Guides. Standard Practices. and Commentaries are intended for guldance in planrnng, designing, executing and inspecting consmction. This document is intended for the use of individuals who are comcetent to evaluate the significance and limitations of its content and recopnendations and who will accept responsibility for the applkation of rhe material itconrains. The American Connete Insnmte discfarms any and aH responsibility for the stated principles. The insticute shall not be liable for any loss or damage arising therefrom. Reference to this docurnent shall not be made in connact documents. If items found in this docurnent are desired by the Architecfingineer to be a pan of the connact documents. they shall be restated in mandatory language for incorporation by the Arch~tecvZngineer.

AMERICAN CONCRETE INSTITUTE P.O. Box 9094 Farmington Hills, MI 48331-9094

international

Phone: 2481848-3700 Fax: 2481848-3701

TABLE OF CONTENTS ACI 3 18-95 Strength Reduction Factors .......................................... xiv FOREWORD ............................................................... xv NOTARON ............................................................... xvii

DESIGN AIDS FLEXURE 1-Reinforcement ratios and anfor quick approximate design of rectanguiar beams with no compression reinforcement ......................... - 5 FLEXURE 2-Nominal siren& coefficients for design of rectangular beams with tension reinforcement only FLEXURE 2.I - - -' = 3000 psi ............................................. 6 4000 psi ............................................ - 7 FLEXURE 2.2-FLEXURE 2-3-f 5000 psi ............................................. 8 FLEXURE 2.4--' = 6000 psi ............................................. 9 FLEXURE 3-Nomirnal strength coefficients for rectangular beams with compression reiaforcement in whichl;' =f,and for flanged sections with I+< o 3000 psi & 4000 psi ................................... 10 FLEXURE 3.1--' FLEXURE 3.2--' = 5000 psi & 6000 psi .................................. - 1 1 FLEXURE 3-3--Coefficient I& for use in computing Ai for flange section with $< a 12 FLEXURE +Nominal stren-4 Md for compression reiniorcement in whichf, ' =f, . . . . . . . 13 FLEXUREC..5 . oefficient F for US. in calculating nominal strengths k&Mnl. and M,, ...... 14 FLEXURE & N o d strength for slab sections 12 in. wide FLEXURE 6.1.1-L = 3000 psi. f, = 40. 000 psi (graph) .................... -15 FLEXURE 6.1.2-A'= 3000 psi. f, = 40. 000 psi (table) . . . . . . . . . . . . . . . . . . . . . . . . 16 FLEXURE 6.2.1-L = 3000 psi. f, = 60. 000 psi (graph) . . . . . . . . . . . . . . . . . . . . . . . 17 = 3000 psi. f, = 60.000 psi (table) ....................... 18 FLEXURE 6.2.2-J,' FLEXURE 6.3.1--J,' = 4000 psi. f, = 40. 000 psi (graph) . . . . . . . . . . . . . . . . . . . . . . . 19 -20 FLEXURE 6.3.2--' = 4000 psi. f, = 40. 000 psi (table) ...................... FLEXURE 6.4.1--' = 4000 psi. J , = 60.000 psi (gaph) . . . . . . . . . . . . . . . . . . . . . . - 2 1 -22 FLEXURE 6.4.2--J,' = 4000 psi. J , = 60. 000 psi (table) ...................... 40. 000 psi (graph) . . . . . . . . . . . . . . . . . . . . . . 23 FLEXURE 6.5.1-L = 5000 psi. f, FLEXURE 6.5.2-d 5000 psi. f, 40.000 psi (table) . . . . . . . . . . . . . . . . . . . . . . . . 24 FLEXURE 6.6.1-A' = 5000 psi. f , = 60.000 psi (graph) . . . . . . . . . . . . . . . . . . . . . . - 2 5 FLEXURE 6.6.2--' = 5000 psi. f , = 60.000 psi (table) . . . . . . . . . . . . . . . . . . . . . . . . 26 FLEXURE 6.7.1-f,' = 6000 psi. f , = 40. 000 psi (graph) . . . . . . . . . . . . . . . . . . . . . . . 27 FLEXURE 6.7.2-f,' = 6000 psi. f , = 40. 000 psi (table) . . . . . . . . . . . . . . . . . . . . . . . . 28 FLEXURE 6.8.1-A' = 6000 psi. f; = 60. 000 psi (graph) . . . . . . . . . . . . . . . . . . . . . . . 29 FLEXURE 6.8.2-J,' = 6000 psi. f, = 60.000 psi (table) . . . . . . . . . . . . . . . . . . . . . . . . 30

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.

J

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REINFORCEMENT 1-Nominal cross section area, weight, and nominal diameter of ASTM standard reinforcing bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 FEWORCEMENT 2.4 ross section areas for various combination of bars . . . . . . . . . . . . . . 34 REINFORCEMJ3T %-Properties of bundled bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 REINFORCEMENT &Sectional properties and areas of plain and deformed welded ??

wirereinforcement ...................................................... 37 REINFORCEMENT 5-Specifications and properties of wire and welded reinforcement REINFORCEMENT 5.1-Specifications covering welded wire reinforcement . . . . . . - 3 8 requirements of steel wires in welded wii-e REINFORCEMENT 5.2--urn reinfoxement .......................................................... 38 REINFORCEMENT Mammon styles of welded wire reinforcement ................. - 3 9 REINFORCEMENT 7-Typic . development and splice length for welded wire reinforcement REINFORCEMENT 7.1.1-Pi& wire reinforcement,.fy = 60,000 psi, J ,' = 3000 psi . . 40 REINFORCEMENT 7.1 -2-Plain wire reinforcementt,. $ = 60,000 psi, J,' = 4000 psi . . 4 1 RENORCEMENT 7.2.1-Deformed wire reinf'o~~ernent; f, = 60,000 psi,f, ' = 3000 psi............................ . .. . . . . . . . . . . . . . . - 4 2 REINFORCEMENT 7.2.2-Deformed wire reinforcement J , = 60,000 psi,f, ' = 4000 psi .......... . .................................. - 4 3 REINFORCEMENT &-Crack control in beams and slabs REINFORCEMENT 8.1-Maximum A values per bar ......................... - 4 4 REINFORCEMENT 8-2-Beam web size and reinforcement required ............- 4 5 REINFORCEMENT 9-Minimum beam web widths required for two or more bars in one layer for cast-in-place nonprestressed concrete . . . . . . . . . . . . . . . . . . . . . . - 4 6 REINFORCEMENT 10--Mhim um beam web widths for various bar combinations (interiorexposure) ...................................................... 47 REMFORCElvEW 1I-Maximum web width b, per bar for single bars used as f l e d 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 bundled bars (interior exposure) .......................................... - 4 9 REINFORCEMENT 13--Maximurn web width b, per bundle, as required for crack control provisions h r bars of one size in one layer .................................. - 5 0 REINFORCEMENT 14-Bar selection table for beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - 5 1 REINFORCEMENT 1%Areas of bars in a section 1 ft. wide ......................... - 5 6 REINFORCEMENT 16-Maximum bar spacing for single bars in one row for one-way slabs ............................................. - 5 7 REINFORCEMENT 17-Basic development length ratios of bars Fn tension . . . . . . . . . . . . . - 5 8 REINFORCEMENT 18.1-Basic development length, Z of standard hooks in tension . . . . . - 6 0 REDFORCEMENT 18.2-Minimum embedment lengths to provide 2 in. cover to tail of standard 180-degree end hook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 IIEINFORCEMENT 19-INFMaximumsize of positive reinforcement bars satisfying Qd =(MflJ +- Q ,,IEq. (12.2) of ACf 318-95] for various span lengths . . . . . . . . . . . . . . - 6 2 FENORCEMENT 19.1-6 = 40,000 psi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - 6 2 R E ~ O R C E 19.2-f, ~ T = 60,000 psi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 REINFORCEMENT 20-Maximum allowable pitch s, in. REINFORCEMENT 20.1-For circular spirzi columns. . . . . . . . . . . . . . . . . . . . . . . . . -64 REINFORCEMENT 20.2-For square columns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 REINFORCEMENT 20.3-Recommended minimum number of spacers with various spiral sizes z..icolumn sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 REINFORCEMENT 21-Minimum face dimension b, in.. of rectangular ued colunlns accommodating various numbers of bars n per face . . . . . . . . . . . . . . . . . . . . . . . . . . . - 6 7

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 ................... 68-7 1 REINFORCEMENT 22.2.1 .22.2.4-Using n o d lap splices ................. 72-75 REINFORCEMENT 22.3.1.22.3 -4--Using tangential lap splices .............. 76-79 REWORCEMENT 23-Maximum number of bars ,n that can be accommodated i n columns having bars arranged in a circle REINFORCEMENT 23.1 .1.23.1 -4-Using bearing splices ................... 80-83 REINFORCEMENT 232.1 .232.&-Using normal lap splices ................. 84-87 REINFORCEMENT 23-3-1-23-3.&Using tangential lap splices .............. 88-9 1

SHEAR 1-Stirmp design requirements for nonprestressed beams with vertical stirrups and normal-weight concrete subjected to flexure and shear only ..................... - 9 4 SHEAR 2-Diagram for selecting spacing of stirmps ................................ - 9 5 SHEAR 3-Minimum beam height to provide embedment required for #6. #7. and #8 vertical stirmpswi&&=60. OOOpsi ............................................... 96 SHEAR P-Design shear strength for U-stirmps SHEAR 4.1-f, = 40 ksi................................................. - 9 7 SHEAR4.2-f,=6Oksi ................................................. 98 SHEAR S E E e t i v e depth of footings and slabs required to provide perimeter shear strength SHEAR 5.1-Interior rectangular column (a,= 40) for which PC= h/Z, 2 2. . . . . . . . . - 9 9 SHEAR 5.2-Interior circular column (a,= 40) .............................. 100 SHEAR &-Maximum nominal torsional moment T, that may be neglected (ACI-3 18-95 Section 11-6.1) and maximum nominal torsional moment T, required for statically indeterminate torsion (ACI 3 18-95 Section 11.62) . . . . . . . . . . . . . . . . . . . . 101 SHEAR 7.1-Values of KS(Idin.) And Y,(kips) SHEAR 7.1.1--' = 3,000 psi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 SHEAR 7.1.2-f,' = 4,000 psi ............................................ 102 SHEAR 7.1 .3-f, . = 5,000 psi ............................................ 103 SHEAR 7.1 -44' = 6,000 psi ............................................ 103 SHEAR 7.2-Values of Kt, (fi-k) SHEAR 7.2.1-A'= 3,000 psi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 SHEAR 7.2.2--' = 4,000 psi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 SHEAR 7.2.3--' = 5,000 psi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 SHEAR 7.2.4+' = 6,000 psi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 SHEAR 7.3-Values of K, (ft-kh.) SHEAR 7.3.1-f . = 40,000 psi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Y. SHEAR 7.3.2-f, = 60,000 psi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 SHEAR 7.4--Values of K,(ft-k) SHEAR 7.4.1--' = 3,000 psi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 SHEAR 7.4.2-f,' = 4,000 psi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 SHEAR 7.4.3--' = 5,000 psi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 SHEAR 7.4.&,(' = 6,000 psi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 DEFLECTION 1--Cracking moment M, DEFLECTION 1.1-For recta& ar sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 DEFLECTION 1-2-For T or L sections with tension at the bottom

steel ananged inacircle-f, ' = 4 ksi ....................................... 138 COLUMNS 5.3-For rectangular tied columns and square coiumns with steel arranged in a circle--- . = 5 ksi........................................ 139 COLUMNS 5 . k F o r rectangular tied columns and square columns with steel arranged In a circle-f, .= 6 ksi ....................................... 139 COLUMNS 5 . M o r rectangular tied columns and square columns with steel arranged Ina circle--- ' = 9 ksi ....................................... 140 COLUMNS 5.6-For rectangular tied c01umn.s and square columns with steel arranged in a circle--- ' = 12 ksi ...................................... 140 COLUMNS 5.7- or circular CO~UTIU~S--- . = 3 ksi ........................... 141 COLUMNS 5.8--~or circular colllmns-- . = 4 ksi ........................... 141 . = 5 ksi ........................... 142 COLUMNS 5 S - ~ o rcircular col-f, . = 6 ksi .......................... 142 COLUMNS 5.10- or circular col-f, COLUMNS 5.1 1- or circular columns-- .= 9 ksi .......................... 143 .= 12 ksi ......................... 143 COLUMNS 5.12-For circular col~1~111~--= COLUMNS &Values of y for column cross sections COLUMNS 6.1-For #3 and #4 ties or spirals................................ 144 COLUMNS 6.2-For #5 ties and spirals .................................... 145 COLUMNS 7-Nominal load-moment strength interaction diagram COLUMNS 7.1.1-M.60.6 ............................................. 146 ............................................. 147 COLUMNS 7.1 .2-R3.60.7 ............................................. 148 COLUMNS 7.1 .3-R3.60.8 COLUMNS 7.1 .4-113-6 0.9 ............................................. 149 ............................................. 150 COLUMNS 7.2.1-R4-60.6 COLUMNS 7.2.2-R4-60.7 ............................................. 151 .............................................. 152 COLUMNS 7.2.3-R4-60.8 COLUMNS 7.2.4434-60.9 ............................................ 153 COLUMNS 7.3.1-R5.60.6 . . . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 COLUMNS 7.3.2-R5.60.7 ............................................. 155 COLUMNS 7.3.3-R5.60.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 COLUMNS 7.3.4-R5-60.9 COLUMNS 7.4.1-R6.60.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 COLUMNS 7.4.2-R6.60.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 COLUMNS 7.4.3-R640.8 COLUMNS 7.4.6R6.60.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 COLUMNS 7.5.1-W.75 -6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 ........... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 COLUMNS 7.5.2-R9.75.7 COLUMNS 7.5.3-R9.75.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 COLUMNS 7.5.4..R9.75.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 COLUMNS 7.6.1 -R12.75.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 COLUMNS 7.6.2-R12.75.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . :. . . . . . . . 167 COLUMNS 7.6.3-R12.75.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16% COLUMNS 7.6.4-R12.75.9 . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

_

COLTJMNS 7.7.2-L3.60.7 COLUMNS 7.7.3-L340.8

.............................................. ..............................................

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COLUMNS 7.19.1-S3.60.6 ............................................ 218 COLUMNS 7.19.2-S3.60.7 ............................................ 219 COLUMNS 7.19.3-S3.60.8 ........................................... -220 ............................................ 221 COLUMNS 7.19.4..S3-60.9 COLUMNS 720.1-S4-60.6 ...................... . . . ................. -222 COLUMNS 7.20.24440.7 ............................................ 223 COLUMNS 7.20.3-S4-60.8 ........................................... -224 COLUMNS 7.20.6S4-60.9 ............................................ 225 COLUMNS 7.21 .l-S5.60.6 ................................... - ...... -226 ........................................... -227 COLUMNS 7.21.2-S5.60.7 COLUMNS 7.21.3--S540.8 ........................................... -228 COLUMNS 7.21 .6S5.60.9 ........................................... -229 COLtTMNS 7.22.1-56-60.6 ........................................... -230 COLUMNS 7.22.2-S6.60.7 ........................................... -231 COLUMNS 7.22.3-S6-60.8 ............................................ 232 COLUMNS 7.22.4-SMO.9 ............................................233 ........................................... -234 COLUMNS 7.23.1-59.75.6 COLUMNS 7.23.2-S9.75.7 ........................................... -235 COLUMNS 7.23.3-S9.75.8 ............................................ 236 COLUMNS 7.23.6S9.75.9 ........................................... -237 COLUMNS 7.24.1-S12.75.6 ........................................... 238 COLUMNS 7.24.2-S12-75.7 ........._................................ 239 COLUMNS 7.24.3-5 12.75.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -240 COLUMNS 7.24.4.S 12.75.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -241 COLUMNS 8-Solution to reciprocal load equation for biaxial bendingPn /A, as a function of PJA, P,/A, and Po/A, ........................... ..242 COLUMNS 9-Solution to reciprocal load equation for biaxial bendingP, /Pow a function of P,/Po, and P,/P, .................................. -243 COLUMNS 10-Biaxial bending design constant F F o r rectangular columns COLUMNS 10.1-With two bars on each of four faces ....................... -244 COLUMNS 10.2-With three bars on each of four fices ..................... -244 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 COLUMNS I 1-Biaxial moment relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -246

SLABS I - m u m slab thiclcness SLABS 1.I-Minimum thickness of slab without interior beams. . . . . . . . . . . . . . . . -248 SLABS 1.2-Minimum slab thickness for deflection of slabs on beams, drop panels or bands SLA3S 1.2.1-- = 40. 000 psi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -249 SLABS 1.2.2-J, = 60. 000 psi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -250 SLABS 2-Factor a f o r calculating cr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -251 SLABS 3.1-Factor k, for perimeter shear-Interior column . . . . . . . . . . . . . . . . . . . -252 SLABS 3.2-Factors ki and k3'for perimeter shear-Square interior column. . . . . . . 253

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 reinforcement for slab subject to simple bending; no compression reinforcement . . . . . . . . . . . . . . . . . . . . . -291 &Determination of tension and compression reinforcement areas for rectangular beam subject to simple bending; compression reinforcement is found not to yield . . . . . . . .293 Reinforcement Design Examples 1-For rectangular beam subject to bending, selection of reinforcement satisfying bar spacing and cover requirements and crack control provisions (using REINFORCEMENT 8.1,s -2, or 11) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -296 2-For a one-way slab, verification that 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) satisfying bar spacing and cover requirements and crack conwl provisions (verified using REINFORCEMENT 8.1) . . . . . . . . . . . -299 4--For rectangular beam subject to simple bending, selection of reinforcement satisfying bar spacing and cover requirements and crack control provisions (verified using REINFORCEMENT 11) . . ... . . . . .. . . . . .. . . .. - . .. . . . . . . . . . . - 3 01 5-Determination of maximum width of a beam reinforced with bundled bars satisfying crack control provisions ... . - .. .. .. . . . . ... . . . . . . . . .. ... . . . .. . . . . . . . . . . . . -302 6-Determination of development length required for positive-moment reinforcement in a continuousbeam ...................................................... 303 7-Determination of development length required for positive-moment reinforcement confinedbystirmps .................................................... 304 8-Determination of development length required for negative-moment reinforcement . . . . -305 %--Determination of splice length required for dowels in tension in the stem ofaretainingwall ..................................................... 306 1&Determination of development length required for bar ending in astandard90deghook ................................................. 307 Shear Design Examples 1-Design of beam for shear strength by method of ACI 3 18-95, Section 11.3.1 . . . . . . . . . - 310 2-Determination of shear strength of concrete in beam by more detailed method ofSection11.3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 3-Determination of shear strength of concrete in beam by method of ACI 3 18-95, Section 11-3.1, and more detailed method of Section 11-3-2 . . . . . . . . . . . . . . . . . . . . - 313 4--Selection of size and spacing of vertical stimps (minimumstirmps required) . . . . . . . . - 314 5-Design of vertical stim~psfor beam for which shear diagram is triangular . . . . . . . . . . . . - 316 6-Desigg of vertical stinups for beam for which shear diagram is [email protected] ar................................................ 319 7-Design of inclined stirrups for beam for which shear diagram is triangular . . . . . . . . . . . .321 8-De~ermination of thickness of slab (or footing) required to provide perimeter shear strength (square) . . . . . . . . . . . - - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .323 9-Determination of thickness of slab (or footing) required to provide perimeter

10-Determination of adequacy of square tied column section subject to biaxial bending. using load contour method and COLUMNS 10 and 1I ........................ -393 Two-way Slab Design Examples l-Two-way slab without beams. designed according to Direct Design Method .......... -396 2-Reinforcement spacing for crack control in panel of d o r m l y loaded two-way slab for severe environment ............................................. -417 Seismic Design Examplies 1-Adequacy of beam flexural design for seismic requirements ...................... -420 2-Design of transverse reinforcement for potential hinge regions of an earthquakeresistantbeam ............................................... 421 3-Design of an earthquake resistant column ..................................... -423 4- Shear strength of a monolithic beam-column joint .............................. -426

COMMENTARY Commentary on Design Aids for Strength of Members in Flexure ..................... -430 Commentary on Reinforcement Design Aids ..................................... -438 Commentary on Design Aids for Shear Strength of Beams and Slabs .................. -453 Commentary on Design Aids for Columns ....................................... -458 Commentary on Design Aids for Deflection Control ............................... -490 Commentary on Slab Design Aids .............................................. -476 Commentary on Two-way Action Reinforcement ................................. -479 CommentaryonSeismicDesignAids ............................................ 481

xiii

Str&,"th Reduction Factors*

FLEXURE, WITHOUT AXTAL LOAD

Nominal s h r strength of the member is 2ess than the nominal shem carresponding to the dmefopment of the nominnlflexuraf strengfbr of the member

Shem in joints of buildings

z-

** ***

Design stren$h prmided fry a m b e r shafl be fakm as the nominal strength, calcutaM f k m the dengn aids gtam in this handbook, multiplied by the ap~rroPfiLZtesi~engthled&$zctor @. Altenuzte strengffi reduction @factors for use with ASCE 7 load factors a7 included in ACI 3 18-95, Appendix C. See ACI 318-95 Section 9-3-22'07 Appendix B fir adjustmePrt to these 4 oafues for low h e k of axial compression. Also see ACf 378-95 Serfion f 8-13.

FOREWORD The ACI Design Handbook is intended for use by persons having a general familiarity with the strength design method and with %&dmg Code Requirements for StnrchPal Concrete (ACI 3 18-95)." This voiume presents information for the engineaing design and andysis of ka&i, slabs, brackets, footings, pile caps, miunms, two-way siabs, and seismic design.

[email protected] Aids are tables and graph intended to save the designex the &OR of' repeatedly p e r f i i g routine calculatMns An Lksign Aids apply to concrete having f: ranging b e e n 3 and I2 h i with Grade 40,60, and 75 steel r e i n f m e n t depending on the type of the struchaal member. A note at the bottom of each Design Aid indicateswhich Design Example illustrates the use of the table or graph. W g i n Examples illusbate the use of the Design Aids (butare not intended to show how to design a sm3u-e).

Commentary on Design Aids gives the basis for the Design Aids

Forjudicious application and optimum etficiency, users of this handbook shouid frrst acquaint themseives with the Commentary. k g n Examples will hefp verify procedures and results. It is not, however, the objective of the handbook to teacb the novice how to design in reinforced concrete. Readers are expected to be competent m design before attempting to use this handbook

to bring it mto accordancewith that code- The d t i n g

second edition of Volume 1, which incorporated some material on coiuums, was issued m 1973 and a second, correctedprinting was published in 1974. The August 1977 ACI Joumai carried "Step-by-step Design Procedures in Accordance with the Strength Design Method of ACI 3 18-7 I ,"subsequentty published as ACI Committee R e p r t 340.3R-77. While ACI 3 18-77 was being prepared for pubfimtion in the falI of 1977, Committee 340 was revising the handbook volumes accordingly. The resuiting new edition of Volume 2 on columns was published in May 1978. In late 1978, a supplanent to the [email protected] Design Handboak with two-way-adon dabs and entitied Slab Design in Accordrmce with ACI 318-77 was pub1ished The third edition of Volume 1, published in 1 98I , contained two divisions: Division I dealt with beams, one-way dabs, brackets, footings, and pile caps and incorporated the Step-by-step Design Procedures--& material being qda& to ACI 3 18-77. Division II consisted of the meway siab design supplement The f d edition of Volume 1 was published in 1984. It was the revisededition of the third edition to Conform to ACI 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 I in 1985. The fifhedition of V o l m 1 was formatted in the same manner as the fourth edition Design of Two-way Slabs (Suppianent to Volume 1) was made a separate volume, Volume 3 of the ACI Design Handbook 'Ibis edition is &-;tioped in accordance with ACI 3 1895. This vasion of the code was prepared in a format to correspond to a strength reduction factor of 1.0. This format was usexi m orrIer to make the handbook more dfor international use.

ACn COMMITTEE 340 AND ITS WORK ACI Committee 340, Design Aids for Building Codes, was o r g d in 1958 for the purpose of preparing a h a n b k that would simplify the design of reinforced concrete stnrcturai etements using the strength design method in accordance with the ACI Building Code. The handbook was prepared in two volumes: Volume 1 covering beams, one-way-action-dabs, footings, and other members except cofumns; and Volume 2 treating columns only. Volume 1 was issued in 1967; Volume 2 was ready first and published in 1964. Ebb volumes were in accordance with the 1%3 version of the ACI

Building Code. 3ri 1971 when ACI 3 18-7 1 was issue& Committee 340 was charged with &g the existing handbook material

MANDBOOK USER'S COMMENTS ACI Commrttee 340 welcomes suggestions&om users of this handbook on how to make future printings more u d . Camments &odd be drrected to ACI Committee 340, American Concrete Institute, P.O. Box 9094, F d g t o n Ws, Michigan 48333.

Many mi~vidualsand organizations have contributed to &e preparation of thisbook, gjving their time and effofi

to the preparation of charts, tables, examples, and

computer programs, as well as u n c h t a k g critical review of the n i a n m t Although it is practicai to ztcbowiedge indiviihlally au of these CDntributians, they are nonekiess greatty appreciatedfor such effortshave cxmtriiuted materialfy to the quality of this handbook The leadership and work of the Committee chairman, Mobsxzn A fss, are m y appreciated forwhich a large portion of the handbook deve1opment p m is attxibuted to. The work of every commiw member involved in the deveiopmeot of the New Design Handbock is appreciated Aka appreciated are the &arts of Dr. Issa's graduate students, AIfred A Yousif and Stanisfav DeicicGratefitI acknowiedgment is made of computer time COILtniuted by the tiniversity of Iliiwis at Chicago.

NOTATION

area of core of spirally reinforced column measured to outside diameter of spirai

area enciosed by outside perimeter of conThis notarion section defines symbols used in this volume covering beams, one-way slabs, footings, pile cap, coiumns, tw~-wayslabs, and their reinforcement Words in parentheses such as "(Flexure)" or "(Shear)" indicate porrions of this handbook in which symbol is used. depth of equivalent reuaxish-ess block, in. (FIexure) length for column section considered rigid (one half slab thickness) or lengtt! of rigid coiumn section at beam end (square column with boxed capital), in. (Two-way slabs) factor for computing K,,in-' depth of equivaIent recclnguiar srress 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, (I 0 . 5 9 ~/) 12000, ft-kip 1 in3,a coefficient for computing reinforcement area A, (Rex=) f, (1 d r / d )l 12000, ft-kip 1 id, a cwfficient for computing reinforcement area A: (Flexure)

-

-

a coefficient for computing reinforcement area A: when compression reinforcement does not yield (Flexure) f, (1 9I 2d)/ 12000, ft-kip 1 in3,a coefficient for evaluating flange effects on moment m T-beams (Flexure) any area, in2 b, t / n = effective tension area of concrete for crack control, in2 per bar (Reinforcement) b, t / n' = e f f h e tension area of concrete for crack contml in w e bundled bars are used, i d , per bar bundle (Reinforcement) ioaded area, in2 the area of l&e lowest base of the largest hsmn 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 I vertical to 2 horizontal, h2 area of individual bar, in'.(Reinforcement) area of concrere at cross section considered, in2(Flexure) area of critical shear section = b& (Twoway slabs)

-

crete cross section

gmss area enclosed by shear flow path, in2 minimurn area of tension reinforcementA, to keep neutral axis low enough for compression reinforcement to reach yield strain under factored load conditions, in2 (Fl-e) area of reinforcement in brackets or corbel resisting factored moment [V, a + N, (h-d)],in2 -grosssection area of column cross section, in2(Shear) area of shear reinforcement parailel to f l e d tension reinforcemenq in2 (Shear) area of tension reinforcemm to resist force N, on brackets, in2 (Shear) area enc1osed by centerhe of tfie outennost closed transverse torsional reinforcemenf in2 area of non-presrressed tension reinforcemen&in2 (Shear, Two-way siabs) area of compression reinforcement, in2 mex= minimum amount of flexmi reinforcemenf

>

inf

area of tension reinforcement in tension zone required to counterbaIance compressive force in overbanging portion of flanges in £iauged section, in2 (Flexure) area of bar or wire h m which spiral is formed, in2 (Columns) total area of Iongitudinal reinforcement in cross section, in2 area of tension reinforcement required to colmterbalancecompressive 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, in2 (Reinforcement) area of tension reinforcement r e q d under hctored load conditions for a rectang u k beam with tension reinforcement ody, in2 (Flexure) area of steel per ft of slab width, in' (Twoway siabs) area of mailer bars in the bundle, in' (Reinforcement) area of tension reinforcement required under factored bad conditions to counterbalance compressive force contributed by compressive reinforcemenf in2 (Flexure) maximum area of tension reinforcement at which depth of stress block a will be equal to or mailer then flange thickness hf (Flexure)

= area of one leg of a closed stimp resisting torsion, within a distance s, in2(Shear)

= total cross section area of dl transverse rciufor~gmentwhich is within the spacing s and which crosses the potential plane of

=

=

= = = =

spfitting throw the reinforcement being developed, in2 total area of web reinforcement in tension within distance s, measured in direction parallel to [email protected] reinforcemenq in2 (Shear) area of shear .friction reinforcement, in2 width of compression face of member, in. (Fie=) overall cross d o n dimension of m a lar column, in. (Columns) capital depth measured from lower s w k e of siab (Two-way slabs) perimeter of critical seaion for nvo-way

shear, in= width of the critical section defined in

=

= =

= = = = = =

11.12.12(a) measured in the direaion of the span for which moments are determiaed, in. width of the critical section defined in 11.12.13a) measured in the direction perpendicuiar to 6 , ratio of Iong side to short side of concentrated load or reaction area width of column -verse to d i d o n of appiied moment (= c, when there is no capital), in. size of square drop panel ft (Two-way slabs) web width, in. wid& of beam stern, in. (Two-way siabs) nominal bearing strength of loaded area spacing or cover dimension, in. distance ffom extreme compression fiber to

nermataxis size of rectangtllar or equivalent recrangular column,capital, or bracket measwed in the direction of the span for which moments are being determined, in. = size of reaaqgular or equivalent rectangular column,capital, or bracket measured @msverse m the direction of the span for which n moments are b5mg determined, i = clear concrete cover to surfke of outer layer of reinforcement, in. (Two-way slabs) = compression force, kips (Flexure) = torsion constanf see Eq.(13-7) (Two-way stabs) = compression force in concrete, kips (Flexure) = f k m r relating actual moment diagram to an equivaient uniform moment diagram (For members braced against sidesway and withom transverse loads between supports,

= =

=

= = =

=

=

=

=

C, = 0.6 + 0.4(M, /Ad, ) but not less than 0.4. For all other cases,C, shall be taka as 1.0.) compression force in reidiorcement, kips We=) &stance from the e m m e compression fiber to centroid of tension reinfoment, in. (Flexure, Two-way siabs) disrance from the exneme compression iiber to centroid of compression reinforcemen&in. (Flexure) nominal diameter of bar, ~IL (Reinforcement) equident diameter for bundled bars, in. (Reinforcement) diameter of a reinforcing bar closest to concrete w e tensile surface, in. (Twoway slabs) diameters of bars in bundles with two different sizes, in. (Reinforcement) disance &om e m e tensile surfice to center of ciosest tensile reinforcing k,in. (Reinforcement, Two-way slabs) disrancefromextremetensile~tocenter of gravity of closest bundle or layer of bundIes, in,(Reinforcement) distance from extreme comprwsion fiber to cgntroid of tension reinforcement of drop

panel in= nominal diameter of stirrups, in. (Shear,

Columns) = distance from e m m e tensile fiber to centroid of tension reinforcement = t/2, in. =

=

=

=

= =

=

~mfoment) ciead loads, or their relative internal moments and forces eccentricity of axial load at end of beam, measured h r n centerbe of beam, in. We=) 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 aiong y-axis, in. (Columns) modulus of elasticity of concrete

rnoduius of eiasticity of beam concrete, ksi (Two-way slabs) = modulus of elasticity of column concrete, ksi (Two-way siabs) = modulus of elasticity of slab concrete, ksi (Two-way slabs) = modulus of elastic* of steel reinforcement (29000 ksi) (Flexure) = flexural stifhess of cross section for frame analysis, k-in2(Flexure)

=

= flexural stiffkess of compression member, = =

=

=

= =

=

=

k-in2 (Flexure) specified compressive strength of concrete, psi average tensile spiirting [email protected] of light weight m e concrete,. psi 7.5

= = =

=

= =

,rnoduius of rupture of con-

crete, psi dcuIated tension stress in reinforcement at se~ce loads, ksi (Reinforcemen&Two-way siabs) caicuiated stress in reinforcement in compression, E, E: if, psi (Flexure) specified yield strength of nonprestressed reinforcement, psi (Flexure, Two-way slabs) yieid strength of closed transverse torsional . reinforcement yieid strength of longitudinal torsional reinforcement

= flexural coefficient =

=

= moment of inertia of gross concrete section

bdZ or M,/K, 12000

= = = =

=

= = = =

=

=

= =

-

me==>

strength factor used in evaluation of h14 (Two-way SMS)

-1

= effective length w o r for compression

members (Columns) column sifhess coefficient (Two-way s b ) = fle& stiffness coefficient (Two-way stabs) = perimeter shear stress t'actor, in" (Two-way stabs) = moment-shear transfer stress fktor, ix2frl (Two-way slabs) = moment-shear transfer stress fkmr, in4 ft-' (Two-way slabs) = moment-shear transfer stress factor for square column or capitai, in-2frl(Two-way slabs) = moment-&ear transfer stress factor for frl(Two-way square coiumn or capital, s-1 = fracture coefficient used in crack width determination to obtain maximum allowable spacing of reinforcement in two way slabs and plates (Two-way siabs) = a constant relaring to EI and having the same units as EI = 1728 P, / 48E; = coefficient for immediate deflection of beam (Deflection) = a d / 6cw = coefficient for approximate i m m d i e deflection of beam (Deflection) = coefficient reiating moment at midspan to deflection at midspan (Deflecrion)

(Flex=) overall thickness of section or thickness of member (Beams, One-way siabs, Two-way siabs) . diameter of round column or side of a rectauguk coiumn, in (Columns) diameter of round column,in. pier or column dimension parallel to investigated direction (= c, when there is no capital, for Two-way slabs), in. (Two-way s&) core diameter of spiral coiumn = outside column dimension minus cover, in. (Coi-

=

-1 =

=

about the cenuoidal axis, neogecting reinforcemen&in4 (Deflection) gross moment of inertia of T-section, in4 (Deflection) moment of inertia of reinforcement about cewoidal axis of member cross section, in. (Columns) property of assumed critical section analogous to polar moment of inertia (Two-way s&) (d - 0.5 4) / 4 ratio of lever ann bemeen flange centroid and centroid of tension reinforcement to effective depth d of a section (Flexure) (d 0.5 a) / 4 ratio of lever arm tierween centroid of compression rectangular saess block and tension reinforcementto effective depth d of a rectanguiar section (Flexure) moment coelKcient for f l e d members

t o t . thickness of drop panei (slab thickness plus drop), in. two-way slabs) e f f i e thichess of a coiumn for sienderness considerations, in. flange thickness, in- (Flexure, Deflection) thickness of slab, in. (Two-way siabs) minimum thickness of slab, governed by deflection requirements, in. (Two-way siabs) minimum thickness of slab, governed by shear requirements, in. (Two-way siabs) 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 cent~oidalaxis of goss section of bean (inctuding p~ of adjacent siab section as defined in AC13 1895, Seaion 13.2.4), in4 (Two-way sibs)

-

X

fr

12000

,coefficient for computing

-

6

cracking moment of T-section (Deflection]

xix

I, / bd 37 coefficient for moment of inertia of cracked reaangular sections with tension reinforcement only (Deflection) I, / bd 37 coefficient for moment of inertia of cracked rectangular sections with compression reMorcemenr, or T-beams (Deflection) I . / 4,coefficient for effective moment of inertia (Deflection) 1, / (6, h / IZ), coefficient for gross mctment of inertia of T-beams (Deflections) 12000 M, / bd = f: o (I 0.59 o), strength coefficient of resistance, psi (Flexure>

-

0.85 fe'

12000

- I]

b"

,coefficient for iom-

plrting reinforcement area A+ psi (Flexure) torsional stifhess of transverse torsional member,moment per unit of rotation =

transverse

reinforcement

-

(bW 3S)(h

12

g

=

, coefficient for

design of torsion reinforcement (Shear) strength coefficient for resistance = IWJF = 12,000 M,l (bcf)=f,'o( l - 0.590) p,, divided by the reinforcement ratio for shear friction reinforcement perpendicufar to &ear plane (Shear) A,&, shear coefficient for stirmps (Shear) 16.5 - 5.1 (N,/ E)Y[lt(64 + 160 ( N , / PI 0.5 (Shear) 2.0 - a / d (Shear) Combined flexural sti&ess of slab and column (Two-way slabs) span length, ft or in. (Reinforcanex& Shear) span leng?h of beam, center-to-center of supports (Two-way siabs) width of siab strip used to calculate a (Two-way slabs) span length of beam or slab, as defined in ACI 3 18-95, Section 8.7, in. (Columns) minimum spans required for bat develop ment depending on type of span and sup port and percentage of bars extended into suDwn. ft and in- (Reinforcement) = length of slab span in the direction in which moments are being determined, measured center-to-center supports (Two-way siabs) -

[I

- 3 -5)

index

L

= length of slab span ;transverse to 8 , ,measured center-to-center supports (Two-way

slabs) = wid& of interior design h

e (transverse to PI), measured h m center h e to center line of adjacent slab panels (ACI 3 18-95, Section 13.62.3) (Two-way slabs) = wi& of exterior design fiame ,measured om center h e to center h e of adjacent slab paneis (ACI 3 18-95, Section 13.623) (Two-way s&) = embedment length at support or at point of inflection, in. (Reinforcement) = average of P, or 4 (Two-way slabs) = length of compressionmember in a frame, measured from center to center of joints in the b e = vertical distance between supports, in. = height of column = development length, in. @einforcement) = usable (available) anchorage length, in. (Reinforcement) = basic deveiopment length of straight bars, mas speciiied in Seaions 1 2 2 2 and 1 2 3 2 of ACI 3 1S-95 (Reinforcement) = development length of hooked bars, to exterior face of bar at the bend, in. (Reinfoment) = basic development length of standard hook in tension, h(Reinforcement) = longer of P, or width of design fiame Qz = cieat span measured f2c.e to face of supports (Reinforcement) = ciear span measured f k e to face of supporn or~to~ofkamsins~witfibearns (Two-way slabs) = shorter of P, or width of design M e 8, = unsupported height of coiumn (Two-way siabs) = length of s h d e a d a m from centroid of concenmted load or reaction, in. (Shear) = h e loads, or their r e M internal moments and forces (Two-way stabs) = magnified f & o d moment to be used for design of column (Columns) = distance h m exterior face of edge panel to center of exterior column (Two-way sfabs) = fixed-end moment coefficient (Two-way slabs) = smaller factored end moment on compression member, positive if member is bent in single c u . , negative if bent in double curvamre7kip8 (Columns) = factored end moment on compression menber at the end at which M, acts, due to loads t k tcause no appreciable side sway, calcufaled using a fkst order elastic fkme analysis

-

= mbatanced 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, am, due to loads that cause appreciable side sway, calculated using a fust order elastic fhme analysis = larger factored end moment on compression member, always positive (Columns) = unbalanced moment perpendicular to M, (Two-way slabs) = minimum value of M2 = faaored end moment on compression member at the end at which M, acts, due to loads t b cause no appreciable side sway, d c u Iated using a firs order efastic frame analysis = fktored end moment on compression memberatrheendatwhich M,acts, dueto loads that cause appreciable side sway, calculated using a first order elastic frame analysis = factored negarive moment at interior column (except first interior column), kipft (Two-way slabs) = fkmred positive moment at interior span , kipft (Two-way siabs) = factored negative moment at exterior sup poq kipft (Two-way slabs) = factored negative moment at first interior suppor&kip% (Two-way slabs) = faaored positive moment at midspan of exterior span, kipfi (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, kipft meflection) = crackiq moment of gross concrere section = i,l,/ y, ,in-ft (Deflection) = moment due to dead load, kipft (Deflection) = moment due to dead and live load, kip-ft (Deflection) = moment due to live load, kipft (Deflection) = reinforcing spacing grid index for m c k control (Two-way slabs) = n o d moment strength of section, k i p f i (Flexure) = nominal moment strength of section with compression and tension reinforcemenf kipft (Flexure) = nominai moment strength of overhanging flanges of T-beam, kipft (Flexure) = nominal moment sen,& of rectangular beam (or web of T-beam) when reinforced for tension only, kip&(Flexure) = nominal moment strength of a cross section before compressionreinforcement and extra

=

=

= =

tension reinforcementare added = M, M , kip-ft (FIexure) thatpomon of M, assigned to compression reinforcement or flange regions of I and T-sections, kipft (Flexure.) total b r e d sratic moment (Flexure) moment at point of zero shear (Shear) moment due to loads causing appreciabie sway

= moment at left suppo* = =

=

=

for deflection, kipfk (Deflection) moment at right suppo& for deflection, kipft (Deflection) applied factored moment at section, e f t (Flexure, Two-way shbs) factored moment acting on section if axial force N, is considered to act at centroid of f t (Flexure) tension reinforcement, e nominal moment strength about x-axis

= nominal moment strength = = = = =

about y-axis (Co~umns) equivalent uniaxial moment strength about x-axis (Columns) equident miaxid moment strength about y-axis (CohmIls) facbredmoment about x-axis (Columns) factoredmoment about y-axis (Columns) service wind load moment, kip-ft (Col=)

modular ratio = Es/ E, (Deflection) equivalent number of bars = tensile reinf o m e n t area over largest bar area, for crack control (Reinforcement) = number of longitudinal torsion bars (Shear) = number of bar diameters bemeen center and peximeter of bend (Reinforcement) = number of bars in f l e d tension reinforcement (Reinforcement) = equivalent number of bar bundles = proj d slnface of bundle over a d surEace 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 psirive for compression, negative for tension, and to include effects of tension due to drinkage and creep, kips (Shear) = factored tensile force on bracket or corbel acting simuftaneousiy with Vmkips (Shear) = service concen.rrared load on beam, kips (Deflection) = nominai axial load strength (balanced smin conditions), kips (Columns) = critical axid load, kips (Columns) = service axial dead load, kips (Columns) = semce axlal live load, kips (Columns) = nominal axial. load siren& at given eccentricity, kips (Columnsj

=

=

-

= approximaion of nominal axid load

at eccentricities e, and % , kips (Coiumns) = nominal zxiai load strength for eccentriciry e, along x axis only, x-axis being axis of bending, kips (Columns) . = nominal axial Iaad strength for eccentricity e, along y axis oniy, y-axis being axis of bending, kips (Columns) = nominal axid load strength at zero eccentricity, kips (Coirtmns) = factored axial Ioad at given eccentricity, kips (Columns) = factored axial load for fxcenmcity e,aiong y-axis ody, kips (Flexure) = faftoredaxial load for d c j . en dong x-axis ody s CpP, kips (Flexure) = faaored aiai load for eccentricity e, aiong y-axis only s +P, kips (Flexure) = outside perimeter of cross-section A, in. = perimeter of center line of outermost closed transverse torsional reinforcemen& in. = stabiIi 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 reinforcema& in. (Shear) = maximum spacing of transverse reinforcement within ,@ center to center7in. = required stirmp distance, ft (Shear) = center to center spacing of reinforcement in either direction "1 " or 'Z",in. (Shear) = reinforcement spacing measured in direction of span for which moments and crack conml are being analyred, in. (Two-way s h ) = reinforcement spacing measured perpendicularto spanwise direction of span for which mornens and crack control are bein,0 analyzed, in. (Two-way siabs) = clear spacing between bars or bundles of bars, in. (Reinforcement) = e W c d o n modulus of section, i d = pitch of spiral, center to center of bar (Col-

1-

= thickness of tension area for crack control

(Reinforcement) = thickness of will of hollow section, in. = load cased by &e curnularive effect of

temperature, creep, shrinkage, differential settlement, and temperature = tension force on reinforcement, kips Flexure) = nominal torsional moment strengfh provided by torsion reinforcement (Reinforcement) = factored torsional moment at section (Shear)

=

= =

= = =

= = =

= = = = = =

beam width fixtor m ratio u / h, used in cafculation of af; u = b for interior beam; u = 2.bfor edge beam (Two-way slabs) (V, / &d), nominal shear sires carried by concrete, psi (Shear) shear stress at diagonal cracking due to ail faaored loads, when mch cricking is result of excessive principal tensile stresses in web, psi (Shear) (V,/ bJ)? nominal shear stress, psi (Shear) (V,/ bd), nominal hear stress, psi (Twoway slabs) (Vs/ b&), nominal shear stress carried by reinforcemenq psi (Shear) nominai &ear strength attn3uQbIe to concrete,kips (Shear, Two-way slabs) nominal shear sarength attributable to shear reinforcement, kips (Shear) nominal shear strength at section, kips (Shear) faaored shear force, lcips (Shear) factoredhorizontal shear in story fktored perimeter shear f o m on critical shear section (Two-way siabs) b r e d hear force caused by wall sup ported slab (Two-way siabs) crack width, in. (Reinforcemen&Two-way s-1 pattern Ioading unit load, psf (Two-way

slabs)

= unit weight of concrete7pcf = uniformiy distributed f&dored dead load,

kips per A (Two-way slabs), or kips per in faaored live load, kips per ft (Two-way slabs), or kips per in maximumtolerabk crack width for type of exposure, in- (Two-way slabs)

= un30miy distnbmed =

= mechanical load per rmit area, psf (Two-

way sl*)

= superimposed dead load, psf (total dead

load not inciuding self weight of slab, Twoway slabs) = factored Ioad per unit Ien-6 of beam (Fie=) = hcmred bad per unit area, psf; = (typically) 1.4 w, + 1 -7 w1(Two-way slabs) = variable distance = shorter o v e d dimension of rectanpart of seaion, in. (Two-way Slabs) = & i c e between cenmid of coiumn and centroid of shear d o n , in. (Two-way slabs) = minimum clear spacing benveen bundled bars, in- (Reinforcement) = distance from extreme tensile fiber to neEtral axis, in. @efle&on) = variable distance = longer overafI dimension of rectangular part of seaion, in. (Shear, Two-way slabs)

= cennoidal distance from bottom of bundled

YI

z

a

01 a2

a& 4 q,

p

p,

(3,

p,

p,

pf

bars, in. (Reinforcement) = distance h m cenaoidd axis of gross section, neglecting reinforcemenq to extreme fiber in tension, in. = quantity limiting distribution of f l e d reinforcement (Reinforcement) = angle between shear reinforcement and longitudinal axis of member, degrees (=ear) = bar location f'actor = relative beam ratio of fie& stifkess of beam section to flexurai stiffness of a width of siab bounded laterally by center Imes of adjacent panels (if any) on each sidk of beam = (E&) I (.E;,Z) (Twoway siabs) = amdirectioni?, = a in direction Pz = b/[email protected]) = constant used to compute V , in nonpreSiESsedslabs = average vaiue of a for dl beams on edges of slab panel (Two-way siabs) = d o of distauce between e m m e tensile fiber and neutral axis to distance bemeen neuaaf axis and centroid of tensile reinforcement ,x, 1xc (Reinforcement) = coatingf8ctor = ratio of long to short clear spans (PJ of a stab panel (Two-way slabs) = biaxid bending design consta~lt= constant portion of uniaxial factored moment s t r e nM ~, and M,, which may be permmedto aa simultaneously on the column cross section (Columns) = a coefficient relating depth of equivalent reaanguiar stress biock to depth h r n compression fice to neunal axis = 0.85 for f,' 1; 4.0 ksi and 0.85 - 0.05(fC ' - 4.0) for fc'> 4.0 ksi, (P, r 0.65), (Flexure) = ratio of dead Ioad per unit area to live load per unit area (in each case wi&out load factors) (Two-way slabs) = design coefficient for deflection = mp'/ n p; = (R-l)pf / np ;= fb/b, - I)hf/dnp wefldon) = ratio of long side to short side of concentrated load or reaction area (Shear, Twoway slabs) = ratio of maximum factored axial dead Ioad to maximum total hctored axial load, where the load is due to gravity effects oniy in the caicuiarion for PCin Eq. (10.7'), or ratio of the maximum factored sustained lateral load to the maximum totai factored lateral load in the story in the dcuiation for PCin Eq. (10.8)(Columns) = ratio between long and short center-tocenter spans (P, / eJ (Two-way siabs)

&/

= h (Deflection) = ratio of torsional s&i~ess of edge beam to

f l e d dfEtess of a width of slab equai to span length of beam, center-to-center of supports = (Ed0 / Gd,)Vwo-way slabs) = ratio of c to d mexure) = sin a + cos a for inched stimrps (Shear) = bar size factor = faaorm calclliating siab thickness required by deflection; = the value of the denominator of Eq. (9-1 I), or (9-13)divided by 1000 (Two-way siabs) = ratio of distance between cenaroid of outer rows of bars and thickness of cross section, in the direction of bending (Columns) = M o n of unbalanced moment transferred to cohnnn by ffexltre, Eq. (13-1) (Two-way slabs) = moment at point of zen> &ear to simple spaa maximum moment (Shear) = M o n of unbalanced moment transferred by eccentricity of shear at slab-coiumn connection; = I y~(Tw0-waysfabs) = coefficient depending on type of span and degree of reinforcement (Deflection) = moment magnification factor for columns braced against sidesway (Columns) = moment mag&cation factor for frames not braced against sidesway, to reflect lateral -driftresuiting h m lateral and gravity ioads (Columns) = unit stlain, in. / in. (Flexure) = unit sttain m concrete (Flexure) = unit strain in tension reinforcement (Flex-

-

=) =

unit strain in compression reinforcement

=

f , / E, nominal yield strain of reinforcement m-1

m=)

= angie of compression diagonais in truss

analogy for torsion = lightweight aggregate concrete factor.

When lightweight concrete is used f,l(6.7Y,'). When normal weight concrete is used 1.0 (Shear) = mi0 of M,, with compression reinforcement to M, without compression reinforcement (Columns) = multiplier for additional long-time deflection, equals to rario of creep and shriakage deflection to immediate deflection due to sustained loads (Deflection) = a coefficient relating development lengtb to minimum required span length = coefficient of kiction = timedependent faaor for sustained load (Deflection) = dimensionless constant used in compuring I* and I, (Columns)

tension iekforcement ntio = A, 1 bd (Rex-

PIX

=)

''

compression reinforcement Patio= A: / bd Wexllfe) reinforcement ratio producing bafanced conditions (Flexme) baianced percentage of r e i n f o m e n t for a section with compression reinforcement

We-) A, / A x =ratio of total resorcement area to

cross-sectional area of coiumn (Columns) U We-)

A#/

= active steel ratio = A

,l (24d .)(Two-way

slabs) r e i n f o m e n t Patio for shear 5iction reinforcement (Shear) @ = strength reduction Eactor as deiined in Section 9 3 of ACf 3 18-95 p,p,k= faaors llsed in distniution of moment m an exterior span (Two-waysiabs) o = coefficient indicating relative men* of reidorcement and concrete in member = pfy lfcr(Flexme, Tweway slabs) = ratio of sum of s t i & e ~ ~Z(I / e j of cornpression members in a plane a one end of a compression member =

Fig. I--Notation for siahs

DESIGN

FLEXURE 1

-

Reinforcement ratios and a, for quick approximate design of r e c t a q u h beams with no compression reinforcement

Reference: ACf 3 18-95 Sections 9.3.2,10.2, 10.3.1-10.3.3, and 10.5.1 and ACI 3 18R-95Section 10.3.1 M" Ax = , , where is in kip-fi and d in in. and

f, = 40,000 psi 4

Pm preferred p Prmx

f, = 60,000 psi

rh Prpip

preferred p

,P f, = 75,000 psi %

Ppreferred p P,

3,000 psi

4,000 psi

p, = 0.85

B, = 0.85

5,000 psi 8, = 0.80

6,000 psi 8, = 0.75

FLEXURE 2.3 - Nominal strength coefficients for design of recbngdar beams with tension reinforcement only, f,' = 4000 psi Reference: ACI 3 18-95 Sections 9.3.2, 10.2, and 10.3.1- 10.3-3 and ACI 3 18R-95 Section 10.3.I

M, 2 Ma4 M, = KF, ft-kips where K, = f: mj, 0= ~ f ~ f : and F = bd2/'12,000 (from FLEXURE 5) Also, M,, = &da, (A, in in.') where a, = fj$12,000

- Values of p above light ruie are less than ;,p,,

p, = 0.85 jna

, ,p

j, = I - (a/2d) = 1 - d1.7

r

= 3f!Ljfy2 200/fy as provided in Section 10.5.1 of ACI 318-95

For use of this Design Aid see Flexure Examples 1,2,3 and 4

7

-

FLEXURE 2.3 Nomind strength coefficients for design of rectarngular beams = 5000 psi with tension reinforcement only, Reference: ACI 3 18-95 Sections 9.3.2, f 0.2, and 10.3.1- 10.3.3 and ACI 318R-95 Secrion 10.3.1

% 2 [email protected] M, = &F, ft-kips where K, = f,'oj, 0= ~

W

p, = 0.80 j, = 1 - (d2d) = 1 - d1.7

f~ft

and F = bd2/12,000 (from FLEXURE 5 ) Also, M, = &da, (A, in in.') where a, = f j$12,000

Valuer of p above iighi mie are less than p-; For use of this Design Ai4 see Re-

8

cld = 1.18(w/P,) a/d = P,(dd)

p- =

Examples 1,2,3 and 4

3tvkLfv 2 ZWif, as pm.ilded in Seaion 105.1 of ACI 318-95

lZEWRl3 2.4

- Nominal strength co&cients

for design of rectangalar be-

with tension reinforcement only, f: = 6000 psi Reference: ACI 3 18-95 Sections 9-32, 10.2, and 10.3.1-1033 and A f f 318R-95 Section 103.1

where 0=

& = ojn

= 0.75

P~,X

j,= I -(a) = 1 - d1.7

MA

and F = hiZ/12,000 (from FLEXfJRE 5 ) Also, M, = A&, (A, in in,') where a,= fAJ12.000

f ' = 6000 psi f,= 40,000 psi

f" = 60,000psi

f" = 75,000 PG

-

FLEXURE 3 3 Coefficient E& for use in computing kffor a flanged section with

4Reference: ACI 318-95 Sections 9.3.2.

10.2 and 10.3.1-10.3.4

and ACI 3 18R-95 Section 10.3.1-10.3.3

Cj, and qffrom FLEXURE 3.1 and 3.2)

FkEXURZ 4 - Nominal strength h%,for compression reinforcement in which f: = f, Reference:ACi 318-95 Sections 9.3.2, 10.2, and 10.3.1- 10.3.4 and ACf 318R-95 Section 10.3.1-10.33

Mu Mn 2 -

4

AS' = As2

12,oooM, , in.2 fy(d d '1

Note: To take into account the effect of the displaced concrete, multiply the value of A: obta&ed from the graph by f,lCf, - O.85f: ).

(d-d'), in.

For use of this Desig Aid, see Flexure Exampie 6

R% (or Ma, or -1

= E;jf where M, 2 h&f$, K, is from EEXb'RE 2, and F = bd312000

FLEXURE 6.1.1 - Nominal strength

for slab sections 12 in. wide

Reference: ACI 318-95 Sections 7.12,8.4.1,8.4.3,9.3.2, 10.2,10.3.1-10.3.3, 10.5.1 and 10.5.3 and ACI: 3 18R-95 Sections 10.3.1 and 10.3.2

f: = 3000 psi fy

= 40,000 psi

y = 3.334d - 2.18~:, k-ft M

M 2-

I(:

4)

Ref-nrce: ACI 3 18-95 Secrioas 7.128.4.1, 8.4.1 . 332, 10.2, 103.1-1033, !051 -and 1053 and ACI 3IS&% Secrions 103.1 and 1032

f,, = 33000 psi

FLEXURE 62.1 - Nominal strength

for slab sections 12 in. wide

Reference: ACf.318-95Sections 7.12,8.4.1,8.4.3,9.3.2, 10.2, 10.3.1-10.3.3, 10.5.1 and 10.5.3 and A f f 3 18R-5 Sections 10.3.1 and 10.3.2

f', = 3000 psi f, = 60,000 psi

?v& = 5.04d - 4.90~:, k-ft

Refmnce: ACI 318-95 Seaions 7-12, 8.4.1,8-43,932, 10.2, 103-1-1033, 105.1 and 1053 and ACI 3 18R-95 Secrions 103-1 md I 0 3 2

jF: = 3080 psi

&& = 5.OAd - 4 . 9 ~ ~ :k-ft ,

F'LEXURE 63.1 - Nominat strength M,, for slab sections 12 in. wide Reference: ACSI318-95 Sections 7.12,8.4.1,8.4.3,9.3.2, ACI 3 18R-95 Sections 10.3.1 and 10.3.2

f: = 4000 psi f,, = 40,000 psi

10.2, 10.3.1-10.3.3, 10.5.1 and 10.5.3 and

M, = 3.33Asd - 1.63~:, k-ft

Reference: ACI 318-95 Sections 7-12,8,4.1,8.43,9-32, 102. 183.1-1033,105-1 asd 1053 and ACX 318R-95 S&O= 103.1 and 1032

FLEXURE 6.4.1 - No-

strength M, for slab sections 12 in. wide

Reference: ACI 318-95 Sections 7.12,8.4.1,8.4.3,9.3.2, 10.2, 10.3.1-10.3.3, 10.5.1 and 10.5.3 and AG1318R-5 Sections 10.3.1 and 10.3-2

:

f = 4000 psi fy

= 60,000 psi

y = 5.04d - 3.68~:,k-fi

FLEXURE 65.1 - Nominal strength RZ, for slab sections 12 in. wide Reference: ACI318-95 Sections 7.12,8.4.1,8.4.3,9.3.2, 10.2, 10.3.1-10.3.3, 10.5.1 and 10.5.3 and ACT 318R-95Sections 10.3.1 and 10.3.2

f ', = 5000 psi f, = 40,000 psi

Reference: A U 318-95 Sections 7-12, 8-41, 8.43, 932, 102, 103.1-1033,105.1 and 1053 and ACI 3 18R-95 Secfions 102.1 and 1032

Reference: ACI 318-95 Sections 7.12, 8.4.1, 8.4.3,9.3.2, 10.2, 10.3.1-10.3.3, 10.5.1 and 10.5.3 and ACI 3 18R-95 Sections 10.3.1 and 10.3.2

f, = 60,000 psi

Reference: ACI 3 18-95 Sections 7.12,8.4.1, 8.4.3,9.3.2, 10.2, 10.3.1-10.3.3, 10.5.1 and 10.5.3 and ACI 3 18R-95 Sections 10.3.1 and 10.3.2

J', = 6000 psi

f,= 40,000 psi

= 33 3 4 d - 1.09~:,k-ft

M Ll

318-95 Seaions 7.12, 8-41, 8-43, 03.2, 10.2, 10.3.i-103-3, 10.51 and 1 0 5 3 5 Smions 10.3.1 aod 1932

Reference: ACI 318-95 Sections 7.12,8.4.1, 8.4.3, 9.3.2, 10.2, 10.3.1-10.3.3, 10.5.1 and 10.5.3 and ACI 3 1SR-95 Sections 10.3.1 and 10.3.2

N O r n A L CROSS

NOMINAL

D

0.m

0.875 1.000 1.128 127Q

Note: The nominal dimensions of a deformed bar ue equivalent to those of a plain bar h e mass per foot as rfie defamed bars.

-

ane to iiws ad

0 5 1 0.71 0.91 1.11 0.82 1.02 1-22 1.42

1.31 1.62

1.44

1.54

1.75

1.95

1.a 2.04 2.15 2.35

0.3 1.19

1-06 1.50

1-37 1.69 1.99 1.81 1.12 2.43

1U7

2.38

2.59

224 255

3.m 3.31

1.96

0.84 1.15 1.46

0.95

1.06

1 3

1137 1.4s

1.57

1.58

1.79

2.16

LM

256

276

1.17

ENY 2 (continued)

Exampie 1: find h e area of 2 455 bars: Go down tht Pmt coiumn to "#5" and read. under the 'LO" column. A = 0.62 sq in. W p i e 2: Find the area of 8 rrY5 bars: Go down the fust 4 u m n to "#5" and read, under h e fmt "5" coiumn ( 5 s 3), A = 2.48 sq in. Exarnpie 3: Fmd the a r a of 2 x"7 + 3 #6 bars: Go down the fusz column to "#7" and prcleeed horizontalty on the "2" line until the "3" coiumn of the #6 group and read A = 2.52 sq in. pie 4: Frnd the area of 3 #8 + 4 #6 bars: Go down tine first column to "W8" and proceed horizondv on the "3" h e unui the "4" coiumn of h e X6 group and read A = 4.13 sq in. This table does not apply for combination of more than m o sizes. This tabie does not appiy for more than Ten bars of one size, or five bars each of two sizes.

5

0.69 0.79

0.87

#3 4 3 5 4

0.8'3

1.13

6

0.41

0.87

0.62

0.a

0.38

Q-83

1.m

!.a 6

0.4

0.75

0.66

0.85

0.81

0.92

8 7

0% 052

0.86 0.85

OX? 0.75

0.98

0.9

031

7

0.44

8 9

050 056

10

0.63

Exampic: Fmd rfit tquivaient diamtrtr of a singit hap for 4 * 9 bars: f o r 4 #9 bars, r e d d, = 2-26 in..and fhe centrolda! &mc= I q u a i s 1.13 in.

013 0.29 028 035 0.34

0.38

0.33

29-41

0.43

035

2-46 0.57 0.55

037 033 0.47

0.49

0 0.

Institute, he., 301 E.Sardusky St,Findlay, OH 45640

Note: Wm sizs 0th- than tixrs listed Wow .wins i x number W22 or D22 including larger sizes may Dc pwductd providai thc quality rcquirai is sufficient tojw rnanuiacturr:

Exampie: A fabric of W6 wim @ 6 in. ccntn to center fras 3 moss-sctionai arta of 0.12 in.',% of width.

3rd edition, 1979,p. 20, pui, ;ACI 3 18-95, Sections 12.3

ire

Ref==:

ACI 318-95, W a n t s 122,112.7,and 1218

Reierence: ACI 3 18-95,Sections 122,12.7. and 1218

WIRESTOBE DEVELOPED OR SF'UCED

Reference: ACI 318-95 Section 10.6.4 and ACI 3 18R-95 Secrion 10.6.4

for interior exposure: Max R =

For exterior exposure: Max A = where<, is in hi

IxQo~e:M e r e actual fs vaiue is used instead of fS = Q.6fy, d x table vaiue shall be multiplied by o.zI~(~;./J,?'. The m i o (6, r/n) 5 A where n is h e number of bars of ihe same diameter. if the reinforcement consisrs of severai sizes. rorzl AJArez of largest bar = n.

Reference: ACI 31%-95 Secron 10.6.4 and AC1 318R-95 Secrion 10.6.4

r = 175 for interior exposure = 145 for exrerior exposure

I,= 0-6fy and

iSt4stiraapassgmtd

cn

a

'1 3

1 1

I

50

_

I

60 70 Steei Xeld Stress, ksi

Nore: The vziue b I jA , from ihis cx area of one bar = A v d u e in EINFORCEMENT 8.1.

I !

80

Reference: ACI 3 18-95 . Sectiors 7.2.2. 7.6.1. and 7.7. I (c)and AASmO Srandard Specifications for Highway Bridges (I6th edition, 1996)1 Division I Sections 8.17.3.1, 8.21.1. 8.22.1. 8.23.2.2, =d Table 8.23.2. i

-

Minunumbgarnwrdrh = 2 ( A - 8 & C ) In-IHD t & ) w k A cova q u i d for foneirudinai bars and k s e aaumpclons are made:

7

B + C - iRd,Z.Otn.

for A C 318

B = 0.375 in. for #3 nirmps = 0.%l

for APSKhO

for hxb ACI 318 and ABSHTO A = 1

in. for #4 naps

B = O.Y5 in. for $3 sdmqx (minimum

112in. c o x m e cover to %mq

nrmrp sizt for #10 and d i e s

B = 0.625 in. for RS snmrps = 0.750 in. for #6 snrrups

OongitUdd bars)

= 0.500 in. for #4 s~imms(minimum

f = nurupkndradiusof2nvnrp bar d i for #5 and smailcr

each added bar.

for

k r u n c a r tor added bar.

2.125 2.255 1.375

3.175

or various bar ce Reference: ACf 318-95 Sections 7.1.'.

7.6.1. and 7.3.11~)

@ -

&I

& A .

= d n r c o m o f I'kin =*mi.. -of * 3 S ~ n ~ p = for or11 apd mdle? htr rp-re~tm~rir3anmpr: for 814 tnd $18 b z ~ :liz

-of* ='m-oftargab

='~spuagforiugrbapltn & 1 m. for 88 btn)

*4

10.0 12.0 13.3

11.5 13.5 15.0

13.0 15.0 16.5

14.5 16.0 16.5 18.0 18.0 193

83

10.0 It3

13.5

113 13.0 13.0 143

14.5 16.5

11.0 15.5 36.0 17.0 17.5 19.0

No. a i s z r d k r b n

L3

8-5 113 120 14.5

14.5 17.0 20.0 17.5 9.5 23.0

1 x 5 213

24.5

1 3 11.0 11.5 11.0

133 16.5

16.0 19.0

18.5 P O

1

2

3

7.0 85 105 120 14.0

8.5 10-0 11.5 135 15.0

10.0 11.5 13.0 15.0 163

15 10.5 11.5 13.5

13.0 16.0

4

5

11.0. ITS

125

14.0

14.5 16.0

16.0 17.5 19.5

-58.0

15.0 11.0

173 a.5

n.o ;c.o

Exanrpics: F m Z f 6 & . rmnunumb. = 7 . 0 i n . Fur8XSbars.mioimumi.. = 17.5in. F o r 2 # 7 b a r s p i u s 5 #6bars.minkmm 6, = 12.5 in. for 3 #6 ban pius 5 #4 bars. inmmum b, = 16.5 in.

For bass in one iayer:

For bars in t$nr layers. 3

Max b ,

kkj

Refexax: ACI318-95 Secrions 7 - 2 2 . 7.6.6.1. 7.6.6.2, 7.6.6.3. 7.6.6.5. and 7.7.1 web widtb'b, rounded

dear cover of 1V 2 iri. #3 ssinups

2 bundles

3 bundles

4 bunelles

R e f m c c : ,43318-95 Secrions 7.6. 7.7.1. and 10.0.4:and "Crack Conmi in Beam Reinforced with Bundeci Bars Using ACI 315-71." Edward G. N a y . ACI JOURNAL.Proceedings V. 69. No. !O. Ocr. 1972. pp. 637-639.

0.788db, in.. for d,, in.. for four

z = I75 for interior exposure z = I45 for exrcnsr exposure ,iS = 0 . 6 j y , b i

d,' = 2

83 m.

+ d,.

ion aabte for Reference: ACI 318-95 Seaions 3.3. 7.6.1. 7.62. 7.6.6.5. 7.7.1. and 10.6.4: 1977'" 1 S.41B)UJ. 1.5.5(.4). (C). and (E3. and 1S.6(A) and (B3

M S h n ~rricfes

SI-=

(interior

#3 simqs.

a,. sq ia.

Qruntily and s k of Bars

314

in

wsf-=w=)

"1L = one h y a of h . U- = two hycrs of barz 3L = t h e z kyas of bas: 2b = two 'emdla of bars: 3b = three b a d k of bars: 4b = four bandies of h. WXth of baadie i s 2z'k-a as 2,. fl-e valPa r o & upward 10 n e a r s t W in. $Tabk values taken from E?.iFORCL&i&V 10 and iZ.

for stirmps largo &an #3. see Hore 2 o i REINFORCLMET 9. f o r atmior. exposnrr. s r r Note 3 of RZNFORCLXENT 9. ZFm inriividnal '&us. d i e d u e s cd&ted from Mius in REWFORCE?dE-?9. For b M d i d b r s . rablr vaiues caladated an &c 'bass of concrete cove? o i IV: m. to s r i m q [ M f l O I3.s(A)]. srzt assumai ro be 5 1 n. for $8 and

#3 slimaps. l in. aggregate)

e E -

r

,,

=alrsi

kkmior e = V

f. =a&

derbarsaPdsd,forHit9~batsinss.For~ixrga tbm #3. w+ Nore 2 of RElldFORCEMLaiT 9. For m u r h 9. -xe srr Note 3 of FSNFOR """IabLrvaiuts r a h h e d on tht basis o f 2 in. cDnocre a v e r LODarn rriniorcenmr. For singic 'ban of one SiZC rable Mhrt; doiiated from REINFORCEMEbT 11. For bundfcd San o i one size. d i e values cafc&& from RE,WORCEMEM i3. For cum'DiEarions o i bar siza. tabis Pains d c u k r u on &e basis of d, = diaanc from t l a e c e r&oo fi :o c e q ~ ~ ; d o i bw- Layer of flcxurai ieinf~su?nut p t E x c ~ &~ U Z D W& ..widrh rceczng,crdck airuoi for exrenor u y .

'1L = one h y a of h: 2L = LWO byers of bars; 2L = &re b y e s of bars: 2b = taro bundles of ban: 3b = three kindles of W. 4b = four bun& of bars. Width oi bun& i S ~ a s Z d , . ?Table dues munziai upwad ro ncarra '12 in. $Table vaiues ~a from REINFORCL%ENT 10 and 12. For xlmtp k r g o than #3. K= Nore 2 of REINFORCEMEEU? 9. f o r urcrior ex-, ~t Nots 3 of E I N F O R C L % E h T 9. s f o r mdividuai bar^ table v d u u cdcuiarcd from values i n E i i F O R C E M W T 9 . For bundid bars. ~ ~ b l t v d ucdcuia~ci u on rhc bass of Enna-ete cover oi 11/2 in.10 sUTT(Ip [AASHTO 1.5.UA)]. .b.gqqac Irx m c d to br 5 i in. for f 8 a d

smakr bas and sd, for H and iargcr bars. FO than $3. wc Note 2 of REINFORCEMEN' -re. see Note 3 of RYNFORCEMEXT 9. on Lhc basis of 2 in. conmvg; 'Table values to main rdniorcemc:. For singie Sars of one s k Qieaiared from R!3?+WXCi5iUENT i 1 . For Sun one sze. ubie vaiues d & a fmm REINFORCEVENT 13. ror cnmbinatiom of bar bzu. tabk M i u s caicuheii on Phe baas oi d, = from uxrcme rclslon fik to cmwolQ' of lowrs; layer of iiexud r d n i o - ~ l . jikcccds maximum 'beam wcu wid& m e c m g aasi =3ni~Tol provisions for cxrerior expsiare.

-

Tz TE qE

TL

*

Tt 'TI -I£

15 4E

?Z ?I 'IZ

TL IIE 9E

Ti!

*

fr

TE

ae ClE

X 'I:

fE 15 71

x

3-z SE -IT SE

QE 4

X ciz

9I

0O'EE

fE 9E

99

12 'IE

15

pie: #9 bars spaced 7% in. apart provide 1.68 in.',%

of section width.

-

Except ahere noted table Milm are gov

by crack sonmi provisions of ACI 318-95, Section 10.6.4 an

Fm # 3 4 l l bars: 34 in. cover Far #14 and #18 bars: 1% in. cover and 6 = 1.35

$ Calculated maximum ?acing of 3.32 in sadsfying crack conml provision of A a 318-95, Section 10.6.4 is fgss M minimum spasing of 2 4 ( A 5 1 4 inj r e q u i d by ACf 318-95, Section 7.6.1.

t Pe

on

References: ACI 3 18-95 SecGons 12.22 and 12-24

Notes: i . See canegory chart for Categories I and II

k = Ligjrweighr aggxgate concrete factor, 1-3 for lighrsiseighf concrete; !-0 for n weight concrete 3. Minirnum spacing

$,

2 12"

o d

Category I:

Clear cover

2

d,

..

! Clear spacing r 2d, ! Clear cover r d,

M

eni length ,,H

of stan

Reference: AC13 18-95. Secrions 7 . I and 12.5.1-12-5.3 Deveiopmenr length, I,, = a. I,, 2 Xd,. 2 6 in. where a represents modifiers from Note 1 below and I,, is basic developrnenr iengtb of srvldanl i-mks in tension

NW

2: Y a i m of 'basic dcvciopmcnr lengrh I,, &.re the heavy line arc iess thdn rhc rnlnrrnum deveior;;nenr ICE* oi 6 in. ikvei-~ ( b a ~ acvc!ournen: i~ [email protected] I,, muirlpiied by rhe applicabic mdiiicauon f x t o r ; ~snail be nor iess ~ m 8n d,. nor less rhari 6 imgh in.. &nchevef IS ere;zrer.

e Reference: AC13 18-95. Seaions 7.1.1 and 7.2.1

Xca

8

133

5-9

i0-9

M

15-9

i94

6-6

9-9

lb9

11-6

66

ii-4

Irj

15-5

7-j

94

11-9

12-9

I , is span between points of inflection in a beam in an interior bay of a continuous span. l2 is span between poinrs of zero moment in a span in which ends of psirive moment reinforcemenr are confined by a so ssive rereaction-=--as for a simply supported span. (, is span lengh in an exterior bay of a ccndnuous

span in which the disconunuous end of the span is unres!i-azned. 1, is span length in an exterior bay of a continuous

span in which the discontinuous end of the span is rcsn-nined. I, is span iengh in an interior bay of a conrinuous span.

_-

: V ~ I s + u r r r ~ 1 p a Y r f r F o m r J o l z n n ~ d w ~ iarga of dr dfecuvr c k p h d or 12 Dar dumcrm. bu: srrcfi crkdment :s nci asmad inan thc d m a n a ro rth md of fh span. Ths cffcccve d for --J8Mrsnm~ ur assumed mmimcni war rarm s LIX ? u n m m m h trom idalc 9.51a) of ACI318-95 Thc dmax= mnr. bns -*I

-. * V a l u n a s u z bzn x e mnflncd bv a co-ivc rexiion at L ~ Cs:mplv SUDpored nxb of and ?xrcmixdmcnr m m a r r s a[ thc porn of rn morrpt

u a t y ~ i n u t o r h c d o i a a ~ r w r s ~ m 1a 5s o0 f t k a s n torccntxruaus a m o r TCSZTX~ suoa& a! munor suoaxs. and 0 :O of m rjan n 3an

rim f fwd

35

3.m

itch s, in., for s A N S I A.38.1; AC1318-95 Seaions 3.3.3(c), 7.10.4.3.

I

Column i -.

h. ia.

!

1

Corr

in.

10.0.and 10.9.3

Number of bars oer face fberween b , . in. b,. in. b,. in.

m.=

4,.

b , . in. 6,. in. b,. in. A, . in.' b,. b,. b,. A,.

in. in.

in. in.'

b , . in. b,. in. b,. in. A ,, in.'

-

b,. b,. b,. A,.

in. in. in. in.'

b l . in.

b,. in. 6,. in. A ,in.: b , . in.

b,. in. b,. in. A , . in:

LF90.O

PT'ci SI

EESO'O MI-S1 SI

-

= =q3

=P30 ===FP

-

pruq Pa=n%$ -=-my1

>-

333 ' S A W DM -S -0 22-J '80'0 10'9 uerp =r ou 'e : a m n p wd ueq n o s 10 u m p g :ueq -sq iknjeds m!3 memanu r / F ueq. &q IOU ar&S;3e :srq gla

-6#

=4 WWO'J

lqr

-Z/I - I 30 -9

s u m z/ 1-1

w ! h 3 ! -3

saqms mno pue

sari usamq SAOJ

pw =qg-* :mp p.r

UWLlnp I C S p

-upz/I -

mBDJ-U! -0,

.. J :nrompuo

L&ZS~Q

JO

1so-O

W% st

Ern0 00-z -d

!LEO-0 WZ9

PIX

I l*

OP

soqids bugsag

' p ; r u t ~ htre ~ e JO q aonearro3ap ~

wnpx

a e

pwq -nl-opq uo i x z m w u q n! e-oj asn -=A= pue s m s aa q o 153 -80-0 uerp ou pue 10.0 rreqr ssq ou 'd : u ~ z l o;ad ~ sreq inoj 30 r n m :rreq uam $0 ==J=EF

I

.

.

19

-

-aq %mEds -3 uzm.m:u! r/: q la% mu m&&ie :veq -6# ~ 0 ==Wp 3 seq l w = o u wrm: Z / I - I prre ueq g#-gp ioj 'q zxE2np -3 rrv p* : m j o JO -i/1- I JO m q F P ~ U I ~ U O ! wquns a n 0 pue a n ruamlq ~ 3 ~ 'u!-Z/ 0 3 1- 1 : N O ~ O > zia.ma

6i

WZI

OZ

'

81

ZEEO'O Q9-6

L1

91

ZLEO-u W 6

91

91

OZ,m-O

mi

51

ZI mo-0 OZ-L Z! '0 QIB-P

'PI

EI

8

EEEO-0 W P

Zi

8

m - 0

W P S OPz~-O OP-Z P

Ii

01

References: 15.8.2.3

ACI 318-95 Seczions 3.3.3. 3.6.3. 7.6.4. 7.7.1(c), 7.10.5.1.

10.9.1- 10.9.2. 12.14.2.1. 1216.2

meax ban: mhimxm oi four bars p a c o i m p, no less rban 0.01 T.kall0.08. For ofhurie sins

Bar size #7

#8

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