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Design **of** **Reinforced** **Concrete** Design **of** **Reinforced** **Concrete** ACI 318-11 Code Edition Jack C McCormac Clemson University Russell H **Brown** Clemson University NINTH EDITION VP & EXECUTIVE PUBLISHER MARKETING MANAGER ACQUISITIONS EDITOR SENIOR PRODUCTION EDITOR CREATIVE DIRECTOR SENIOR DESIGNER PHOTO EDITOR COVER PHOTO Don Fowley Christopher Ruel Jennifer Welter Sujin Hong Harry Nolan Thomas Nery Sheena Goldstein Frank Leung/iStockphoto This book was set in 10/12 Times by Laserwords Private Limited and printed and bound by Courier The cover was printed by Courier This book is printed on acid free paper ∞ Founded in 1807, John Wiley & Sons, Inc has been a valued source **of** knowledge and understanding for more than 200 years, helping people around the world meet their needs and fulﬁll their aspirations Our company is built on a foundation **of** principles that include responsibility to the communities we serve and where we live and work In 2008, we launched a Corporate Citizenship Initiative, a global effort to address the environmental, social, economic, and ethical challenges we face in our business Among the issues we are addressing are carbon impact, paper speciﬁcations and procurement, ethical conduct within our business and among our vendors, and community and charitable support For more information, please visit our website: www.wiley.com/go/citizenship Copyright © 2014, 2009, 2006, 2005 John Wiley & Sons, Inc All rights reserved No part **of** this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 **of** the 1976 United States Copyright Act, without either the prior written permission **of** the Publisher or authorization through payment **of** the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, website www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201) 748-6011, fax (201) 748-6008, website www.wiley.com/go/permissions Evaluation copies are provided to qualiﬁed academics and professionals for review purposes only, for use in their courses during the next academic year These copies are licensed and may not be sold or transferred to a third party Upon completion **of** the review period, please return the evaluation copy to Wiley Return instructions and a free **of** charge return mailing label are available at www.wiley.com/go/returnlabel If you have chosen to adopt this textbook for use in your course, please accept this book as your complimentary desk copy Outside **of** the United States, please contact your local sales representative ISBN: 978-1-118-12984-5 ISBN: 978-1-118-43081-1 (BRV) Printed in the United States **of** America 10 Brief Contents Preface Introduction Flexural Analysis **of** Beams Strength Analysis **of** Beams According to ACI Code Design **of** Rectangular Beams and One-Way Slabs Analysis and Design **of** T Beams and Doubly **Reinforced** Beams Serviceability Bond, Development Lengths, and Splices Shear and Diagonal Tension Introduction to Columns 10 Design **of** Short Columns Subject to Axial Load and Bending 11 Slender Columns 12 Footings 13 Retaining Walls 14 Continuous **Reinforced** **Concrete** Structures 15 Torsion 16 Two-Way Slabs, Direct Design Method 17 Two-Way Slabs, Equivalent Frame Method 18 Walls 19 Prestressed **Concrete** 20 **Reinforced** **Concrete** Masonry A Tables and Graphs: U.S Customary Units B Tables in SI Units C The Strut-and-Tie Method **of** Design D Seismic Design **of** **Reinforced** **Concrete** Structures Glossary Index xv 35 65 82 112 154 184 223 263 281 317 347 394 431 470 492 532 547 567 602 631 669 675 683 699 703 v Contents Preface Introduction xv 1.1 **Concrete** and **Reinforced** Concrete, 1.2 Advantages **of** **Reinforced** **Concrete** as a Structural Material, 1.3 Disadvantages **of** **Reinforced** **Concrete** as a Structural Material, 1.4 Historical Background, 1.5 Comparison **of** **Reinforced** **Concrete** and Structural Steel for Buildings and Bridges, 1.6 Compatibility **of** **Concrete** and Steel, 1.7 Design Codes, 1.8 SI Units and Shaded Areas, 1.9 Types **of** Portland Cement, 1.10 Admixtures, 1.11 Properties **of** Concrete, 10 1.12 Aggregates, 18 1.13 High-Strength Concretes, 19 1.14 Fiber-Reinforced Concretes, 20 1.15 **Concrete** Durability, 21 1.16 Reinforcing Steel, 22 1.17 Grades **of** Reinforcing Steel, 24 1.18 SI Bar Sizes and Material Strengths, 25 1.19 Corrosive Environments, 26 1.20 Identifying Marks on Reinforcing Bars, 26 1.21 Introduction to Loads, 28 1.22 Dead Loads, 28 1.23 Live Loads, 29 1.24 Environmental Loads, 30 1.25 Selection **of** Design Loads, 32 1.26 Calculation Accuracy, 33 1.27 Impact **of** Computers on **Reinforced** **Concrete** Design, 34 Problems, 34 Flexural Analysis **of** Beams 35 2.1 Introduction, 35 2.2 Cracking Moment, 38 2.3 Elastic Stresses—Concrete Cracked, 41 2.4 Ultimate or Nominal Flexural Moments, 48 2.5 SI Example, 51 2.6 Computer Examples, 52 Problems, 54 vii viii CONTENTS Strength Analysis **of** Beams According to ACI Code 65 3.1 Design Methods, 65 3.2 Advantages **of** Strength Design, 66 3.3 Structural Safety, 66 3.4 Derivation **of** Beam Expressions, 67 3.5 Strains in Flexural Members, 70 3.6 Balanced Sections, Tension-Controlled Sections, and Compression-Controlled or Brittle Sections, 71 3.7 Strength Reduction or φ Factors, 71 3.8 Minimum Percentage **of** Steel, 74 3.9 Balanced Steel Percentage, 75 3.10 Example Problems, 76 3.11 Computer Examples, 79 Problems, 80 Design **of** Rectangular Beams and One-Way Slabs 82 4.1 Load Factors, 82 4.2 Design **of** Rectangular Beams, 85 4.3 Beam Design Examples, 89 4.4 Miscellaneous Beam Considerations, 95 4.5 Determining Steel Area When Beam Dimensions Are Predetermined, 96 4.6 Bundled Bars, 98 4.7 One-Way Slabs, 99 4.8 Cantilever Beams and Continuous Beams, 102 4.9 SI Example, 103 4.10 Computer Example, 105 Problems, 106 Analysis and Design **of** T Beams and Doubly **Reinforced** Beams 112 5.1 T Beams, 112 5.2 Analysis **of** T Beams, 114 5.3 Another Method for Analyzing T Beams, 118 5.4 Design **of** T Beams, 120 5.5 Design **of** T Beams for Negative Moments, 125 5.6 L-Shaped Beams, 127 5.7 Compression Steel, 127 5.8 Design **of** Doubly **Reinforced** Beams, 132 5.9 SI Examples, 136 5.10 Computer Examples, 138 Problems, 143 Serviceability 6.1 6.2 6.3 Introduction, 154 Importance **of** Deﬂections, 154 Control **of** Deﬂections, 155 154 708 INDEX Lateral loads: (continued ) design **of** two-way slabs for, 496 in seismic design, 688–691 Lateral pressure, on retaining walls, 399–404, 408 Lateral support, for rectangular beams, 95 Laurson, P G., L beams, 127 Le Brun, F., Leet, K., 15 Length effect, 582 Leyh, George F., 212 Lightweight aggregate concrete, 224 Lightweight concrete, 18 Lightweight **concrete** modiﬁcation factor, 192 Limit design: continuous structures, 434–444 under ACI Code, 442–444 collapse mechanism, 436–437 plastic analysis (equilibrium method), 438–441 plastic design vs., 435 Limit states, 154 Lintels, masonry, 611–616 cracking moment, 613, 616 deﬂections, 613–616 shear design of, 612–613 Live loads, 29–30 Loads, 28–36 axial: columns, 266, 274–277 footings subjected to, 380–382 short columns subject to bending and, 281–316 balanced, 288 dead, 28 design, 32–33 environmental, 30–32 factored, 65 on footings, 378–382 ice, 30–31 impact, 29 lateral: for continuous structures, 454–458 design **of** two-way slabs for, 496 in seismic design, 688–691 live, 29–30 longitudinal, 29 miscellaneous, 29 rain, 31 seismic (earthquake), 32, 84 in seismic design, 687–691 service, 36, 41, 65 snow, 30–31 trafﬁc, 29 vertical: for continuous structures, 445–454 in seismic design, 687–688 wind, 31–32, 84 working, 36, 65 Load and resistance factor design (LRFD), 435 Load-bearing walls: empirical design method, 549–551 masonry walls with out-of-plane loads, 616–623 rational design method, 552–554 Load factors: and effective moment **of** inertia, 160 rectangular beams, 82–84 Long columns, 263 Longitudinal loads, 29 Long-term deﬂections, 160–162, 589 LRFD (load and resistance factor design), 435 M MacGregor, J G., 36, 127 Masonry, 602–630 **concrete** masonry units, 602–603 ﬂexural tensile reinforcement of, 607 grout, 605 lintels, 611–616 mortar, 603–605 reinforcing bars in, 605–606 shear walls with in-plane loading, 623–628 speciﬁed compressive strength of, 606–607 walls with out-of-plane loads: load-bearing, 616–623 non–load-bearing, 607–611 Mass density, 13 Mat (raft, ﬂoating foundation) footings, 348, 349 Maximum considered earthquake, 684 Maximum steel percentage, 73 Mechanically anchored bars, 214–215 Middle strips (two-way slabs), 496–497 Minimum steel percentage, 74–75 Modular ratio, 41 Modulus **of** elasticity, 12, 13, 16, 25 apparent, 12 dynamic, 13 initial, 12 long term, 12 secant, 12 slender columns, 324 static, 12–13 tangent, 12 Modulus **of** rupture, 16, 35, 38–39 Moment frames, classes of, 691–698 Moment magniﬁer procedure (slender columns), 328 INDEX nonsway (braced) frames, 328–333 sway (unbraced) frames, 333–337 Moments **of** inertia: effective, 158–160 slender columns, 324 Moment strength, torsional, 477 Monier, J, Mortar, 603605 Măuller-Breslau, Heinrich, 432 N National **Concrete** Masonry Association (NCMA), 602 Nawy, E G., 13 Nilson, A H., 13 Nominal strength, 48–51 Nominal values (CMUs), 603 Nonlinear second-order analysis (slender columns), 328 Non–load-bearing walls, 547–548, 607–611 Nonsway (braced) frames (slender columns), 317–318, 320, 328–333 O One-way slabs, 99–102 deﬁned, 492 simple-span, 99–102 Ordinary moment frames, 691–692 P Partially prestressed members, 596 Pedestals, 263 Pile caps, 348, 349 Plain **concrete** footings, 383–386 Plastic analysis (equilibrium method), 438–441 Plastic centroid, 282–284 Plastic design, limit design vs., 435 Plastic hinge, 435–440 Points **of** inﬂection, assumed, 454, 455 Poisson’s ratio, 13–14 Ponding, 31 Portal method, 454, 456–458 Portland cement, 7–9 Posttensioning, 570, 575 Pozzolana, Precast walls: non-prestressed, 548 retaining walls, 397 Prestressed concrete, 567–601 advantages of, 569 for composite construction, 595 continuous members, 596 deﬂections of, 586–590 disadvantages of, 569 709 elastic shortening in, 580–581 friction along ducts, 582 materials used for, 570–572 partial prestressing, 596 posttensioning, 570, 575 prestress losses, 579–582 pretensioning, 569–570 relaxation and creep in tendons, 581 shapes **of** prestressed sections, 576–579 shear in, 590–595 approximate method, 590 design **of** reinforcement, 591–595 shrinkage and creep in, 581 stress calculations, 572–576 stresses in end blocks, 595 ultimate strength **of** sections, 582–587 Pretensioning, 569–570 Primary moments (columns), 263 Principal stresses, 223–224 Proportions (rectangular beams), 85 Q Qualitative inﬂuence lines, 431–434 R Raft footings, 348, 349 Rain loads, 31 Ransome, E L., Rational design method (load-bearing walls), 552–554 Rectangular beams, 82–111 bundled bars, 98 cantilever, 102 continuous, 102 design of, 85–94 lateral support, 95 load factors, 82–84 one-way slabs as, 99–102 sizes of, 96 skin reinforcement, 95 steel area for predetermined dimensions, 96–98 Rectangular isolated footings, 369–372 **Reinforced** concrete: advantages, 1–2 deﬁned, disadvantages, 2–3 history, 3–5 use **of** structural steel vs., 5–6 Reinforcement location factor, 191 Reinforcement size factor, 192 Reinforcing bars: bond stresses, 187–189 bundled, 98 710 INDEX Reinforcing bars: (continued ) development lengths for, 197–199 lap splices for, 212 cutting off or bending, 184–187, 208–211 headed, 214–215 in masonry, 605–606 mechanically anchored, 214–215 rectangular beams: minimum spacing of, 87–89 selection of, 86 splices: compression, 213–214 in ﬂexural members, 211–212 tension, 213 Reinforcing steel, 22–26 axle, 24, 27 billet, 24, 27 coatings, 26 compatibility **of** **concrete** and, corrosion, 9, 25, 26 deformed, 4, 22–25 epoxy coated, 26 grades, 24–25 identifying marks, 26–27 maximum percentage of, 73 minimum percentage of, 74–75 plain, 22–23 rail, 26–27 SI sizes, 25–26 welded wire fabric, 22–25 Relaxation, in prestressed **concrete** tendons, 581 Retaining walls, 394–430 bridge abutments, 396, 397 buttress, 395, 396 cantilever, 394–396 design procedure for, 413–424 estimating sizes of, 409–413 without heel, 396 without toe, 396, 397 counterfort, 395, 396 cracks in, 424–425 drainage for, 397–398 failures of, 398 footing soil pressures for, 404–405 gravity, 394, 395 joints in, 424–426 lateral pressure on, 399–404 precast, 397 semigravity, 394, 395, 405–407 surcharge on, 408 types of, 394–397 Retroﬁtting, 32 Righting moment (retaining walls), 396 Roman cement, Rusch, H., 15 S Safety, 65–67 with cantilever retaining walls, 414–415 with columns, 271–272 Salmon, C G., Schlaich, J., 681 SDC (seismic design category), 683, 687 Secondary moments (columns), 263 Seismic design, 683–698 categories of, 683, 687 for classes **of** moment frames, 691–698 loads, 687–691 maximum considered earthquake, 684 risk and importance factors, 686–687 soil site class, 684–685 Seismic design category (SDC), 683, 687 Seismic (earthquake) loads, 32, 84 Self-consolidated concrete, 10 Semigravity retaining walls, 394, 395, 405–407 Service, 36 Serviceability, 154–183 cracks, 170–176 ACI Code provisions, 175–176 ﬂexural, 170–175 types of, 170–171 deﬂections, 154–164 calculation of, 157–160 continuous-beam, 164–170 control of, 155–156 importance of, 154–155 long-term, 160–162 simple-beam, 162–164 effective moments **of** inertia, 158–160 Serviceability limit states, 154 Service loads, 36, 41, 65 Settlement (footings), 378–379 Shear: ACI Code requirements for, 232–237 column, 457 in column footings, 359–364 design for, 231–232 deep beams, 253–254 design problems, 237–247 stirrup spacing, 237–242, 247–249 and development length, 206–207 girder, 458 in prestressed concrete, 590–595 INDEX approximate method, 590 design **of** reinforcement, 591–595 in short columns subject to axial load and bending, 301–302 and tensile strength, 223 two-way slabs: shear resistance, 497–500 transfer between slabs and columns, 522–528 Shear cracking (reinforced **concrete** beams), 226–230 Shear friction, 249–251, 382–383 Shearheads, 492, 498, 499 Shear spans, 675–676 Shear strength: **of** concrete, 17–18, 225–226 and lightweight aggregate concrete, 224 **of** members subjected to axial forces, 251–253 Shear stresses: in **concrete** beams, 223–224 in two-way slabs, 497–500 Shear walls, 554–562 ACI provisions for, 558–559 arrangements of, 556–557 masonry, with in-plane loading, 623–628 Short columns: compression blocks and pedestals, 263 subject to axial load and bending, 281–316 biaxial bending, 302–309 capacity reduction factors, 309–311 interaction diagrams, 284–301 plastic centroid, 282–284 shear in, 301–302 Shotcreting, 8, 21 Shrinkage, 14–15 SI examples: axially loaded columns, 277–278 beam analysis, 51 cracking, 176 development length, 215–216 rectangular beam design, 103–104 SI units, 7, 25 stirrup spacing, 256–257 T beams and doubly **reinforced** beams, 136–138 torsion, 483–486 wall footings, 386–388 Silica fume, 19–20 Simple-beam deﬂections, 162–164 Single-column footings, see Isolated footings, Skin reinforcement (deep rectangular beams), 95 Slabs: continuous, 446–450 minimum thicknesses for, 155 711 one-way: deﬁned, 492 simple-span, 99–102 two-way, 492–531 analysis of, 495, 517–522 with beams, 492, 494, 517–522 columns, 522–528 column strips, 496–497 deﬁned, 492 depth limitations and stiffness, 500–505 design of, 495–496 direct design method, 495–531 distribution **of** moments in, 506–511 equivalent frame method, 495–496 factored moments in columns and walls, 528 ﬂat plates, 492, 493, 511–514 ﬂat slabs, 492, 493 for lateral loads, 496 live load placement, 514–517 middle strips, 496–497 openings in slab systems, 528 shear resistance, 497–500 transfer **of** moments and shear between slabs and columns, 522–528 wafﬂe slabs, 492–493 Slate, F., 13 Sleeve splices, 212 Slender columns, 263, 317–346 ACI Code treatment **of** slenderness effects, 328 analyses of: ﬁrst-order, 323–324 second-order, 328 avoiding, 325–326 effective length factors, 318–323 determined with alignment charts, 321–322 determined with equations, 322–323 in nonsway (braced) frames, 317–318, 320 magniﬁcation **of** column moments in, 328–333 sway (unbraced) frames vs., 324–327 in sway (unbraced) frames, 317–318, 320 analysis of, 336–341 magniﬁcation **of** column moments in, 333–337 nonsway (braced) frames vs., 324–327 unsupported lengths, 318 Slippage, in prestressed concrete, 582 Smith, Albert, 454 Snow loads, 30–31 Soil pressures: active, 401 actual, 350–351 allowable, 351–352 712 INDEX Soil pressures: (continued ) for footings: actual, 350–351 allowable, 351–352 **of** retaining walls, 404–405 on retaining walls, 399–404 Soil site class, 684–685 Special moment frames, 692–693 Spiral columns, 264 ACI Code requirements for, 270–271 failure of, 266–268 Splices: compression, 213–214 in ﬂexural members, 211–212 tension, 213 Split-cylinder tests, 16 Spreadsheets: beam analysis, 52–54 columns, 278–279 deﬂection calculator, 177–178 development length, 216–217 doubly **reinforced** beams, 141–143 footings, 388–390 masonry shear walls, 628–629 prestressed concrete, 597 rectangular beams, 105–106 shear design, 257–258 short columns, 311–312 slender columns, 342–343 T beams, 138–141 torsion, 487 two-way slabs, 528–530 walls, 564–565 Square isolated footings, 357–364 Stability index, 317–318 Statically determinate torsion, 474 Statically indeterminate torsion, 474 Static moment, 506 Steel: prestressed, 571–572 reinforcement with, see Reinforcing steel, Steel area, for rectangular beams **of** predetermined dimensions, 96–98 Stems: cantilever retaining walls, 409–410, 413–414, 424 T-beams, 112 Stirrups, 201, 207 ACI Code requirements, 232–235 and design for shear, 231–235 in footings, 353 purpose of, 231 spacing of, 233–234, 237–246 ACI Code requirements, 232–235 economical, 247–249 torsional reinforcing, 471–474 for web reinforcement, 227–230 Straight-line design, 65 Strains in ﬂexural members, 70–71 Straub, H., Strength analysis (beams), 65–81 balanced sections, 71 balanced steel percentage, 75–76 brittle sections, 71 compression-controlled sections, 71 derivation **of** beam expressions, 67–70 design methods, 65–66 minimum percentage **of** steel, 74–75 strains in ﬂexural members, 70–71 strength design advantages, 66 strength reduction factors, 67, 71–74 structural safety, 66–67 tension-controlled sections, 71 Strength design: advantages, 66 deﬁned, 65 Strength limit states, 154 Strength reduction factors, 67, 71–74 Stresses: bond, 187–189 in prestressed concrete: calculation of, 572–576 in end blocks, 595 principal, 223–224 shear, 223–224 torsional, 475–476 Stress-strain curves, 11–12 Strut and tie design, 675–682 Superplasticizers, 10, 20 Surcharge, on retaining walls, 408 Sway (unbraced) frames (slender columns), 317–318, 320 analysis of, 336–341 magniﬁcation **of** column moments in, 333–337 T Tables: balanced ratios **of** reinforcement: SI units, 672–674 U.S customary units, 636–645 circular column properties, 647 column properties, 655 live loads (typical), 29 minimum web widths for beams: SI units, 671 U.S customary units, 635 INDEX moduli **of** elasticity: SI units, 669 U.S customary units, 631 moment distribution constants for slabs, 648–654 reinforcing bar tables (areas, diameters, etc.): SI units, 669–671 U.S Customary units, 631, 634, 635 spirals for columns (size and pitch), 646 weights **of** common building materials, 28 welded wire reinforcement, 633 welded wire reinforcement sheets: U.S customary units, 632 T-beams, 112–127 analysis of: general method, 114–117 speciﬁc method for T beams, 118–119 deﬂections, 164–170 design of, 120–127 Tensile strength **of** concrete, 16–17, 223 modulus **of** rupture, 16, 18 split cylinder test, 16–17 Tension, diagonal, 224 Tension controlled section, 71 Tension reinforcing: development lengths for, 189–197, 203–204 hooks for, 199–203 Tension splices, 213 Ties, 201 circular, 271 spacing of, 270 Tied columns, 264 ACI Code requirements for, 270 as economical, 274 failure of, 266–268 Toe (retaining walls), 394, 414, 416–418 Torsion, 254–255, 470–491 ACI design requirements, 479–480 compatibility, 474–475 design of, 478–479 equilibrium, 474 moment strength, 477 reinforcing, 471–474 required by ACI, 476–480 using U.S customary units, 480–483 stresses, 475–476 and toughness **of** concrete, 21 using SI units, 483–486 Torsional moment strength, 477 Torsional reinforcing, 471–474 required by ACI, 476–480 using U.S customary units, 480–483 713 Torsional stresses, 475–476 Torsion cracks, 171 Trafﬁc loads, 29 Transformed area, 36, 41 Transverse reinforcement index, 192 Trial-and-error (iterative method), 97–98 Truss analogy, 229, 677 Truss models, 679–681 Two-way slabs, 492–531 analysis of, 495, 517–522 with beams, 492, 494 direct design method, 517–522 equivalent frame method, 535–537 columns: equivalent frame method, 538–540 factored moments in, 528 transfer **of** shear and moments between slabs and, 522–528 column strips, 496–497 deﬁned, 492 depth limitations and stiffness, 500–505 with interior beams, 503–505 without interior beams, 500–502 design of, 495–496 direct design method, 495–531 with beams, 517–522 depth limitations and stiffness with interior beams, 503–505 depth limitations and stiffness without interior beams, 500–502 factored moments in columns and walls, 528 interior ﬂat plates, 511–514 live load placement, 514–517 transfer **of** shear and moments between slabs and columns, 522–528 equivalent frame method, 495–496, 532–546 properties **of** columns, 538–540 properties **of** slab beams, 535–537 ﬂat plates, 492, 493, 511–514 ﬂat slabs, 492, 493 for lateral loads, 496 live load placement, 514–517 middle strips, 496–497 moments in: distribution for nonprismatic members, 532–533 distribution of, 506–511 transfer between slabs and columns, 522–528 openings in slab systems, 528 shear: shear resistance, 497–500 transfer between slabs and columns, 522–528 714 INDEX Two-way slabs, (continued ) wafﬂe slabs, 492–493 walls, factored moments in, 528 U Ultimate strength, **of** prestressed **concrete** sections, 582–587 Ultimate-strength design, 65, 66 See also Strength design Ultimate-strength stage (ﬂexural analysis), 36–38, 48–51 Unbraced frames, see Sway (unbraced) frames, Uncracked **concrete** stage (ﬂexural analysis), 35, 38–40 U.S customary units: tables and graphs, 631–668 torsional reinforcing using, 480–483 United States Geological Service (USGS), 684 V Van Ryzin, G., 31 Vertical loads: for continuous structures, 445–454 in seismic design, 687–688 Vibrations, 154 W Wafﬂe slabs, 492–493 Walls, 547–566 economy in construction of, 563 load-bearing: empirical design method, 549–551 masonry walls with out-of-plane loads, 616–623 rational design method, 552–554 masonry: load-bearing walls with out-of-plane loads, 616–623 non–load-bearing walls with out-of-plane loads, 607–611 shear walls with in-plane loading, 623–628 non–load-bearing, 547–548, 607–611 shear, 554–562 Wall footings, 347, 348, 352–357 Wang, C K., Ward, W E., Wayss, G., Web reinforcement: ACI Code requirements for, 232–237 behavior **of** beams with, 229–230 deﬁned, 224 for prestressed sections, 590 for shear cracking in beams, 227–229 T-beams, 112 Web–shear cracks, 171, 226, 227 Weep holes, 398 Weischede, D., 681 Welded wire fabric, 22–25 and shear cracks, 228–229 in tension, development lengths for, 203–204 Whitney, C S., 68, 289 Wilkinson, W B., Wind loads, 31–32, 84 Wire Reinforcement Institute, 23 Wobble effect, 582 Working loads, 36, 65 Working stress design (WSD), 65–67 McCormac bend01.tex V2 - January 10, 2013 6:43 P.M Frequently Used Notation α Ab Ac Ag Al As As Ask Ast At Av A1 A2 b b bo bw c cb = = = = = = = = = = = = = = = = = = = Cm d d db dc Dc Ec Es fc fc fm fct fr fs fs ft fy h hf Icr Ie Ig = = = = = = = = = = = = = = = = = = = = = = depth **of** equivalent compression rectangular stress block for ﬂexural members cross-sectional area **of** a reinforcing bar area **of** core **of** a spirally reinforcing column measured out to out **of** spiral gross cross-sectional area **of** a **concrete** member total area **of** longitudinal reinforcing to resist torsion area **of** nonprestressed tensile reinforcing area **of** compression reinforcement area **of** skin reinforcement for a deep beam per unit **of** height on one side face **of** beam total area **of** nonprestressed longitudinal reinforcing (bars or steel shapes) area **of** one leg **of** a closed stirrup resisting torsion within a distance s cross-sectional area **of** shear reinforcing in a distance s in a ﬂexural member loaded area maximum area **of** a supporting surface that is geometrically similar and concentric with the loaded area A1 width **of** the compression face **of** a ﬂexural member effective width **of** the ﬂange **of** a T or L beam perimeter **of** critical section for shear for slabs or footings web width or diameter **of** a circular section distance from extreme compression ﬁber to neutral axis smaller of: (a) the distance from center **of** a bar or wire to nearest **concrete** surface, and (b) one-half the center-to-center spacing **of** bars or wires being developed a factor relating an equivalent uniform moment diagram to the actual diagram effective depth **of** a section measured from extreme compression ﬁber to centroid **of** tensile reinforcement distance from extreme compression ﬁber to centroid **of** compression steel bar diameter **concrete** cover thickness measured from extreme tensile ﬁber to closed reinforcing bar or wire diameter **of** core **of** spiral column measured out to out **of** column modulus **of** elasticity **of** **concrete** modulus **of** elasticity **of** steel computed compression ﬂexural ﬁber stress at service loads speciﬁed compression strength **of** **concrete** speciﬁed compressive strength **of** masonry average splitting tensile strength **of** lightweight aggregate **concrete** modulus **of** rupture **of** **concrete** computed ﬂexural stress in tensile steel at service loads computed ﬂexural stress in compression steel computed tensile ﬂexural stress in **concrete** speciﬁed yield strength **of** nonprestressed reinforcing total thickness **of** member thickness **of** compression ﬂange **of** a T, L, or I section transformed moment **of** inertia **of** cracked **concrete** section effective moment **of** inertia **of** a section used for deﬂection calculations gross moment **of** inertia **of** a section about its centroidal axis Page McCormac bend01.tex V2 - January 10, 2013 6:43 P.M k ld ldb ldh ldt lhb ln lu Mcr M1 M2 M1ns M2ns Ma Mo Mu n Pc Pno P0 qa qe Rn s Vnm Vns Vtu w wc yt z β = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = βdns = βds = β1 = δ δs λ = = = = = = λ μ ξ ρ ρ ρb φ = = = = = = = c s s effective length factor for a compression member development length **of** a straight bar embedded in conﬁned **concrete** basic development length development length **of** a bar with a standard hook development length in tension **of** headed deformed bar basic development length **of** a standard hook in tension clear span measured face to face **of** supports unsupported length **of** a compression member cracking moment **of** **concrete** smaller end factored moment in a compression member, negative if double curvature larger end factored moment in a compression member smaller factored end moment in a compression member due to loads that result in no appreciable sidesway larger factored end moment in a compression member due to loads that result in no appreciable sidesway maximum moment in member due to service loads at stage deﬂection is computed total factored static moment factored moment at section modular ratio (ratio **of** modulus **of** elasticity **of** steel to that **of** concrete) Euler buckling load **of** column pure axial load capacity **of** column nominal axial load strength **of** a member with no eccentricity allowable soil pressure effective soil pressure a term used in required percentage **of** steel expression for ﬂexural members (Mu /φbd 2) spacing **of** shear or torsional reinforcing parallel to longitudinal reinforcing nominal shear strength provided by masonry (see Chapter 20) nominal shear strength provided by shear reinforcement (see Chapter 20) torsional stress crack width unit weight **of** **concrete** distance from centroidal axis **of** gross section to extreme ﬁber in tension a term used to estimate crack sizes and specify distribution **of** reinforcing ratio **of** long to short dimensions: clear spans for two-way slabs; sides **of** column, concentrated load or reaction area; or sides **of** a footing ratio used to account for reduction **of** stiffness **of** columns due to sustained axial loads ratio used to account for reduction **of** stiffness **of** columns due to sustained lateral loads a factor to be multiplied by the depth d **of** a member to obtain the depth **of** the equivalent rectangular stress block moment magniﬁcation factor to reﬂect effects **of** member curvature between ends **of** compression member moment magniﬁcation factor for slender columns in frames not braced against sidesway strain in compression **concrete** strain in tension reinforcement strain in compression reinforcement modiﬁcation factor reﬂecting the reduced mechanical properties **of** lightweight concrete; all relative to normal weight **concrete** **of** the same compressive strength a multiplier used in computing long-term deﬂections coefﬁcient **of** friction a time-dependent factor for sustained loads used in computing long-term deﬂections ratio **of** nonprestressed reinforcement in a section ratio **of** compression reinforcing in a section ratio **of** tensile reinforcing producing balanced strain condition capacity reduction factor Page McCormac bend02.tex V2 - January 9, 2013 8:08 P.M Typical SI Quantities and Units Quantity Unit Length Area Quantity Symbol Unit (N/m2 ) Symbol meter m Stress pascal square meter m2 Moment newton meter N•m Pa Volume cubic meter m Work newton meter Nm Force newton N Density kilogram per cubic meter kg/m3 Weight newton per cubic meter N/m3 Mass kilogram kg SI Preﬁxes Prefix Symbol tera T Multiplication Factor 10 12 = 000 000 000 000 giga G 10 = 000 000 000 mega M 106 = 000 000 k 10 = 000 h 10 = 100 da 10 = 10 kilo hecto deca deci centi d c 10 10 −1 = 0.100 −2 = 0.010 −3 milli m 10 = 0.001 micro μ 10−6 = 0.000 001 nano n 10−9 = 0.000 000 001 pico p −12 10 = 0.000 000 000 001 Conversion **of** U.S Customary Units to SI Units U.S Customary Units in in.2 SI Units 25.400 mm = 0.025 400 m 645.16 mm2 = 6.451 600 m2 × 10−4 ft 304.800 mm = 0.304 800 m lb 4.448 222 N l kip 448 222 N = 4.448 222 kN psi 6.894 757 kN/m2 = 0.006 895 MN/m2 = 0.006 895 N/mm2 psf 47.880 N/m2 = 0.047 800 kN/m2 ksi 6.894 757 MN/m2 = 6.894 757 MPa in-lb 0.112 985 N • m ft-lb 1.355 818 N • m in-k 112.985 N • m ft-k 355.82 N • m = 1.355 82 kN • m Page McCormac bend02.tex V2 - January 9, 2013 8:08 P.M Page ... Contents Preface Introduction xv 1.1 Concrete and Reinforced Concrete, 1.2 Advantages of Reinforced Concrete as a Structural Material, 1.3 Disadvantages of Reinforced Concrete as a Structural Material,... Shear Stresses in Concrete Beams, 223 Lightweight Concrete, 224 Shear Strength of Concrete, 225 Shear Cracking of Reinforced Concrete Beams, 226 Web Reinforcement, 227 Behavior of Beams with Web... the penetration of water into porous concretes but probably don’t help dense, well-cured concretes very much 1.11 Properties of Concrete A thorough knowledge of the properties of concrete is necessary

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- moment curvature relationship of reinforced concrete members
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- design of reinforced concrete7th edition according to aci 31805by j c maccormac
- the laws of motion father brown
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- Cover
- Title Page
- Copyright
- Contents
- Preface
- Chapter 1: Introduction
- 1.1 Concrete and Reinforced Concrete
- 1.2 Advantages of Reinforced Concrete as a Structural Material
- 1.3 Disadvantages of Reinforced Concrete as a Structural Material
- 1.4 Historical Background
- 1.5 Comparison of Reinforced Concrete and Structural Steel for Buildings and Bridges
- 1.6 Compatibility of Concrete and Steel
- 1.7 Design Codes
- 1.8 SI Units and Shaded Areas
- 1.9 Types of Portland Cement
- 1.10 Admixtures
- 1.11 Properties of Concrete
- 1.12 Aggregates
- 1.13 High-Strength Concretes
- 1.14 Fiber-Reinforced Concretes
- 1.15 Concrete Durability
- 1.16 Reinforcing Steel
- 1.17 Grades of Reinforcing Steel
- 1.18 SI Bar Sizes and Material Strengths
- 1.19 Corrosive Environments
- 1.20 Identifying Marks on Reinforcing Bars
- 1.21 Introduction to Loads
- 1.22 Dead Loads
- 1.23 Live Loads
- 1.24 Environmental Loads
- 1.25 Selection of Design Loads
- 1.26 Calculation Accuracy
- 1.27 Impact of Computers on Reinforced Concrete Design
- Problems

- Chapter 2: Flexural Analysis of Beams
- Chapter 3: Strength Analysis of Beams According to ACI Code
- 3.1 Design Methods
- 3.2 Advantages of Strength Design
- 3.3 Structural Safety
- 3.4 Derivation of Beam Expressions
- 3.5 Strains in Flexural Members
- 3.6 Balanced Sections, Tension-Controlled Sections, and Compression-Controlled or Brittle Sections
- 3.7 Strength Reduction or ö Factors
- 3.8 Minimum Percentage of Steel
- 3.9 Balanced Steel Percentage
- 3.10 Example Problems
- 3.11 Computer Examples
- Problems

- Chapter 4: Design of Rectangular Beams and One-Way Slabs
- Chapter 5: Analysis and Design of T Beams and Doubly Reinforced Beams
- Chapter 6: Serviceability
- 6.1 Introduction
- 6.2 Importance of Deflections
- 6.3 Control of Deflections
- 6.4 Calculation of Deflections
- 6.5 Effective Moments of Inertia
- 6.6 Long-Term Deflections
- 6.7 Simple-Beam Deflections
- 6.8 Continuous-Beam Deflections
- 6.9 Types of Cracks
- 6.10 Control of Flexural Cracks
- 6.11 ACI Code Provisions Concerning Cracks
- 6.12 Miscellaneous Cracks
- 6.13 SI Example
- 6.14 Computer Example
- Problems

- Chapter 7: Bond, Development Lengths, and Splices
- 7.1 Cutting Off or Bending Bars
- 7.2 Bond Stresses
- 7.3 Development Lengths for Tension Reinforcing
- 7.4 Development Lengths for Bundled Bars
- 7.5 Hooks
- 7.6 Development Lengths for Welded Wire Fabric in Tension
- 7.7 Development Lengths for Compression Bars
- 7.8 Critical Sections for Development Length
- 7.9 Effect of Combined Shear and Moment on Development Lengths
- 7.10 Effect of Shape of Moment Diagram on Development Lengths
- 7.11 Cutting Off or Bending Bars (Continued)
- 7.12 Bar Splices in Flexural Members
- 7.13 Tension Splices
- 7.14 Compression Splices
- 7.15 Headed and Mechanically Anchored Bars
- 7.16 SI Example
- 7.17 Computer Example
- Problems

- Chapter 8: Shear and Diagonal Tension
- 8.1 Introduction
- 8.2 Shear Stresses in Concrete Beams
- 8.3 Lightweight Concrete
- 8.4 Shear Strength of Concrete
- 8.5 Shear Cracking of Reinforced Concrete Beams
- 8.6 Web Reinforcement
- 8.7 Behavior of Beams with Web Reinforcement
- 8.8 Design for Shear
- 8.9 ACI Code Requirements
- 8.10 Shear Design Example Problems
- 8.11 Economical Spacing of Stirrups
- 8.12 Shear Friction and Corbels
- 8.13 Shear Strength of Members Subjected to Axial Forces
- 8.14 Shear Design Provisions for Deep Beams
- 8.15 Introductory Comments on Torsion
- 8.16 SI Example
- 8.17 Computer Example
- Problems

- Chapter 9: Introduction to Columns
- 9.1 General
- 9.2 Types of Columns
- 9.3 Axial Load Capacity of Columns
- 9.4 Failure of Tied and Spiral Columns
- 9.5 Code Requirements for Cast-in-Place Columns
- 9.6 Safety Provisions for Columns
- 9.7 Design Formulas
- 9.8 Comments on Economical Column Design
- 9.9 Design of Axially Loaded Columns
- 9.10 SI Example
- 9.11 Computer Example
- Problems

- Chapter 10: Design of Short Columns Subject to Axial Load and Bending
- 10.1 Axial Load and Bending
- 10.2 The Plastic Centroid
- 10.3 Development of Interaction Diagrams
- 10.4 Use of Interaction Diagrams
- 10.5 Code Modifications of Column Interaction Diagrams
- 10.6 Design and Analysis of Eccentrically Loaded Columns Using Interaction Diagrams
- 10.7 Shear in Columns
- 10.8 Biaxial Bending
- 10.9 Design of Biaxially Loaded Columns
- 10.10 Continued Discussion of Capacity Reduction Factors, ö
- 10.11 Computer Example
- Problems

- Chapter 11: Slender Columns
- 11.1 Introduction
- 11.2 Nonsway and Sway Frames
- 11.3 Slenderness Effects
- 11.4 Determining k Factors with Alignment Charts
- 11.5 Determining k Factors with Equations
- 11.6 First-Order Analyses Using Special Member Properties
- 11.7 Slender Columns in Nonsway and Sway Frames
- 11.8 ACI Code Treatments of Slenderness Effects
- 11.9 Magnification of Column Moments in Nonsway Frames
- 11.10 Magnification of Column Moments in Sway Frames
- 11.11 Analysis of Sway Frames
- 11.12 Computer Examples
- Problems

- Chapter 12: Footings
- 12.1 Introduction
- 12.2 Types of Footings
- 12.3 Actual Soil Pressures
- 12.4 Allowable Soil Pressures
- 12.5 Design of Wall Footings
- 12.6 Design of Square Isolated Footings
- 12.7 Footings Supporting Round or Regular Polygon-Shaped Columns
- 12.8 Load Transfer from Columns to Footings
- 12.9 Rectangular Isolated Footings
- 12.10 Combined Footings
- 12.11 Footing Design for Equal Settlements
- 12.12 Footings Subjected to Axial Loads and Moments
- 12.13 Transfer of Horizontal Forces
- 12.14 Plain Concrete Footings
- 12.15 SI Example
- 12.16 Computer Examples
- Problems

- Chapter 13: Retaining Walls
- 13.1 Introduction
- 13.2 Types of Retaining Walls
- 13.3 Drainage
- 13.4 Failures of Retaining Walls
- 13.5 Lateral Pressure on Retaining Walls
- 13.6 Footing Soil Pressures
- 13.7 Design of Semigravity Retaining Walls
- 13.8 Effect of Surcharge
- 13.9 Estimating the Sizes of Cantilever Retaining Walls
- 13.10 Design Procedure for Cantilever Retaining Walls
- 13.11 Cracks and Wall Joints
- Problems

- Chapter 14: Continuous Reinforced Concrete Structures
- 14.1 Introduction
- 14.2 General Discussion of Analysis Methods
- 14.3 Qualitative Influence Lines
- 14.4 Limit Design
- 14.5 Limit Design under the ACI Code
- 14.6 Preliminary Design of Members
- 14.7 Approximate Analysis of Continuous Frames for Vertical Loads
- 14.8 Approximate Analysis of Continuous Frames for Lateral Loads
- 14.9 Computer Analysis of Building Frames
- 14.10 Lateral Bracing for Buildings
- 14.11 Development Length Requirements for Continuous Members
- Problems

- Chapter 15: Torsion
- 15.1 Introduction
- 15.2 Torsional Reinforcing
- 15.3 Torsional Moments that Have to Be Considered in Design
- 15.4 Torsional Stresses
- 15.5 When Torsional Reinforcing Is Required by the ACI
- 15.6 Torsional Moment Strength
- 15.7 Design of Torsional Reinforcing
- 15.8 Additional ACI Requirements
- 15.9 Example Problems Using U.S. Customary Units
- 15.10 SI Equations and Example Problem
- 15.11 Computer Example
- Problems

- Chapter 16: Two-Way Slabs, Direct Design Method
- 16.1 Introduction
- 16.2 Analysis of Two-Way Slabs
- 16.3 Design of Two-Way Slabs by the ACI Code
- 16.4 Column and Middle Strips
- 16.5 Shear Resistance of Slabs
- 16.6 Depth Limitations and Stiffness Requirements
- 16.7 Limitations of Direct Design Method
- 16.8 Distribution of Moments in Slabs
- 16.9 Design of an Interior Flat Plate
- 16.10 Placing of Live Loads
- 16.11 Analysis of Two-Way Slabs with Beams
- 16.12 Transfer of Moments and Shears between Slabs and Columns
- 16.13 Openings in Slab Systems
- 16.14 Computer Example
- Problems

- Chapter 17: Two-Way Slabs, Equivalent Frame Method
- Chapter 18: Walls
- Chapter 19: Prestressed Concrete
- 19.1 Introduction
- 19.2 Advantages and Disadvantages of Prestressed Concrete
- 19.3 Pretensioning and Posttensioning
- 19.4 Materials Used for Prestressed Concrete
- 19.5 Stress Calculations
- 19.6 Shapes of Prestressed Sections
- 19.7 Prestress Losses
- 19.8 Ultimate Strength of Prestressed Sections
- 19.9 Deflections
- 19.10 Shear in Prestressed Sections
- 19.11 Design of Shear Reinforcement
- 19.12 Additional Topics
- 19.13 Computer Example
- Problems

- Chapter 20: Reinforced Concrete Masonry
- 20.1 Introduction
- 20.2 Masonry Materials
- 20.3 Specified Compressive Strength of Masonry
- 20.4 Maximum Flexural Tensile Reinforcement
- 20.5 Walls with Out-of-Plane Loads-Non-Load-Bearing Walls
- 20.6 Masonry Lintels
- 20.7 Walls with Out-of-Plane Loads-Load-Bearing
- 20.8 Walls with In-Plane Loading-Shear Walls
- 20.9 Computer Example
- Problems

- Appendix A: Tables and Graphs: U.S. Customary Units
- Appendix B: Tables in SI Units
- Appendix C: The Strut-and-Tie Method of Design
- Appendix D: Seismic Design of Reinforced Concrete Structures
- Glossary
- Index

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