Wight macgregor reinforced concrete mechanics design 6th txtbk

www.elsolucionario.net This page intentionally left blank www.elsolucionario.net REINFORCED CONCRETE Mechanics and Design www.elsolucionario.net About the Cover The photos that appear on the cover of this book are of the Aqua Tower, an 82-story multiuse high-rise in downtown Chicago, Illinois Its undulating faỗade gives it a distinct appearance and demonstrates both architectural and technical achievements Architect: Studio Gang Architects www.elsolucionario.net REINFORCED CONCRETE Mechanics and Design SIXTH EDITION JAMES K WIGHT F E Richart, Jr Collegiate Professor Department of Civil & Environmental Engineering University of Michigan JAMES G MACGREGOR PhD, P Eng., Honorary Member ACI D Eng (Hon.), D.Sc (Hon.), FRSC University Professor Emeritus Department of Civil Engineering University of Alberta Boston Amsterdam Delhi Columbus Cape Town Mexico City Indianapolis Dubai London New York Madrid Sao Paulo Sydney San Francisco Milan Hong Kong Munich Seoul www.elsolucionario.net Upper Saddle River Paris Singapore Montreal Taipei Toronto Tokyo Vice President and Editorial Director, ECS: Marcia J Horton Executive Editor: Holly Stark Editorial Assistant: William Opaluch Vice President, Production: Vince O’Brien Senior Managing Editor: Scott Disanno Production Liaison: Irwin Zucker Production Editor: Pavithra Jayapaul, TexTech International Operations Specialist: Lisa McDowell Executive Marketing Manager: Tim Galligan Market Assistant: Jon Bryant Art Editor: Greg Dulles Art Director: Kenny Beck Cover Images: Photos of Aqua Building, Chicago IL: Close-up photo: MARSHALL GEROMETTA/AFP/Getty Images/Newscom; Full view photo of building: © Wilsons Travels Stock / Alamy Composition/Full-Service Project Management: TexTech International Copyright © 2012, 2009, 2005 by Pearson Education, Inc., Upper Saddle River, New Jersey 07458 All rights reserved Manufactured in the United States of America This publication is protected by Copyright and permissions should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise To obtain permission(s) to use materials from this work, please submit a written request to Pearson Higher Education, Permissions Department, Lake Street, Upper Saddle River, NJ 07458 The author and publisher of this book have used their best efforts in preparing this book These efforts include the development, research, and testing of the theories and programs to determine their effectiveness The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs Library of Congress Cataloging-in-Publication Data Wight, James K Reinforced concrete : mechanics and design / James K Wight, F.E Richart, Jr., James G Macgregor – 6th ed p cm Rev ed of: Reinforced concrete / James G MacGregor, James K Wight 5th ed 2009 ISBN-13: 978-0-13-217652-1 ISBN-10: 0-13-217652-1 I Richart, F E (Frank Edwin), 1918– II MacGregor, James G (James Grierson), 1934– III MacGregor, James G (James Grierson), 1934– Reinforced concrete IV Title TA683.2.M34 2011 624.1'8341—dc23 2011019214 10 ISBN-13: 978-0-13-217652-1 ISBN-10: 0-13-217652-1 www.elsolucionario.net Contents CHAPTER PREFACE xiii ABOUT THE AUTHORS xvii INTRODUCTION 1-1 1-2 1-3 1-4 1-5 1-6 CHAPTER Reinforced Concrete Structures Mechanics of Reinforced Concrete Reinforced Concrete Members Factors Affecting Choice of Reinforced Concrete for a Structure Historical Development of Concrete and Reinforced Concrete as Structural Materials Building Codes and the ACI Code 10 References 10 THE DESIGN PROCESS 2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8 12 Objectives of Design 12 The Design Process 12 Limit States and the Design of Reinforced Concrete 13 Structural Safety 17 Probabilistic Calculation of Safety Factors 19 Design Procedures Specified in the ACI Building Code 20 Load Factors and Load Combinations in the 2011 ACI Code 23 Loadings and Actions 28 v www.elsolucionario.net vi • Contents 2-9 2-10 2-11 2-12 2-13 2-14 CHAPTER MATERIALS 3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9 3-10 3-11 3-12 3-13 3-14 3-15 3-16 CHAPTER Design for Economy 38 Sustainability 39 Customary Dimensions and Construction Tolerances 40 Inspection 40 Accuracy of Calculations 41 Handbooks and Design Aids 41 References 41 43 Concrete 43 Behavior of Concrete Failing in Compression 43 Compressive Strength of Concrete 46 Strength Under Tensile and Multiaxial Loads 59 Stress–Strain Curves for Concrete 67 Time-Dependent Volume Changes 73 High-Strength Concrete 85 Lightweight Concrete 87 Fiber Reinforced Concrete 88 Durability of Concrete 90 Behavior of Concrete Exposed to High and Low Temperatures 91 Shotcrete 93 High-Alumina Cement 93 Reinforcement 93 Fiber-Reinforced Polymer (FRP) Reinforcement 99 Prestressing Steel 100 References 102 FLEXURE: BEHAVIOR AND NOMINAL STRENGTH OF BEAM SECTIONS 4-1 4-2 4-3 4-4 4-5 4-6 4-7 4-8 4-9 Introduction 105 Flexure Theory 108 Simplifications in Flexure Theory for Design 119 Analysis of Nominal Moment Strength for SinglyReinforced Beam Sections 124 Definition of Balanced Conditions 131 Code Definitions of Tension-Controlled and Compression-Controlled Sections 132 Beams with Compression Reinforcement 142 Analysis of Flanged Sections 152 Unsymmetrical Beam Sections 165 References 172 www.elsolucionario.net 105 Contents CHAPTER FLEXURAL DESIGN OF BEAM SECTIONS 5-1 5-2 5-3 5-4 5-5 CHAPTER 6-5 6-6 6-7 6-8 6-9 6-10 CHAPTER 7-3 7-4 7-5 7-6 CHAPTER 312 Introduction and Basic Theory 312 Behavior of Reinforced Concrete Members Subjected to Torsion 323 Design Methods for Torsion 325 Thin-Walled Tube/Plastic Space Truss Design Method 325 Design for Torsion and Shear—ACI Code 339 Application of ACI Code Design Method for Torsion 345 References 366 DEVELOPMENT, ANCHORAGE, AND SPLICING OF REINFORCEMENT 8-1 8-2 8-3 8-4 8-5 243 Introduction 243 Basic Theory 245 Behavior of Beams Failing in Shear 250 Truss Model of the Behavior of Slender Beams Failing in Shear 261 Analysis and Design of Reinforced Concrete Beams for Shear—ACI Code 268 Other Shear Design Methods 295 Hanger Reinforcement 300 Tapered Beams 302 Shear in Axially Loaded Members 303 Shear in Seismic Regions 307 References 310 TORSION 7-1 7-2 173 Introduction 173 Analysis of Continuous One-Way Floor Systems 173 Design of Singly Reinforced Beam Sections with Rectangular Compression Zones 195 Design of Doubly Reinforced Beam Sections 220 Design of Continuous One-Way Slabs 228 References 242 SHEAR IN BEAMS 6-1 6-2 6-3 6-4 • vii Introduction 367 Mechanism of Bond Transfer 372 Development Length 373 Hooked Anchorages 381 Headed and Mechanically Anchored Bars in Tension 386 www.elsolucionario.net 367 Index force transfer as, 367–368 pull-out test for, 370–371 splitting loads, 374–375 stresses 1m2, 367–371 transfer mechanisms, 372–373 true (in-and-out), 367, 369–370 Boundary elements in shear walls, 1002–1004 Braced (nonsway) frames, 469–470, 564–565, 584–589 design of, 589–590 effective length (kl) of columns for, 564–565, 579 end restraints, effects of on, 584–587, 589–592 moment magnifier design for, 568–570 reinforced concrete floor systems and, 469–471 relative stiffness 1c2 of columns for, 590, 621 sustained loads, effects on, 576–577 Brackets, see Corbels Bresler reciprocal load method for, biaxial columns, 549, 555–556 columns and, 546–556 equivalent-eccentricity method for, 548, 554–555 strain-compatibility method for, 548–553 Buckling, 563–565, 576–577, 948–998 concrete properties and, 1016–1017 creep, 577 edge restraint factor for, 1017 Euler load, 564 slender columns, 563–565, 577 walls, 973–1022 Building codes, 10, 20–28, 50–51 Button-head anchorages, 100 C Cantilever retaining walls, 975 Capacity design, 21, 1044–1045 Capitals, 6, 632, 732 Carbonation shrinkage, 74 Carryover factors (COF), 668–669 Cement, 7–8, 41, 51–52, 93 Centroids of reinforcement bars, 201–202 Checkerboard loading, 179 Chemical attack causes of breakdown in concrete, 91 Circular columns, 523–524, 722–723 Circulatory torsion, 318–322 Coating factor 1ce2, 378 Coefficient of variation (V), 48–49 Cohesion-plus-friction model, 864–865 Collapse mechanism, 22 Columns, 499–629, 645–647, 651, 667, 808–810, 817–818, 1050–1059, 1085–1132 axially loaded, 503–506, 563–565 bar spacing requirements for, 531 biaxially loaded, 546–558 circular, 523–524, 722–723 concentrated loads applied from, 807–810 critical shear sections of, 719–723 eccentrically loaded, 502–503 edge (exterior), 656, 667, 721–722, 726–731 fan yield-line patterns at, 808–810 interaction diagrams for, 508–527, 583, 1084–1132 interior, 651, 667, 723, 724 load transfers to footings from, 817–818 material properties for, 529–530 maximum axial load for, 512, 513 moment-resisting frames for, 1050–1059 pin-ended, 566–584 polar moment of inertia 1Jc2 for, 720–721 reinforced concrete, 508–527 reinforcement ratio for, 529–530 second maximum load of, 502 shear and moment transfer in, 714–731 shear strength at slab–column connections and, 709 short, 499, 527–544 size estimation of, 529–530 www.elsolucionario.net • 1143 slabs supported by, 643–645, 646, 653–667 slender, 499, 530–531, 561–629 spiral, 500–506, 530–531, 543–544 splices for reinforcement of, 531–535 stiffness and carryover factors for, 1100 strength, steel and concrete contributions to, 544–546 strength-reduction factor 1f2 for, 511–512 tied, 499, 500–506, 530, 539–542, 544 torsional members and, 674–683 unsymmetrical, 525 Combined footings, 812, 844–854 Companion-action loads, 23, 29 Compatibility torsion, 336–338, 493 Composite beams, 867, 869–878 deflections in, 873–874 design of, 874–878 horizontal shear in, 871–873 Loov and Patnaik shear transfer equation for, 867 shored and unshored construction of, 869–870 Compression, 43–46, 67–72, 142–151, 195–219, 297–298, 861–862 axial, 306 concrete behavior in, 43–46 microcracking from, 43–44 mode failure changes from, 145 permanent force 1Nu2, 861–862 stress–strain curves, 43–44, 67–73 transverse, 153–155 Compression-controlled beam sections, 132–142 Compression-controlled limit (CCL), 134 Compression fans, 901 Compression fields, 263, 267, 297–298, 902 Compression lap splices, 423–424 Compression reinforcement, 107, 118–119, 142–151 doubly-reinforced beam sections area of 1A sœ 2, 112, 142 1144 • Index Compression reinforcement (Continued) ductility increased from, 117, 144 fabrication ease from, 145 flexural behavior, effect of on, 144–145 nominal moment 1Mn2 strength and, 146–149 strength, effect of on, 140–141 strength-reduction factors 1f2 and, 149 sustained load deflections reduced by, 144 ties for, 149 Compressive strength 1fcœ 2, 46–59, 60–61, 63–65, 92, 471 aggregates and, 52 biaxial loadings and, 62–63 building codes for, 50–51 cement type and, 51 coefficient of variation (V) of, 47–48 concrete, 43–59, 60, 63–65 control data for, 49 core tests for, 55–59 curing conditions, 53 distribution of, 47–49 effective, 461 œ equivalent specified strength 1fceq 57–59 pozzolans for, 51–52 rate of loading and, 54 standard deviation (s) of, 48 standard tests for, 46 stress–strain curves and, 43–44 supplementary materials for, 51–52 tensile strength and, 59–65 water/cement ratio for, 51 water quality and, 53 Compressive stress block, 110 Concentrated loads, 807–811, 824, 894, 903 columns and, 807–811, 824 strut-and-tie models and, 896–898, 901–903 Concrete, 8, 43–101, 256–257, 280, 544–546 See also Reinforced concrete age of, 53 air entrainment, 51, 91 chemical attack causes of breakdown, 91 columns, reinforcement in, 574 compression, behavior of in, 43–46, 67–72 compressive strength 1fcœ 2, 46–59, 60–61, 63–65 corrosion of steel in, 90 creep and, 78–85, 87 critical stress of, 44–45 discontinuity limit of, 44 durability of, 90–91 fiber-reinforced, 90 high-strength, 49, 85–87, 280 lightweight, 49, 87, 257 maturity of, 54 microcracking, 43–44 multiaxial loading of, 59–66 normal-weight, 67–73 shear strength 1Vc2 of beams and, 256–259, 278 shotcrete, 93 shrinkage, 73–78, 87 strength of in structures, 58–59, 565–566 stress–strain curves for, 43–45, 67–73, 1018–1019 temperature effects on, 91–92 tensile strength of, 59–65, 72–73, 256 tests for strength of, 45, 55–59 thermal expansion and contraction, 85 volume changes, time-dependent, 73–85 walls and, 1018–1025 Concrete beams, 1–4, 8, 197, 268–295, 443–451, 858, 869–878 composite, 858, 869–878 deflections of, 443–451, 873 flexural stiffness (El) of, 444–447 load–deflection behavior of, 444 moment of inertia (I) for, 444, 445–447 reinforced, 1–4, 8, 197, 268–295 Concrete buildings, 983 Concrete Reinforcing Steel Institute (CRSI), 41 www.elsolucionario.net Connections, 953–965, 714–736 beam-column, see Beam-column joints slab-column, 714–736 Construction loads, 34, 772–773 Continuity reinforcement, 405–406 Continuous beams, 188–194, 289–292, 468–498, 922–935 deep, 922–935 design of, 472–498 floor system design using, 184–194, 471 moment coefficient 1Cm2 for, 185–191 moment redistribution for, 496–498 reinforced concrete for, 468–472 stirrup design for, 289–292 structural analysis of, 188–194 strut-and-tie models for, 922–935 Control data for concrete compressive strength, 48–49 Corbels (brackets), 6, 935–947 ACI code method of design for, 943–947 structural action of, 934–935 strut-and-tie model design of, 937–943 Core of spiral columns, 502 Core tests, 55–59 Corner joints, 954–956 Coupled shear walls, 984–988 Coupling beams, 1078 construction of, 1080 high-performance fiber-reinforced concrete (HPFRC), 1080 with diagonal reinforcement, 1079–1080 Covers, 228–229, 239, 733–734 Cracked moment of inertia 1Icr2, 191 Cracking point, 114–116 Cracks, 14, 43–45, 63–65, 247–248, 254–255, 264, 275, 332–333, 338, 434–443, 882–888 angle 1u2, 267–268, 338 beam sections, 248–249, 254–255 bond, 43–44, 436 concrete, 43–44 control of, 438–440, 443 development of, 436–438 flexural, 246–247 Index flexure-shear, 254 heat-of-hydration, 435 inclined, 246, 249–250, 254–255 load-induced, 434–443 longitudinal, 882–888 map, 435–436 microcracking, 43–44 mortar, 43–44 plastic slumping, 435 reinforced concrete, 63–65 reinforcement for, 249–250, 441 serviceability and, 427–465 shear between, 247–248 skin reinforcement for, 443 temperature reinforcement for, 442 torsion and, 332, 333 web face reinforcement for, 443 web-shear, 254 widths, 14, 275, 332–333, 440–442 Creep, 78–85, 87, 577 age-adjusted effective modulus for, 83 buckling, 577 calculation of, 81–83, 85 coefficient, 79–80 compliance function, 82 high-strength concrete, 87 restrained, 83–85 unrestrained concrete, 78–83 variability of, 80–81 Critical loads for walls, 1016–1022 Critical sections, 340–341, 698–703, 711–713, 716–717, 821–822 beams, 340–341 footings, 821–822 torsion and, 340 two-way slabs, 698–703, 719–722 Critical stress, 44–45 Crushing strength of webs, 268, 333 Curing concrete, 53 Curvature relationships to moments in slabs, 641–643 Cut-off bars, 195, 394–421 bending-moment diagrams for, 417–421 development of, 398–404 equations of moments for, 407–416 flexural reinforcement and, 394–404 inflection, point of, 401–402 location of, 195, 394–421 maximum force, points of, 398–400 positive-moment regions, 400–404 required-moment diagram for, 395 shear, effect of on, 397–398 structural integrity requirements, 404–421 D D-regions, see Discontinuity regions Dapped ends, 947–953 Dead loads (D), 25, 30 Deep beams, 250, 908–935 continuous, 922–935 discontinuity regions in, 908–935 elastic analysis of, 909–910 strut-and-tie models design of, 912–922 Deflections, 15, 144–145, 212, 443–462, 574–576, 773–778, 873–874 allowable, 453 buckling, 563–565 compression reinforcement effects on, 142–144 concrete beams, 443–451, 873–874 design considerations for, 451–461 dimensions for control of, 197–198 first-order, 566–567 flexural stiffness (El) and, 444–451, 462, 575 frames, 462, 574–575 instantaneous, 447–451 lateral, 462, 562 moments (M) of, 567 nonstructural elements, damage to from, 451–453 second-order, 574–575 serviceability limit states (SLS) from, 452–453, 463 singly-reinforced beam sections, 197–198 slender columns, 574–576 www.elsolucionario.net • 1145 span-to-depth limits for control of, 454–461 structural stability and, 14 sustained-load, 144, 450–451, 587–589 two-way slabs, 774–778 vertical, 462 visual appearance of, 451 Depth (d), 113, 133, 202–203, 250 effective (d), 113, 133, 202–203 shear 1dv2, 250 Design, see Flexural design; Seismic design; Structural design Design equations, 882 Design loads for continuous floor systems, 471 Design pressure (p), 35 Development length, 373–381 Diaphragms, 989, 1035, 1071–1073 discontinuity irregularities for seismic design, 1035 earthquake loads and, 1035, 1071–1073 flexural strength of, 1071 shear strength 1Vc2, 1072 stiffness effects on load distribution, 1072–1073 walls, 989 Direct-design method for slabs, 652–667 Direct loads, load factors for, 24 Directionality factor 1Kd2, 35 Discontinuity limit, 44 Discontinuity regions, 263, 879–971 beam–column joints, 953–966 bearing strength, 966–968 behavior of, 881 continuous deep beams, 922–935 corbels (brackets), 935–947 dapped ends, 947–953 deep beams, 908–922 design equations for, 882 Saint Venant’s principle, 879 shear spans, 250–251 strut-and-tie models for, 879–971 T-beam flanges, 968–971 Discontinuous corners of slabs, 806–807 Distribution factors (DF), 668 1146 • Index Doubly-reinforced beam sections, 113, 142, 220–228 compression reinforcement and, 142–151 flexural analysis of, 149 flexural behavior of, 111, 142 flexural design of, 220–228 nominal moment 1Mn2 strength of, 145–148 strength-reduction factors 1f2 for, 149 ties for, 149–150 Drop panels, 6, 669–670, 731–732 Drying shrinkage, see Shrinkage Ductility, 117–119, 144, 1031–1033 beam section variables, effects on, 117–119 compression reinforcement and, 119, 144 earthquake loads and, 1031–1033 Dynamic loads, 29 E Earthquake loads (E), 24–25, 962–963, 1013–1016 beam–column joints and, 1069–1071 beam cross sections, geometric limits of, 1045 columns and, 1059–1068 design for resistance of, 1027–1081 distribution of, 1038–1040 ductility and, 1040–1042 equivalent lateral force method for, 1037–1038 flexural members and, 1045–1059 foundations and, 1080 load factors for, 25 load-resisting systems for, 962–963, 1013–1016 moment-resisting frames for, 1045–1071 nonductile frame members for, 1080–1081 precast structures for, 1081 reinforced concrete and, 1040–1042 reinforcement for, 1042–1068 resisting moments for, 1042 response-modification factor (R) for, 1038 seismic design, 1028–1040, 1042–1045 seismic response spectra, 1028–1033, 1037 shear walls and seismic load resistance, 1013–1016 structures, seismic forces on, 1031–1033 walls and, 974, 980, 981 Eccentrically loaded columns, 529 Eccentricity (e) of load for interaction diagrams, 529, 555 Edge beams, 644–645, 659 Edge (exterior) columns, 648, 667, 708, 718–719 Effective compressive strength, 471 Effective depth (d), 133, 199–203 Effective flange width, 153–154 Effective length (kl), 564, 579 Elastic analysis, 428–432, 785–787, 909–911 beam sections, 428–432 deep beams, 909–911 flexural stiffness (EI) for, 428–432 modular ratio for, 428 modulus of elasticity (E) for, 428 serviceability and, 428–432 two-way slabs, 785–787 Elastic distribution of soil pressure, 816–817 Elasticity (E), moduli of, 67, 428 End restraints, effects on braced frames, 584–587, 589–600 Equilibrium, 13, 124, 336–338, 563–565, 881 columns, states of, 563–565 internal forces for flexural analysis, 124 structural stability and loss of, 13 strut-and-tie models and, 881 torsion, 336–338 Equivalent eccentricity method for biaxial columns, 548–549, 555–556 Equivalent-frame methods for slabs, 647, 667–695 columns, properties of, 674 www.elsolucionario.net computers used for analysis, 689–692 flexural stiffness (El) for, 668–669 live load arrangement for, 683 moment distribution for, 684 slab–beams, properties of, 669–670 Equivalent lateral force method for earthquake loads, 1037–1038 œ Equivalent specified strength 1fceq 2, 57–59 Euler buckling load, 564 Extended nodal zones, 890–893 External pressure coefficient 1Cp2, 36 F Factored loads (U), 17, 20–21, 23–27, 106, 180–183, 190 computation of effects, 26–27 design moment 1Mu2, 106, 187 flexure and, 106 floor system design for, 180–182 load combinations and, 23–27, 184–188 moment coefficient 1Cm2 for, 182–188 structural design and, 17, 20–23 Failure, 14, 18–19, 34, 131, 144, 243, 256, 267–268, 453, 502, 505–506, 561 balanced, 131–132, 507, 511 compression, 144–145, 243 consequences of, 18–19 mode, 145 ponding, 14, 34, 453 probability of 1Pf2, 19–20 shear, 248, 259, 810 stability, 567 structural safety and, 19–20 transition, 511 Fan-shaped yield patterns, 807–810 Fatigue, 14, 96–97, 464 Fiber-reinforced concrete (FRC), 88–90, 261 Fiber-reinforced polymer (FRP) reinforcement, 99–100 Fillers, 494 Index Finite-element analysis for slabs, 787–789 Fire resistance of structures, First-order analysis, 566 Fixed-end moments (FEM), 668–669 Flanged beam sections, 152–165 area of tension reinforcement 1A s2 for, 161 compression of, 152–155 effective width of, 153–155 flexural analysis of, 159–163 inverted L-beam, 152, 154 nominal moment 1Mn2 strength of, 155–158 overhanging portions, 155 spandrel beam for, 152–153 strength-reduction factors 1f2 for, 159 T-beams, 152–153, 155, 163–165 transverse compression of, 153–155 Flat (plates) slabs, 6, 632–633, 660–667, 685–689 direct-design method for, 660–667 equivalent-frame method for, 685–689 system, 632–633 Flexural cut-off points, 416–421 Flexural design, 119–124, 173–239 beam sections, 173–239 continuous beams, 184–194 doubly-reinforced beam sections, 220–228 flexural theory simplifications for, 119–124 floor sections, 173–194 one-way slabs, 188–191, 228–239 singly-reinforced beam sections, 195–220 Flexural reinforcement, 379, 397, 1047 Flexural-resistance factor (R), 211, 1087–1088 Flexural stiffness (El), 444–445, 449, 575, 603–605, 668–669 concrete beams, 443–445 lateral reduction factor for, 603 serviceability and, 428–429 slabs, 668–669 slender columns, 575, 603–605 sway (unbraced) frames, 603–605 ultimate limit state, 603–604 Flexural strength, 105, 117–119, 999–1005, 1071 design for, 106–107 diaphragms, 1071–1072 ductility and, 117–119 required, 106–107 shear walls, 999–1005 Flexure, 28, 105–168, 634–636, 820–822 analysis of reinforced concrete, 106 balanced conditions for, 131–132 beam sections, 105–168 code definitions for, 132–142 compression reinforcement and, 142–151 design and concrete, 106 equilibrium of internal forces for, 124 failure in, 634–636 footings, 820–822 loads and, 27–28, 105–108 moments, 105–108 nominal moment 1Mn2 strength, 106, 116, 124–130, 136–138, 146–149, 155–158 slabs, 105–106, 634–636 strength-reduction factors 1f2, 106–107 stress–strain relationships for, 120–122, 124 structural design and, 28 symbols and notation for, 107–108 theory, 108–124 Flexure-shear cracking in walls, 1009 Flexure theory, 108–124 assumptions of, 111 beam action, statics of, 108–111 bending moments, 108 compressive stress block, 109–110 cracking point, 114–116 elastic, 109–111 internal resisting moments for, 108–111 moment–curve relationships for, 114 reinforced concrete, 111–119 simplifications in for design, 119–124 www.elsolucionario.net • 1147 stress blocks, 123–124 stress–strain relationships for, 120–122 uncracked-elastic range, 114 Whitney stress block, 122–124 yield point, 112, 116–117 Floor systems, 173–194, 471–472, 493–494, 778–780, 998 See also Girders; Slabs column loads transferred through, 471–472 continuous beams for, 184–194 design loads for, 471 factored load combinations for, 184–188 flexural design of, 173–194 girders for, 175, 493–494 influence lines for, 177–178 joist, 494–496 live load reductions for, 181–182 load paths in, 175–176 moment coefficient 1Cm2 for, 182–188 Mueller-Breslau principle for, 178–180 one-way, continuous, 173–194 pattern loadings in, 177–180 post-tensioning, 778–780 shear coefficient 1Cv2 for, 182–184 slabs for, 188–191, 778–780 spandrel beams for, 184 structural analysis for, 188–194 tributary areas in, 176–177 wall load transfer through, 998 Fly ash, 51–52 Footings, 4, 812–856 allowable stress design of, 814 combined, 812, 844–854 flexure of, 820–822 limit-states design of, 814–816 load transfers in, 824–827, 838–839 mat (raft) foundations, 812, 854 pile caps, 812, 854–856 rectangular, 836–838 reinforcement, 820–822 shear in, 822–824 soil pressure under, 812–820 spread, 812, 820–827, 830–844 strip (wall), 812, 820–830 1148 • Index Force whirls (U-turns), 902–903 Forms, construction of, 1–3, Foundations, 993–994, 1081 Frames, 462, 469–471, 564–565, 579–581, 584–626, 957–959, 981–982, 1013–1016, 1080 beam–column joints in, 957–959, 1068–1071 braced (nonsway), 469–471, 564–565, 578–580, 584–600 deflections of, 462, 574–575 design of, 584–626 earthquake loads and, 1013–1016, 1080 effective length of columns for, 564–565 first-order analysis for, 608 moment-resisting, 981–982, 1045–1071 moments in, 579–580, 603–604 reinforced concrete, 469–471 second-order analysis for, 603–607 slender columns and, 565–566, 579, 584–626 stability index (Q) for, 578 sway (unbraced), 469–471, 564–565, 578, 600–626 Free loads, 29 Friction, 858–869 ACI code design rules for, 863–864 coefficients of 1m2, 863 cohesion and, 859–861 cohesion-plus-friction model for, 864–865 inclined reinforcement, 862 lightweight concrete and, 862–863 permanent compression force 1Nu2 for, 861–862 push-off specimens for, 858–859 shear-friction model for, 861–862 upper limits on, 864 Walraven model for, 865–867 G Girders, 175–176, 292–295, 493–494 compatibility torsion and, 493–494 load paths and, 175–176 shear reinforcement of, 292–295 Gravity loads, 613–625 Gross moment of inertia 1Ig2, 189 Gross soil pressure, 818–820 Gust-effect factor, (G), 36 H Internal forces, 124, 255–256, 265–268 beams, 255–256, 265–268 equilibrium of, 124 plastic-truss model and, 265–268 shear failure and, 255–256, 265–268 Internal moments, see Moments (M) Inverted L-beam, 152 J Hanger reinforcement, 300–302 Heat-of-hydration cracks, 435 High-alumina cement, 93 High-performance fiber-reinforced concrete (HPFRC), 1080 High-strength concrete, 49, 85–87, 280 Hollow members, torsion in, 315–318, 328 Hoops, 1041, 1048–1049, 1060–1061 Horizontal shear, 870–872 Hydrostatic nodal zones, 889–891 I Impact factor, 29 Imposed deformation, 28, 37 Inclined cracks, 246, 249–250, 253–255 Inertia (I), moment of, 444, 445–447 Influence area 1AI2, 31, 181–182 Influence lines, 179–180 Instantaneous deflections, 447–450 Interaction diagrams, 506–527, 568, 1084 balanced failures in, 507, 511 compression-controlled failures, 486 computational method for, 513–523 eccentricity (e) of load for, 506, 525 nondimensional, 524, 1084 significant points of, 509–512 strain compatibility solution for, 508–509 strain limits for, 511–512 transition failures in, 511 www.elsolucionario.net Joints, see Beam–column joints Joists, 4, 494–496 K Kinematically admissible mechanism, 22, 791 L Lap splices, 422–423, 1047–1048, 1084 Lateral deflections, 462 Lateral earth pressure, 25 Lateral loads, see Earthquake loads; Windloads Lateral stiffness-reduction factor, 603 Leaning columns, 601 Lightweight-aggregate-concrete factor 1l2, 379 Lightweight concrete, 49, 87–88, 257, 862–863 Limit design, 21 Limit states, 13–15, 427–428, 452–454, 463 deflections and, 452–454, 463 design, 15 reinforced concrete design and, 13–15 serviceability (SLS), 14, 427–428, 452–453, 463 special, 14 ultimate, 13–14 vibrations, 463 Limit-states design of footing, 814–816 Index Limiting slenderness (kl/r) ratio, 577–579 Live loads (L), 25, 28–33, 176–182, 452, 683 adjacent span, 179 alternate span, 179 arrangement of for structural analysis, 683 checkerboard, 179 deflection, 452 floor systems, 176–182 impact factor for, 29 influence area for 1A l2 31, 181–182 load factors for, 25 pattern loadings for, 177–180 reductions for, 181–182 specifications for, 29–30 sustained (quasi-permanent), 29 tributary area 1A T2 for, 32, 176–177 use and occupancy, due to, 31–33 Load and resistance design factor (LRFD), 21, 817–818 Load–deflection behavior, 443–444 Load-induced cracks, 434–441 Loadings, 28–37 Loads, 15–17, 18, 20–37, 62–66, 176–180, 417, 613–615, 807–809, 824–827, 806, 901–903, 907–908 See also Earthquake Loads; Wind loads accidental, 28 ACI building codes for, 20–28 actions, 28–37 axial, 28 biaxial, 62–65 classification of, 28–29 combinations, 23–24, 427 companion-action, 23–24, 29 concentrated, 807–809, 824–827, 901–903, 907–908 concrete strength and, 62–66 construction, 34 dead (D), 24, 30 direct, 24 dynamic, 28 factored (U), 17, 20–21, 23–27 factors, 16–17, 20, 23–25 fixed, 29 flexure and, 28 footings, 824–827, 838–839 gravity, 613–625 imposed deformation, 28, 37 internal resisting moment for, 16 lateral, 24–25 live (L), 25, 28–33, 176–182 multiaxial, 62–66 nominal moment strength for, 16–17, 23 occupancy categories for, 33 permanent, 28 rain (R), 34 required strength for, 20–21, 23 roof 1Lr2, 24, 34 snow (S), 34 static, 29 strength-reduction factors 1f2 for, 16, 20–21, 27 structural design and, 15–37 strut-and-tie models, spreading regions of, 901–903, 906–907 sustained, 28–29 triaxial, 65–66 variable, 28 vertical, 838–839 walls for resistance of lateral, 981–982 working (service), 21 Long columns, see Slender columns Longitudinal cracking, failure of struts by, 882–888 Longitudinal reinforcement, 256, 330–334, 1046–1047, 1060 Lower-bound plastic theorem, 22 M Map cracking, 435–436 Mat (raft) foundations, 812–813, 854 Materials, 7, 43–101, 567 choices for structures, compressive strength 1fcœ 2, 46–59, 60–61, 63–66, 86 concrete, 43–92 failure, 567 fiber-reinforced concrete, 88–89 fiber-reinforced polymer (FRP) reinforcement, 99–100 www.elsolucionario.net • 1149 high-alumina cement, 93 high-strength concrete, 49, 85–87 lightweight concrete, 49, 87 prestressing steel, 100–101 shotcrete, 92 steel reinforcement, 97, 93–99 stress–strain curves, 44–46, 67–73 volume changes, time-dependent, 7, 73–86 Mechanical splices, 424–425 Microcracking, 43–46 Mill tests, 95 Modular ratio, 428 Modulus of rupture 1fr2 test, 59–60 Mohr rupture envelope, 66–67 Mohr’s circle of computability, 297 Moment coefficient 1Cm2 for floor systems, 178–183 Moment curve relationships, 111–114 Moment-resisting frames, 981–982, 1045–1067 beam–column joints and, 1047–1049 columns in, 1059–1067 earthquake loads and, 1046–1068 flexural members in, 1045–1057 reinforcement for, 1046–1066 walls, 981–982 wind loads and, 981–982 Moments (M), 16–17, 105–111, 116, 124–130, 189, 312, 323–325, 334, 338–364, 444, 445–447, 568–573, 579–580, 603–607, 637–647, 653–667, 683–685, 714–731, 787–789, 1045 analysis of in two-way slabs, 637–641 bending, 16, 108–109 curvature and, 641–643 deflection, 568–573 distribution of, 641–647, 653–667, 683–685 equivalent factor 1Cm2, 572–573 factored design 1Mu2, 106 finite-element analysis for, 787–789 first-order 1Mo2, 568–570 flexure and, 105–107, 124–130 inertia (I), 189, 444, 445–447 1150 • Index Moments (M) (Continued) internal resisting, 16, 108–110, 1045 magnifiers for columns, 568–570, 579–580, 609 maximum, 610 minimum, 610 negative, 107 nominal 1Mn2 strength, 16–17, 105–107, 116, 124–130 nonsway 1Mns2, 602 positive, 107 second-order 1Mc2, 568–570, 603–607 shear and torsion combined with, 323–325, 339–364 shear transfer and, 714–731 slabs and, 637–647, 653–667, 683–685, 714–731 slender columns and, 568–573, 579–580, 603–607 statistical 1Mo2, 640, 647, 653–657 sway 1Ms2, 603 torsional (T), 312, 335, 338–339 transfer of, 667, 714–731 yield 1My2, 116 Mortar cracks, 43–44 Mueller-Breslau principle, 178–180 Multiaxial loads, 62–66 biaxial, 62–65 compressive strength 1fcœ 2, and, 63–65 concrete strength under, 62–66 Mohr rupture envelope for, 65–66 triaxial, 65–66 strut-and-tie model for design of, 896–901 subdivision of, 894 Nodes, 881, 889 Nominal moment 1Mn2 strength, 16–17, 105, 116, 124–130, 136–138, 146–149, 151–154, 999, 1002–1004 beam sections, 116, 124–130, 138, 146–149, 155–158 compression reinforcement and, 146–149 flexure and, 105, 116, 124–130, 136–138 load effects and, 16–17 reinforcement ratio 1r2 and, 136–138 shear walls, 999, 1002–1004 Nomographs, 592–593 Notation, 107–108, 547, 975, 1133–1139 N P Net soil pressure, 818–820 Nichols’ analysis of moments, 634, 638–641 Nodal zones, 881, 889–901 anchorages in, 895–896 extended, 890–893 forces acting on, resolution of, 895–896 hydrostatic, 889–890 strength of, 893 Pans, 494 Pattern loadings in floor systems, 176–180 Perimeter of a section, 1rcp2, 327–328 Permanent loads, 28 Pile caps, 812, 854–856 Pin-ended columns, 566–584 deflections of, 566–570 design of, 581–584 O One-way slabs, 5, 105–106, 188–191, 228–239 concrete covers for, 228–229 flexural behavior of, 105–106 flexural design of, 188–191, 228–229 floor systems and, 188–191 reinforcement of, 229–231 thickness of, 228–229 One-way walls, 975 Over-reinforced beam sections, 138 www.elsolucionario.net failure of materials and stability of, 567–568 moments for, 568–573, 579–580 sustained loads, effects of on, 567–568 symmetrically loaded, 568–570 unequal end moments of, 570–573 Planes, equivalence of shear on, 298–299 Plastic design, 21 Plastic distribution of soil pressure, 817 Plastic mechanisms, structural stability and, 14 Plastic slumping cracks, 435 Plastic-truss model, 262, 265–267 Poisson’s ratio, 73 Polar moment of inertia 1Jc2, 720–722 Ponding failure 14, 34, 453 Post-tensioning, 778–780 Pozzolans, 51 Pressure, 25, 34–36, 818–820 Prestress losses, 100 Prestressed beams, Prestressing steel, 100–101 Principal stresses, 246, 318 Probability of failure 1Pf2, 19–20 Probable moment strength 1Mpr2, 1046 Progressive collapse, 13–14, 404 Pull-out test, 370–371 Punching (two-way) shear, 695–697, 700–703, 823–824 R Radius of curvature (r), 641 Rain loads (R), 34 Rectangular footings, 836–844 Reentrant corner irregularities for seismic design, 1035 Reinforced concrete, 1–11, 13–15, 106, 111–114, 197, 268–295, 323–325, 468–472, 1040–1042 ACI building codes for, 10 analysis versus design, 106 beams, 1–4, 197, 268–295 building elements, cement and, 7–8 Index compressive strength 1fcœ of cracked, 63–65 continuity in, 468–472 design specifications for, 9, 268–270 ductility of, 1040–1042 earthquake loads and, 1040–1042 factors effecting choice of, 6–7 flexure theory for, 111–114 floor systems, 471–472 footings, frames, 469–471 joists, limit states, 13–15 mechanics of, 1–2 members, 2–6, 323–325 shear, design and analysis for, 268–295 slabs, 4–6, 197 stirrups, failure due to, 270–275 structures, 1, 468–472 torsion, subjected to, 323–325 Reinforcement, 93–99, 113, 132–151, 195–209, 229–231, 249–252, 259–261, 268, 272–275, 277–278, 281–292, 300–302, 328–330, 341–345, 367–424, 441–443, 707–713, 731–736, 820–827, 862, 963–921, 996–999, 1007–1008, 1045–1068 See also Area (A) anchorages, 272–275, 341–343, 381–394 ASTM specifications for, 93–95, 98–99 bars, 195–196, 198–203, 344–345, 373–380, 394–404, 734 beam–column joints, 953–966 beam sections, 195–220 bolsters (chairs), 197 bonds, 367–373, 374–375 code definitions for, 132–142 compression, 142–151 concentrated, 996, 998 continuity, 404–421 cracks and, 250–251, 332, 441 coupling beams, 1079 design of, 204–209, 709–711 development of, 367–381 distributed, 996 extreme layer of tension, 133 fabrication ease, 145 fatigue strength of, 96–97 fiber-reinforced polymer (FRP), 99–100 flexural, 379, 394–397, 820–822, 1047–1048 footings, 820–822 hanger, 300–302 hoops, 1041–1042, 1048–1049 inclined shear friction, 862 length, 373–381 location of (placing sequence), 195–199, 733 longitudinal, 330–334, 345, 1046–1048, 1060 minimum, 115, 203, 996–997 seismic design, 1045–1068 shear, 249–250, 397–398, 707–709, 1007–1008, 1049–1050, 1062–1063 shearheads, 708 shrinkage, 230, 442 skin (web face), 443 slabs, 229–231, 707–709, 731–736 spiral, 135 splices for, 422–424, 1047 steel, 93–99, 734 stirrups (transverse bars), 196–197, 249, 259–261, 281–292, 328–330, 341–345, 707–708 structural integrity requirements, 404–421, 440–442, 736 studs, 708–709 temperature, 230, 442 torsional, 323–325, 341–345 transverse, 1048–1050, 1060–1062 upper limits on, 136–138 walls, 996–998, 1007–1008 web, 249, 250–252, 256–257, 443 welded-wire, 97–99, 380–381 Reinforcement ratio 1r2, 132, 136–138, 256, 529–530 balanced 1rb2, 132 columns and, 529–530 longitudinal 1rw2, 256 nominal moment 1Mn2 strength and, 136–138 over-reinforced beams sections, 138 www.elsolucionario.net • 1151 Relative humidity effects on shrinkage, 73–75 Relative stiffness 1c2, 590, 593–594 Restrained columns, 584–602 Retaining (nonbearing) walls, 974–975, 980 Rigidity, see Stiffness Roof loads 1Lr2, 24, 34 Rupture, structural stability and, 13 S Safety index 1b2, 19–20 Saint Venant’s principle, 879 Sand-heap analogy, 315 Secant modulus of elasticity, 67–69 Second maximum load in columns, 502 Second-order analysis, 566–567, 603–607 Seismic design, 1033–1036, 1042–1045, 1046, 1050 ACI code for, 1042–1043 building configurations and, 1033–1037 capacity design for, 1044–1045 categories, 1033 columns, 1059–1068 lateral force-resisting systems for, 1033–1034 load and resistance factors for, 1043 plan irregularities for, 1034–1035 reinforcement for, 1045–1068 strong column–weak beam design for, 1045 structures, seismic forces on, 1037–1040 vertical irregularities for, 1036–1037 walls, 1073–1080 weight (W) for, 1038 Seismic regions, shear in, 307 Seismic response spectra, 1028–1033, 1037–1038 acceleration response, 1028–1029 coefficient 1Cs2, 1037–1038 damping effects on, 1031 displacement response, 1029–1030 ductility effects on, 1031–1032 1152 • Index Seismic response spectra (Continued) period of building for, 1029–1031 soil effects on, 1033 velocity response, 1029 Self-straining effects, 25 Self-straining forces, 37 Serviceability, 14, 427–428, 604 concrete beams, 443–451 cracks, 434–443 deflections, 443–451 elastic analysis of stresses for, 428–434 fatigue, 464 frames, 462 limit states (SLS), 14, 427–428, 451–453, 468, 604 service-load stresses for, 432–433 transformed beam sections, 428–432 vibrations, 462–463 Shake-down limit, 45 Shear (V), 182–184, 243–310, 317–322, 323–325, 338–365, 695–713, 823–824, 858–873, 1005–1016, 1038, 1039, 1045, 1049–1050 See also Failure; Friction area of flow 1A o2, 315–316, 325–326 average stress, 247–248 axially loaded members and, 303–307 B-regions (Bernoulli) of, 252–253 beam-action (one way), 695, 761–762, 823 beam sections, 243–310 coefficient 1Cv2, 182–184 column–slab connections and, 714–731 compression failure, 250–251 compression field theories for, 297–298 cracks, between, 247–248 critical section for, 279, 340–341, 697, 698–699, 703–705, 823–824 D-regions (discontinuity) of, 252–253 depth 1dv2, 248 equivalence of on planes, 298–299 floor systems, 184–188 flow (q), 249, 315–316, 326 footings, failure in, 823–824 friction, 858–869 girder design for, 302 hanger reinforcement for, 300–302 horizontal, 870–873 inclined cracking and, 250–251, 254–255 maximum, 278–279 models for, 243–310 Mohr’s circle of compatibility for, 296 moment and torsion combined with, 323, 331, 334, 339–365 moment transfer, and, 714–731 punching (two-way), 700–706, 823–824 reinforcement, 249–250, 483–486, 707, 1007–1008, 1049–1050 seismic base, 1037 seismic regions and, 307 shear friction method for, 298 smeared-crack models for, 297 stirrups for, 196–197, 251, 255–256, 259–260, 270–275, 281–285, 328–330, 707–708 story 1Vx2, 989–993 strength-reduction factor 1f2 for, 278 stresses1t2, 245–248, 312–318 strut-and-tie models for, 296 torsion, due to, 312–318 traditional ACI method for, 297 transfer, 858–873 tributary areas for, 699–700 truss model for, 261–268 two-way slabs, 695–713 whole-member design methods for, 296 Shear caps, 732–733 Shear-friction model, 861–862 Shear-force envelope, 280, 285 Shear strength 1Vc2, 256–259, 695–713, 961, 1005–1016, 1070 beam–column joints, 953–966 beam sections, 256–261 diaphragms, 1072–1073 seismic load resistance from, 1008–1009, 1050 www.elsolucionario.net shear walls, 1005–1016 two-way slabs, 695–713 Shear-wall–frame buildings, 983–984 Shear walls, 975, 980–981, 984–988, 996–1016, 1073–1080 boundary elements in, 1002–1004 coupled, 984–988, 1077–1080 flexural strength of, 999–1005 nominal moment 1Mn2 strength of, 1001, 1002–1005 reinforcement in, 996–998, 1004–1005 seismic design of, 1073–1080 shear strength 1Vc2 of, 1005–1016 strength-reduction factors 1f2 for, 999, 1076 structural behavior of, 994–995 wall assemblies and, 980–981, 1004–1005 Shearheads, 708 Shoring structures, Short columns, 499, 527–544 Shotcrete, 93 Shrinkage, 73–78, 87, 230–231, 442 basement walls, 76 calculation of, 76–78 carbonation, 74 drying, 73–74 floor slabs, 85 high-strength concrete, 87 reinforcement for slabs, 229–231 relative humidity effects on, 75–76 temperature reinforcement and, 442 Sidesway buckling, 610 Silica fume, 52 Simply supported beams, 281–289 Singly-reinforced beam sections, 114, 124–130, 138–142, 195–219 area of tension reinforcement 1A s2 for, 210 bars of reinforcement in, 198–199, 214–216 concrete cover spacing for, 198–199 deflections, dimensions for control of, 198 effective depth (d) of, 199–203 flexural analysis of, 146 flexural behavior of, 111–114 Index flexural design of, 195–242 flexural-resistance factor (R) for, 211 nominal moment 1Mn2 strength of, 128–130 rectangular compression zones, with, 195–242 reinforced concrete, construction of, 197 reinforcement of, 195–197, 203–206 strength requirements for, 203–204 unknown dimensions, design of for, 209–220 Skew bending theory, 325 Skin reinforcement, 443 Slab-beams, 669–674 Slabs, 5–6, 76–77, 105, 197–198, 228–239, 632–782, 785–811, 1098–1099 direct-design method for, 652–667 elastic analysis of, 785–789 equivalent-frame method for, 647–648, 667–689 finite-element analysis for, 787–789 flat (plates), 6, 632, 660–667, 670–672 flexural design of, 197–198, 228–239 flexure of, 105, 634–636 floor system design using, 76, 191–194, 775–778 moment-distribution factors for, 1098–1099 one-way, 5, 106, 188–194, 228–239 plate rigidity (D) of, 786–787 reinforcement for, 229–231, 774 shrinkage of, 76–77 structural analysis of, 188–194 thickness of, 785 two-way, 5, 175, 632–811 waffle, 632 yield-line analysis of, 636, 789–809 Slag, ground granulated blast-furnace, 52 Slender beams, 261–268 Slender columns, 499, 530–531, 561–629 See also Frames braced (nonsway) frames and, 589–600 buckling, 564–565, 577 deflections of, 568–569 effective length (kl) of, 564–565, 579 equilibrium states of, 563–564 flexural rigidity (EI) of, 573–575 interaction diagrams for, 568 limiting slenderness (kl /r) ratio for, 577–578 moments for, 567, 568–573, 602 pin-ended, 566–584 restrained, 584–589 size estimation of, 582 structures, 565–566 sway frames and, 600–626 torsional critical load for, 627–629 Smeared-crack models, 297 Snow loads (S), 34 Soap-film analogy, 312–315 Soil pressure, 813–820 elastic distribution of, 816–818 footing design and, 813–820 gross, 818–820 limit states and, 815 net, 818–820 plastic distribution of, 817 Solid members, torsion in, 312–315, 317 Spandrel beams, 152, 184 Span-to-depth limits, 454–461 Span-to-depth ratio (a/d), 257 Special moment-resisting frames (SMF), see Moment-resisting frames Spiral columns, 500–506, 524, 530–531, 543–544 behavior of, 501–503 design of, 543–544 requirements for, 537–544 size estimation of, 530 Spiral reinforcement, 135 Splices, 422–424, 531–535, 1048 column reinforcement using, 531–535 compression lap, 423–424 mechanical, 424 www.elsolucionario.net • 1153 seismic design and, 1047–1048 tension lap, 422–423 welded, 424 Split-cylinder 1fct2 test, 59–60 Spread footings, 4, 813–814, 820–827, 830–844 St Anthony Falls Bridge, Stability failure, 567–568 Stability index (Q), 578 Standard deviation (s), 48 Static loads, 29 Static yield strength, 96 Statically admissible structure, 22 Steel reinforcement, 97, 99, 544–546, 734 ASTM specifications for, 93–95, 98–99 columns, 544–546 corrosion of, 90–91 fatigue strength of, 96–97 hot-rolled deformed bars, 93–99 mechanical properties of, 95–96 prestressing, 100–101 required area 1A s2 for slabs, 730 yield strength of, 95 welded-wire, 97–99 Stiffness, 7, 335–336, 580, 585, 603–605, 648–650, 786–787, 1036, 1072–1073 See also Flexural stiffness (EI) beam-to-slab ratio 1af2, 648–650 diaphragm effects on load distribution, 1072–1073 importance of for structural rigidity, irregularities for seismic design, 1036 plate rigidity (D), 786–787 relative 1c2, 590, serviceability limit state, 604–605 torsional 1Kt2, 335–336 Stirrups, 197, 249, 255–256, 262–263, 265–268, 281–289, 328–330, 349, 707–708 anchorage for, 283–284, 341–343 closed, 341–343 design of, 289–292 failure of reinforced concrete beams due to, 270–275 1154 • Index Stirrups (Continued) internal forces of, 265–268 location of, 195–197 shear flow area of, 1A o2, 328–330, 341 shear reinforcement using, 249–250, 709–713 torsional reinforcement using, 335, 341–345 web reinforcement using, 249, 259–261 yielding of, 270–272 Story drift 1dmax2, 995, 1034 Story shear 1Vx2, 1039 Story torsion 1Tx2, 1039–1040 Straight-line theory, see Elastic analysis Strain-compatibility method for biaxial columns, 548 Strain limits, 511 Strength, 23–24, 58, 59–66, 96–97, 149, 203–204, 256–259, 268, 278, 503–506, 544–546, 695–713, 825–827, 893 See also Compressive strength 1fcœ 2; Flexural strength; Nominal moment 1Mn2 strength; Shear strength 1Vc2, beam sections, 203–204, 257–258 bearing, 825–827 columns, 544–546 compression reinforcement effect on, 149–150 concrete in structures, 58–59, 544–546 crushing of the web, 275, 296 design, 20–21 fatigue, 96–97 flexural, 105, 119–124, 999–1005 loads and, 59–66 nodal zones, 881–882 steel reinforcement contributions to, 544–546 structural design, 20–21 Strength-reduction factors 1f2, 16, 20–21, 27–28, 106–107, 133, 149, 159, 278, 511–512, 999, 1076 beam sections, 106–107, 142, 149, 159, 278 code definition for, 139–140 columns, 511–512 flexure, 106, 139, 149, 159 loads, 16, 20–21, 27 shear and, 278 shear walls, 999, 1076 Stress, 122–124, 245–248, 312–318, 368–371, 428–434 blocks, 122–124 bond 1m2, 367–371 elastic analysis of, 428–434 principal, 245 service-load, 432–434 shear 1t2, 245–248, 312–318 torsion, due to, 312–318 trajectories, 246 Stress–strain curves, 43–46, 67–73, 1018–1019 compression, 43–46, 67–72 concrete properties and, 43, 67–73, 1018–1019 equations for, 69–72 modified Hognestad, 69 moduli of elasticity (E), 67, 1020–1021 normal-weight concrete, 67–69, 72–73 Poisson’s ratio and, 73 tension, 72–73 wall buckling loads determined from, 1019–1022 Stress–strain relationships, 112–113, 120, 124 Strip (wall) footings, 813–814, 820–830 Strong column–weak beam design for earthquake loads, 1045 Structural analysis, 13, 188–194 Structural design, 10, 12–41, 1037–1040, 1083–1132 accuracy of calculations for, 41 ACI building code procedures, 20–28 dimensions and tolerances for, 40 economic factors for, 12, 38 handbooks and aids for, 41 inspection and, 40–41 limit states, 15 load effects and factors, 15–18, 23–37 plastic, 21 process, 12–41 www.elsolucionario.net reinforced concrete specifications for, safety, 17–20 seismic forces and, 1037–1040 seismic requirements for, 1033–1037 strength, 20–21 tables for, 1083–1132 Structural integrity, 404–421, 488–489, 736 ACI requirements for, 406–416 bending-moment diagrams for, 417–421 continuity requirements for, 405–406 cracking and, 434–443 equations of moments for, 407–416 flexural cut-off points, 416–421 slabs, 736 standard cut-off points, 421 Structures, 1–7, 12–41, 468–472, 565, 1081 beams, 1–3 building elements, continuity in, 468–472 design process for, 12–41 economic factors for, fire resistance of, forms and shoring, load effects and factors, 15–17, 23–37 material choices for, members for, 3–4, 13 precast, 1081 reinforced concrete, 1–3, 8–9, 462–463 rigidity of, safety of, 17–20 slender columns in, 565–566 stability of, 14 time-dependant volume changes in, Strut-and-tie models, 296, 879–971 compression fans in, 901 compression fields of, 902 corbels (brackets), 935–947 deep beams, 922–935 direction of struts and ties in, 901–903 Index discontinuity regions and, 879–882 equilibrium of, 904 force whirls (U-turns), 902 layout of, 903–908 load-spreading regions of, 903, 906–907 longitudinal cracking, failure by, 884–888 minimum steel content of, 907 nodal zones, 881, 889–901 nodes, 881, 889 struts, 882–888, 901–903, 907–908 T-beam flanges, 968–970 ties, 888–889, 895–896, 904–905, 907–908 Struts, 882–888, 901–903, 907–908 design of, 882–888 direction of, 904–905 strut-and-tie model layout using, 903–908 Studs, 708 Sustainable/green construction aesthetics and occupant comfort, 39 and cement industry, 40 durability factor, 39 economic impact, 39 in terms of CO2 emissions, 39–40 Sustained loads, 28–29, 144, 576 beams, compression reinforcement of, 144 characteristics of, 28–29 pin-ended columns, effects of on, 576 Sway (unbraced) frames, 469–471, 600–626 design of, 600–602, 608–626 direct P- ¢ analysis of, 608–609 flexural stiffness (El) of, 603–605 gravity loads and, 610–626 iterative P- ¢ analysis of, 605 lateral stiffness-reduction factor for, 603 moments, calculation of in, 603–607 reinforced concrete floor systems and, 471–472 second-order analysis of, 603–607 sidesway buckling, 610 slender columns and, 600–626 statics of, 600–602 wind loads and, 621–623 T T-beams, 152, 154, 468–498, 968–970 compression zone for, 152–153 continuous, design of, 468–498 effective flange width for, 153–155 flanges, 968–970 flexural analysis of, 159–163 strut-and-tie model for, 968–970 T joints, 957 Tangent modulus of elasticity, 67 Tapered beams, 302–303 Temperature, 85, 91–92, 236–237, 442–443 cold, 92 concrete, effects of on, 85, 91–92 high (fire), 91 reinforcement, 236–237, 442 shrinkage and, 442 slabs, effects of on, 236–237, 442 thermal expansion and contraction, 85 Tensile-controlled limits, 511, 822 Tensile strength, 7, 59–65, 72–73, 256 compressive strength 1fcœ and, 60–61 concrete, 59–61, 71–72, 256 low, importance of, modulus of rupture 1fr2, 59–60 split-cylinder 1fct2, 60 standard tests for, 59–60 stress–strain curves for, 72–73 Tension, 72–73, 107, 113, 117–119, 133, 195, 246, 305 area of reinforcement 1A s2, 107, 119, 129–131, 137–138, 204 axial, 305 extreme layer of reinforcement, 133 singly-reinforced beam sections, 204 stress–strain curves, 72–73 Tension chord, failure of, 275–276 www.elsolucionario.net • 1155 Tension-controlled beam sections, 132–142 Tension-controlled limit (TCL), 134–136 Tension lap splices, 422–423 Tests for concrete, 45, 55–59 compressive strength 1fcœ 2, 47, 56–59 core, 55–59 modulus of rupture 1fr2, 60–61 split-cylinder 1fct2, 60 standard, 46, 59–60 tensile strength, 59–65 Thermal expansion and contraction of concrete, 85 Thin-walled tube/plastic space truss design method, 325–339 hollow members, 328 shear flow area 1A o2 of for, 330–331 solid members, 326–327 Thin-walled tube theory, 317–318 Threshold temperature, 54 Tied columns, 500, 501–503, 530, 535–537, 539–543 behavior of, 501–503 design of, 539–543 requirements for, 535–537 size estimation of, 530 Ties, 149, 888–889, 895–896, 903–908, 998 anchorage of in nodal zone, 895–896 design of, 888–889 direction of, 904–906 doubly-reinforced beam sections and, 148 strut-and-tie model layout using, 895–896, 903–908 vertical reinforcement, as, 998 Tilt-up walls, 975, 980 Torsion, 312–365, 493, 1035, 1039–1040 ACI code design for, 345–364 anchorages for, 341–343 circulatory, 318–322 compatibility, 336–338, 493 crack width limit for, 332–333 critical section for, 340–341 cross sections for, 312–313, 340 1156 • Index Torsion (Continued) earthquake loads and, 1035, 1039–1040 equilibrium, 336–338 girder design and, 493–494 hollow members, 315–317, 328 irregularities for seismic design, 1034–1035 moment combined with, 334 principal stresses due to, 318 pure, 323 reinforced concrete members subjected to, 323–325 reinforcement, 330–334, 341–345 shear and moment combined with, 323–325, 334–336 shearing stresses due to, 312–318 skew bending theory for, 325 soap-film analogy for, 312–313 solid members, 312–315, 326–327 stirrups, area of for, 328–330 story 1Tx2, 1039–1040 thin-walled tube/plastic space truss, design method for, 325–339 thin-walled tube theory for, 317–318 threshold, 343 warping, 318–322 web crushing limit for, 333–334 Torsional critical load, 627–629 Torsional members and columns, 674–683 Torsional moments (T), 312, 338–339 Torsional stiffness 1Kt2, 337–338 Transfer beam, 983 Transfer width, 716–717 Transformed beam sections, 429–432 Transition failures, 511 Transition-zone section, 134–135 Transverse reinforcement, 494, 1048–1050, 1060–1062 See also Hoops; Stirrups confinement, 1048–1049, 1060–1062 index 1Ktr2, 379 shear, 1049–1050, 1062 Triaxial loads, 65–66 Tributary area 1A T2, 32, 176–177, 699 Trump International Hotel and Tower, Truss (bent-up) bars, 197 Truss models, 261–268 analogy, 263–265 compression fans for, 263 compression field region, 263, 267 crushing strength and, 268 failure in shear and, 261–268 internal forces in, 265–268 plastic, 262, 265–268 slender beams, 261–268 Two-way slabs, 5, 105, 632–782 beams in two directions, 762–772 capitals for, 632, 732 columns, supported by, 645–647, 651, 653–667 construction loads on, 772 deflections in, 773–778 design of, 647–652, 736–762 direct-design method for, 652–667 discontinuous corners of, 806–807 drop panels for, 632, 731–732 edge beams for, 645, 649–650 elastic analysis of, 785–789 equivalent-frame methods for, 652–666, 667–689 fan-shaped yield patterns of, 807–810 finite-element analysis for, 787–789 flexural failure in, 115, 634–636 minimum thickness of, 650–652 moments in, 635–636, 637–647, 653–667, 714–731 Nichols’ analysis of moments for, 634, 638–641 post-tensioning, use of, 778–780 radius of curvature (r) for, 641 reinforcement of, 707–713, 726–731 shear and moment transfer in, 714–731 shear caps for, 732–733 shear strength of, 695–713 walls, supported by, 643–645 without beams, 736–762 www.elsolucionario.net yield-line analysis of, 636, 789–810 Two-way walls, 975 U Ultimate limit states, 13–14, 603–604 Unbraced frames, see Sway frames Uncracked-elastic range, 114 Under-reinforced beam sections, 112, 116, 124–130 Uniqueness plastic theorem, 22 Unsymmetrical beam sections, 167–168 Unsymmetrical columns, 525 Upper-bound plastic theorem, 22 V Variable loads, 28 Velocity pressure (q), 35–36 Vertical deflections, 462 Vertical loads, 838–839 Vibrations, 14, 462–463 Virtual work method for yield-line analysis, 792–795 Volume changes of concrete, 7, 73–85 W Waffle slabs, 632 Walls, 643–645, 973–1025, 1073–1080 assemblies, 975, 980 axially loaded, 1005, 1016–1025 bearing, 976–979 buckling of, 1016–1017 building floor plans for, 989 cantilever retaining, 975 concrete properties of, 1018–1022 critical loads for, 1018–1022 design of, 989–998 diaphragms for, 989 floor systems, load transfer through, 998 Index foundations for, 974–975 lateral load-resisting systems for, 954, 981–983 minimum thickness of, 996 moment-resisting frames, 981–982 one-way, 975 reinforcement in, 978–979, 996–998 retaining (nonbearing), 975, 980 seismic design of, 1073–1080 seismic load resistance, 1008–1009 shear, 973, 974, 975, 980, 983–988, 1073–1080 shear-wall–frame buildings, 982–983 size requirements of, 994–996 slabs supported by, 643–645 story drift limits for, 995–996 story forces (shears) and, 989–993 ties for vertical reinforcement of, 996 tilt-up, 975, 980 two-way, 975 Walraven model, 865–867 Warping torsion, 318–322 Water/cement (w /c) ratio, 51 Water quality and concrete strength, 53 Weak story for seismic design, 1036 Web-shear cracking in walls, 1007 Web width 1bw2, 115, 202, 206 Webs, 250, 259–261, 268, 270–277, 333, 443 crushing strength of, 268, 333 minimum specifications for, 277–278 reinforcement, 255, 256–261, 268, 270–277, 443 stirrups for, 249, 255–256 Wedge anchors, 100 Weight (mass) for seismic design, 1036 Welded splices, 424 Welded-wire reinforcement, 97–99, 380–381, 1086 ASTM specifications for, 98 development length of, 373–381 Whitney stress block, 122–124 Whole-member design methods, 296 Wind loads, 26, 34–36, 621–623, 995–996, 1010–1013 design pressure (p) for, 35 directionality factor 1Kd2 for, 35 external pressure coefficient 1Cp2 for, 36 load factors for, 25 moment-resisting frames for, 981–982 sway frame design for, 603–607 velocity pressure (q) for, 35–36 walls, load-resisting systems for, 981–983 Wind turbine foundation, www.elsolucionario.net • 1157 Working (service) loads, 21 Working-stress design, 21 Y Yield-line analysis of slabs, 636, 789–810 applications of, 796–806 axes location for, 790–792 concentrated loads and, 807–810 criterion for, 789–790 discontinuous corners and, 806–807 equilibrium method for, 792 failure in flexure from, 636 virtual work method for, 792–795 yield-line patterns, 790–792, 806–810 Yield moment 1My2, 116 Yield points, 116–117 Yielding, 112, 116, 270–272 ductility and, 117 flexural behavior and, 111–114 stirrups, 270–272 under-reinforced beam sections, 112, 116 Z Zero tension, 511 ... Data Wight, James K Reinforced concrete : mechanics and design / James K Wight, F.E Richart, Jr., James G Macgregor – 6th ed p cm Rev ed of: Reinforced concrete / James G MacGregor, James K Wight. .. CHAPTER Reinforced Concrete Structures Mechanics of Reinforced Concrete Reinforced Concrete Members Factors Affecting Choice of Reinforced Concrete for a Structure Historical Development of Concrete. .. of Reinforced Concrete: Mechanics and Design A multitiered approach makes Reinforced Concrete: Mechanics and Design an outstanding textbook for a variety of university courses on reinforced concrete