Structural analysis by kassimali

Licensed to: iChapters User Structural Analysis THIRD EDITION Aslam Kassimali Southern Illinois University—Carbondale Australia  Canada  Mexico  Singapore  Spain  United Kingdom  United States Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User Structural Analysis, Third Edition by Aslam Kassimali Associate Vice-President and Editorial Director: Evelyn Veitch Publisher: Bill Stenquist Sales and Marketing Manager: John More Developmental Editor: Kamilah Reid Burrell Production Service: RPK Editorial Services Cover Design: Vernon Boes Copy Editor: Shelly Gerger-Knechtl Compositor: Asco Typesetters Indexer: Aslam Kassimali Printer: Quebecor World Proofing: Jackie Twoney Production Manager: Renate McCloy Creative Director: Angela Cluer COPYRIGHT 2005 by Nelson, a division of Thomson Canada Limited Printed in the United States 07 06 05 04 For more information contact Nelson, 1120 Birchmount Road, Toronto, Ontario, Canada, M1K 5G4 Or you can visit our internet site at http://www.nelson.com Library of Congress Control Number: 2003113087 ISBN 0-534-39168-0 ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced, transcribed, or used in any form or by any means—graphic, electronic, or mechanical, including photocopying, recording, taping, Web distribution, or information storage and retrieval systems—without the written permission of the publisher For permission to use material from this text or product, submit a request online at www.thomsonrights.com Every effort has been made to trace ownership of all copyrighted material and to secure permission from copyright holders In the event of any question arising as to the use of any material, we will be pleased to make the necessary corrections in future printings North America Nelson 1120 Birchmount Road Toronto, Ontario M1K 5G4 Canada Asia Thomson Learning Shenton Way #01-01 UIC Building Singapore 068808 Australia/New Zealand Thomson Learning 102 Dodds Street Southbank, Victoria Australia 3006 Europe/Middle East/Africa Thomson Learning High Holborn House 50/51 Bedford Row London WC1R 4LR United Kingdom Latin America Thomson Learning Seneca, 53 Colonia Polanco 11560 Mexico D.F Mexico Spain Paraninfo Calle/Magallanes, 25 28015 Madrid, Spain Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User IN MEMORY OF AMI Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User Contents Preface PART ONE INTRODUCTION TO STRUCTURAL ANALYSIS AND LOADS Introduction to Structural Analysis 1.1 1.2 1.3 1.4 xiii Historical Background Role of Structural Analysis in Structural Engineering Projects Classification of Structures Analytical Models 12 Summary 16 Loads on Structures 17 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 Dead Loads 18 Live Loads 21 Impact 24 Wind Loads 24 Snow Loads 32 Earthquake Loads 35 Hydrostatic and Soil Pressures 37 Thermal and Other EÔects 37 Load Combinations 37 v Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User vi Contents Summary 38 Problems 39 PART TWO ANALYSIS OF STATICALLY DETERMINATE STRUCTURES Equilibrium and Support Reactions 43 3.1 3.2 3.3 3.4 3.5 3.6 3.7 Equilibrium of Structures 43 External and Internal Forces 46 Types of Supports for Plane Structures 47 Static Determinacy, Indeterminacy, and Instability Computation of Reactions 60 Principle of Superposition 78 Reactions of Simply Supported Structures Using Proportions 78 Summary 80 Problems 82 47 Plane and Space Trusses 89 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 41 Assumptions for Analysis of Trusses 91 Arrangement of Members of Plane Trusses—Internal Stability 95 Equations of Condition for Plane Trusses 100 Static Determinacy, Indeterminacy, and Instability of Plane Trusses 101 Analysis of Plane Trusses by the Method of Joints 106 Analysis of Plane Trusses by the Method of Sections 122 Analysis of Compound Trusses 129 Complex Trusses 134 Space Trusses 135 Summary 145 Problems 146 Beams and Frames: Shear and Bending Moment 161 5.1 5.2 Axial Force, Shear, and Bending Moment 162 Shear and Bending Moment Diagrams 168 Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User Contents 5.3 5.4 5.5 5.6 6.2 6.3 6.4 6.5 6.6 DiÔerential Equation for Beam Deection 229 Direct Integration Method 232 Superposition Method 235 Moment-Area Method 236 Bending Moment Diagrams by Parts 250 Conjugate-Beam Method 255 Summary 271 Problems 271 Deflections of Trusses, Beams, and Frames: Work–Energy Methods 277 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 Qualitative Deflected Shapes 173 Relationships between Loads, Shears, and Bending Moments 175 Static Determinacy, Indeterminacy and Instability of Plane Frames 196 Analysis of Plane Frames 202 Summary 217 Problems 219 Deflections of Beams: Geometric Methods 228 6.1 vii Work 278 Principle of Virtual Work 280 Deflections of Trusses by the Virtual Work Method 284 Deflections of Beams by the Virtual Work Method 295 Deflections of Frames by the Virtual Work Method 304 Conservation of Energy and Strain Energy 314 Castigliano’s Second Theorem 318 Betti’s Law and Maxwell’s Law of Reciprocal Deflections Summary 328 Problems 330 Influence Lines 339 8.1 8.2 Influence Lines for Beams and Frames by Equilibrium Method 340 Mueller-Breslau’s Principle and Qualitative Influence Lines 355 Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part 327 Licensed to: iChapters User viii Contents 8.3 8.4 8.5 9.2 9.3 9.4 Response at a Particular Location Due to a Single Moving Concentrated Load 403 Response at a Particular Location Due to a Uniformly Distributed Live Load 405 Response at a Particular Location Due to a Series of Moving Concentrated Loads 410 Absolute Maximum Response 417 Summary 423 Problems 424 Analysis of Symmetric Structures 427 10.1 10.2 10.3 10.4 PART THREE 11 369 Application of Influence Lines 403 9.1 10 Influence Lines for Girders with Floor Systems Influence Lines for Trusses 379 Influence Lines for Deflections 392 Summary 395 Problems 395 Symmetric Structures 428 Symmetric and Antisymmetric Components of Loadings Behavior of Symmetric Structures under Symmetric and Antisymmetric Loadings 445 Procedure for Analysis of Symmetric Structures 449 Summary 457 Problems 458 ANALYSIS OF STATICALLY INDETERMINATE STRUCTURES 434 461 Introduction to Statically Indeterminate Structures 463 11.1 11.2 Advantages and Disadvantages of Indeterminate Structures 464 Analysis of Indeterminate Structures 467 Summary 472 Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User Contents 12 Approximate Analysis of Rectangular Building Frames 473 12.1 12.2 12.3 12.4 13 13.2 13.3 13.4 14.2 14.3 Derivation of Three-Moment Equation 589 Application of Three-Moment Equation 594 Method of Least Work 601 Summary 608 Problems 609 Influence Lines for Statically Indeterminate Structures 611 15.1 15.2 16 Structures with Single Degree of Indeterminacy 511 Internal Forces and Moments as Redundants 533 Structures with Multiple Degrees of Indeterminacy 546 Support Settlements, Temperature Changes and Fabrication Errors 570 Summary 579 Problems 580 Three-Moment Equation and the Method of Least Work 588 14.1 15 Assumptions for Approximate Analysis 474 Analysis for Vertical Loads 477 Analysis for Lateral Loads—Portal Method 483 Analysis for Lateral Loads—Cantilever Method 499 Summary 506 Problems 507 Method of Consistent Deformations—Force Method 510 13.1 14 ix Influence Lines for Beams and Trusses 612 Qualitative Influence Lines by Muller-Breslau’s Principle Summary 634 Problems 634 629 Slope-Deflection Method 637 16.1 16.2 16.3 Slope-Deflection Equations 638 Basic Concept of the Slope-Deflection Method Analysis of Continuous Beams 653 646 Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User x Contents 16.4 16.5 17 Moment-Distribution Method 709 17.1 17.2 17.3 17.4 17.5 18 Analysis of Frames without Sidesway 675 Analysis of Frames with Sidesway 683 Summary 704 Problems 704 Definitions and Terminology 710 Basic Concept of the Moment-Distribution Method Analysis of Continuous Beams 727 Analysis of Frames without Sidesway 743 Analysis of Frames with Sidesway 746 Summary 763 Problems 764 719 Introduction to Matrix Structural Analysis 769 18.1 18.2 18.3 18.4 18.5 18.6 Analytical Model 770 Member StiÔness Relations in Local Coordinates 774 Coordinate Transformations 782 Member StiÔness Relations in Global Coordinates 788 Structure StiÔness Relations 789 Procedure for Analysis 797 Summary 815 Problems 816 Appendix A Areas and Centroids of Geometric Shapes 818 Appendix B Review of Matrix Algebra 821 B.1 B.2 B.3 B.4 Definition of a Matrix 821 Types of Matrices 822 Matrix Operations 824 Solution of Simultaneous Equations by the Gauss-Jordan Method 831 Problems 835 Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User 842 APPENDIX C Computer Software FIG C.8 Member Data Screen (b) the end joint, (c) the material number, and (d) the cross-sectional property set number (Fig C.8) For frames and beams, the member releases option can be used to define any hinges at the member ends The origin of the local coordinate system for a member is located at the beginning of the member, with the x axis directed from the beginning joint to the end joint The positive direction of the local y axis is defined by the right-hand rule, with the z axis pointing out of the plane of the page A plot of the structure appears on the screen, which can be used to verify that the geometry of the structure have been entered correctly Joint Loads When analyzing a frame, enter for each joint that is loaded, the joint number, the forces in the global X and Y directions, and the moment (Fig C.9) In the case of a beam, input only the force in the Y direction and the moment; whereas, for a truss, input only the forces in the X and Y directions Since the software does not consider member concentrated loads, frame and beam members subjected to such loads must be subdivided into elements (i.e., smaller members) connected together by rigid joints at the locations of the concentrated loads, for the purpose of analysis Uniformly Distributed Loads on Frame and Beam Members For each member subjected to uniformly distributed loading, enter the member number and the load intensity (w), as shown in Fig C.10 Note that Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User Inputting Data FIG C.9 Joint Loads Screen FIG C.10 Member Loads Screen Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part 843 Licensed to: iChapters User 844 APPENDIX C Computer Software the uniformly distributed load, w, is considered to be positive if it acts in the direction opposite to the member local y axis Support Settlements, Temperature Changes and Fabrication Errors These eÔects can be input in a manner similar to that for the joint and member loads RESULTS OF THE ANALYSIS Once all the necessary data have been entered, click the menu title Analysis of the main screen to analyze the structure (Fig C.11) The software will automatically compute the joint displacements, member end forces, and support reactions by using the matrix stiÔness (displacement) method described in Chapter 18 The results of the analysis are displayed on the screen The input data as well as the results of the analysis can be printed by clicking on the menu title Project and then clicking on the menu item Print, of the main screen, as shown in Fig C.12 FIG C.11 Main Screen Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User Results of the Analysis FIG 845 C.12 Results of the Analysis Example C.1 Analyze the two-story frame shown in Fig C.13(a) using the computer software FIG C.13 continued Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User 846 APPENDIX C Computer Software Solution This frame was previously analyzed in Example 16.12 by the slope-deflection method, which takes into account only the bending deformations of structures The analytical model of the frame is shown in Fig C.13(b), and the input data are shown on the screen displays given in Figs C.3 through C.12 The computer printout, which contains the input data and the results of the analysis, is shown in Fig C.14 Note that the results of the computerized analysis are in agreement with those determined previously by the slope-deflection method FIG C.14 Computer Printout for Two-Story Frame Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User Results of the Analysis FIG 847 C.14 (contd.) continued Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User 848 APPENDIX C Computer Software FIG C.14 (contd.) Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User Problems 849 PROBLEMS C.1 and C.2 Using the computer software, determine the smallest cross-sectional area A for the members of the trusses shown in parts (a) through (c) of Figs PC.1 and PC.2, so that the maximum vertical deflection does not exceed the limit of 1/360 of the span length (i.e., D max a L=360) FIG FIG PC.1 PC.2 C.3 Using the computer software, determine the smallest moment of inertia I required for the frame shown, so that the horizontal deflection of its top right joint does not exceed 1.33 inches Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User 850 FIG APPENDIX C Computer Software PC.3 Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User BIBLIOGRAPHY ASCE Standard Minimum Design Loads for Buildings and Other Structures (2003) SEI/ASCE 7-02, American Society of Civil Engineers, Virginia Arbabi, F (1991) Structural Analysis and Behavior McGraw-Hill, New York Bathe, K.J., and Wilson, E.L (1976) Numerical Methods in Finite Element Analysis Prentice Hall, Englewood CliÔs, N.J Beer, F.P., and Johnston, E.R., Jr (1981) Mechanics of Materials McGraw-Hill, New York Betti, E (1872) Il Nuovo Cimento Series 2, Vols and Boggs, R.G (1984) Elementary Structural Analysis, Holt, Rinehart & Winston, New York Chajes, A (1990) Structural Analysis, 2nd ed Prentice Hall, Englewood CliÔs, N.J Colloquim on History of Structures (1982) Proceedings, International Association for Bridge and Structural Engineering, Cambridge, England 13 Hibbler, R.C (1990) Structural Analysis, 2nd ed Macmillan, New York 14 Holzer, S.M (1985) Computer Analysis of Structures Elsevier Science, New York 15 International Building Code (2003) International Code Council, Falls Church, Virginia 16 Kassimali, A (1999) Matrix Analysis of Structures Brooks/Cole, Pacific Grove, California 17 Kennedy, J.B., and Madugula, M.K.S (1990) Elastic Analysis of Structures: Classical and Matrix Methods Harper & Row, New York 18 Laible, J.P (1985) Structural Analysis Holt, Rinehart & Winston, New York 19 Langhaar, H.L (1962) Energy Methods in Applied Mechanics Wiley, New York 20 Laursen, H.A (1988) Structural Analysis, 3rd ed McGraw-Hill, New York Cross, H (1930) ‘‘Analysis of Continuous Frames by Distributing Fixed-End Moments.’’ Proceedings of the American Society of Civil Engineers 56, 919–928 21 Leet, K.M (1988) Fundamentals of Structural Analysis Macmillan, New York 10 Elias, Z.M (1986) Theory and Methods of Structural Analysis Wiley, New York 22 McCormac, J (1984) Structural Analysis, 4th ed Harper & Row, New York 11 Gere, J.M., and Weaver, W., Jr (1965) Matrix Algebra for Engineers Van Nostrand Reinhold, New York 23 McCormac, J., and Elling, R.E (1988) Structural Analysis: A Classical and Matrix Approach Harper & Row, New York 12 Glockner, P.G (1973) ‘‘Symmetry in Structural Mechanics.’’ Journal of the Structural Division, ASCE 99, 71– 89 24 McGuire, W., and Gallagher, R.H (1979) Matrix Structural Analysis Wiley, New York 851 Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User 852 Bibliography 25 Maney, G.A (1915) Studies in Engineering, Bulletin University of Minnesota, Minneapolis 34 Smith, J.C (1988) Structural Analysis Harper & Row, New York 26 Manual for Railway Engineering (2003) American Railway Engineering and Maintenance of Way Association, Maryland 35 Spillers, W.R (1985) Introduction to Structures Ellis Horwood, West Sussex, England 27 Maxwell, J.C (1864) On the Calculations of the Equilibrium and StiÔness of Frames.’’ Philosophical Magazine 27, 294–299 28 Noble, B (1969) Applied Linear Algebra Prentice Hall, Englewood CliÔs, N.J 29 Norris, C.H., Wilbur, J.B., and Utku, S (1976) Elementary Structural Analysis, 3rd ed McGraw-Hill, New York 30 Parcel, J.H., and Moorman, R.B.B (1955) Analysis of Statically Indeterminate Structures Wiley, New York 31 Petroski, H (1985) To Engineer Is Human—The Role of Failure in Successful Design St Martin’s Press, New York 32 Popov, E.P (1968) Introduction to Mechanics of Solids Prentice Hall, Englewood CliÔs, N.J 33 Sack, R.L (1989) Matrix Structural Analysis PWSKENT, Boston 36 Standard Specifications for Highway Bridges, 17th ed (2002) American Association of State Highway and Transportation O‰cials, Washington, D.C 37 Tartaglione, L.C (1991) Structural Analysis McGrawHill, New York 38 Tezcan, S.S (1963) Discussion of Simplied Formulation of StiÔness Matrices.’’ by P.M Wright Journal of the Structural Division, ASCE 89(6), 445–449 39 Turner, J.J.; Clough, R.W.; Martin, H.C.; and Topp, L.J (1956) StiÔness and Deection Analysis of Complex Structures. Journal of Aeronautical Sciences 23(9), 805– 823 40 Wang, C.K (1983) Intermediate Structural Analysis McGraw-Hill, New York 41 West, H.H (1989) Analysis of Structures: An Integration of Classical and Modern Methods, 2nd ed Wiley, New York Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User Index Absolute maximum response, 417–423 American Association of State Highway and Transportation O‰cials (AASHTO), 22 American Institute of Steel Construction, 236 American Railway Engineering and Maintenance of Way Association (AREMA), 23 American Society of Civil Engineers (ASCE), 17 Analysis, Analytical model, 12–16, 770–774 Antisymmetric loads, 434–458 Approximate analysis, 473–507 assumptions for, 474–477 cantilever method, 499–506 lateral loads, 483–506 portal method, 483–499 vertical loads, 477–482 Arch, 9–10 three-hinged, 70, 119–122 Areas and centroids, 818–820 Argyris, J H., Axial force, 162–167 diagrams, 204–217 sign convention, 164–165 Baltimore truss, 92, 96 Beam-column, Beam deflections, 228–271, 295–304, 318– 327 Castigliano’s second theorem, 318327 conjugate beam method, 255270 diÔerential equation for, 231 direct integration, 232–235 influence lines, 392–394 moment-area method, 236–249 superposition, 235–236 virtual work method, 295–304 Beams, 11, 161–196 conjugate, 255 continuous, 653–674, 727–743, 780–781 fixed, 642 floor, 13, 369 inuence lines, 339395 member stiÔness, 780781 nonprismatic, 754757 Beam sign convention, 163–165 Bending moment, 162–168 diagrams, 168–173, 202–217, 250–254, 537 relation to shear force, 175178 sign convention, 163165 Bending stiÔness, 710–715 Bernoulli, John, 5, 280 Bernoulli-Euler beam equation, 231 Betti, E., 327 Betti’s law, 327–328 Bridge: framing, 13–14 live loads, 21–24 suspension, 8–9 truss, 10, 92 Building codes, 17–18 Building live loads, 21–22 Cable, 8–9 Cantilever method, 499–506 Carryover factor, 713 Carryover moment, 713 Castigliano, Alberto, 5, 318 Castigliano’s second theorem, 318–327 Centroids, 818–820 Checkerboard load pattern, 633 Clapeyron, B P., Clough, R W., Code number technique, 795 Column, matrix, 822 Compatibility conditions, 463, 467–471 Compatibility equations, 546–549 Complex trusses, 134–135 Compound trusses, 97, 129–134 Computer software, 837–850 input data, 838–844 results, 844 Concurrent force systems, 45–46 Condition equations, 54–60 frames, 198–200 trusses, 100–101 Conjugate beam, 255 method, 255–270, 392–393 Connections, 14–16 hinged, 14–16 rigid, 14–16 Conservation of energy, 314 Consistent deformation method, 510–580 Construction materials, 19 Continuous beams, 653–674, 727–743, 780–781 Cooper loadings, 23 Coordinate systems, 771–772 Coordinate transformations, 782–787 Cross, Hardy, 5, 709 Dead loads, 18–20 de Coulomb, C A., Deflected structure, 173–174 Deflections: of beams, see Beam deflections of frames, see Frame deflections geometric methods, 228–271 influence lines, 392–394 of trusses, see Truss deflections work-energy methods, 277–330 Deformations, 228 Degree: of indeterminacy, 53, 103, 196–202, 474– 475, 510–511 of kinematic indeterminacy, 648 Degrees of freedom, 648, 772–774 861 Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User 862 Index Determinacy, 47–58, 101–104, 138, 196– 202 Diagonal matrix, 823 Direct integration method, 232235 Direct stiÔness method, 794 Displacement methods, 471472, 637817 matrix stiÔness, 769817 moment-distribution, 709768 slope-deection, 637708 Distributed moments, 720 Distribution factors, 715–718 Earthquake loads, 35–37 Elastic curve, 173–174, 229 Energy, 314 strain, 314–317 Equations of condition, 54–60 frames, 198–200 trusses, 100–101 Equilibrium, 43–46 equations of plane structures, 44–46 equations of space structures, 44 Euler, Leonhard, External forces, 46 Fabrication errors, 285–286, 466, 570–579 Fink truss, 93, 96, 112–113, 132–134 Fixed beams, 642 Fixed-end forces, 778 Fixed-end moments, 559, 642–645, 718– 719 Flexibility coe‰cients, 328, 513, 548 Flexibility methods, 471–472, 510–610 Flexural rigidity, 232 Floor beam, 14, 369 Force: applied, 46 axial, 94 compressive, 94 external, 46 internal, 46 reaction, 46 tensile, 94 Force methods, 471–472, 510–610 consistent deformations, 510–580 least work, 601–608 three-moment equation, 589–601 Frame deflections, 304–314, 318–327 Castigliano’s second theorem, 318–327 virtual work method, 304–314 Framed structures, 11 Frames, 11, 196–217 approximate analysis, 473–507 degree of static indeterminacy, 196–202 equations of condition, 198–200 inuence lines, 340355 member stiÔness, 774780 multistory, 690, 699703, 762763 portal, 483 statically determinate, 202–217 statically indeterminate, 510–580, 675– 703, 743–763 static determinacy, 196–202 without sidesway, 675–683, 743–745 with sidesway, 683–703, 746–763 Free-body diagram, 60–61, 113–114, 123 Galilei, Galileo, Gauss-Jordan elimination method, 831–835 Geometric instability, 54 Geometric stability, 54 Global coordinate system, 771 Greene, Charles E., 5, 236 Gusset plate, 10 Highway bridge loadings, 22–24 Hooke, Robert, Howe truss, 92, 93 Hydrostatic pressure, 37 Impact, 24 Inflection points, 171 Influence lines, 339–395, 611–636 application of, 403–424 for beams, 340–369, 611–636 for deflections, 392–394 envelopes, 417–419 for frames, 340–355, 632–633 for girders with floor systems, 369–379 moving concentrated loads, 410–417 Muller-Breslau principle, 355–360, 613 qualitative, 360, 629–633 for statically determinate structures, 339– 395 for statically indeterminate structures, 611–636 for trusses, 379–391, 611–636 uniformly distributed live loads, 405–410, 629–633 Internal forces, 46 Internal stability, 47–50 trusses, 95–98 International Building Code, 18 Inverse of matrix, 828–829, 834–835 Joint: ball-and-socket, 91 hinged, 1416 rigid, 1416 stiÔness, 716 Kelsey, S., Kinematic determinacy, 648 King Post truss, 93 K truss, 92, 127–128 Line diagram, 13–14 Live loads, 21–24 bridge, 22–24 building, 21–22 Livesley, R K., Loads, 17–40 antisymmetric, 434–458 bridge, live, 22–24 building, live, 21–22 combinations, 37–38 dead, 18–20 earthquake, 35–37 environmental, 17 impact, 24 lateral, 483–506 live, 21–24 moving, 339–340, 403–424 seismic, see Earthquake loads snow, 32–35 symmetric, 434–458 vertical, 477–482 wind, 24–32 Local coordinate system, 771–772 Maney, George A., 5, 637 Martin, H C., Matrix, 821–836 addition and subtraction, 824 definition, 821–822 equality, 824 inverse, 828–829, 834–835 multiplication, 825–828 operations, 824–831 order, 822 partitioning, 830–831 transpose, 829–830 types, 822–824 Matrix stiÔness method, 769817 analytical model, 770774 computer software, 837850 coordinate systems, 771772 degrees of freedom, 772774 member stiÔness, 774789 procedure for analysis, 797815 structure stiÔness, 789797 Matrix structural analysis, 769–817 Maxwell, James C., 5, 327, 510 Maxwell’s law of reciprocal deflections, 327–328, 392 Member end forces, 197 Member force-deformation relations, 467 471 Member stiÔness matrices, 774789 in global coordinates, 788–789 in local coordinates, 774–781 Method: cantilever, 499–506 conjugate-beam, 255–270, 393 consistent deformations, 510–580 Gauss-Jordan, 831–835 joints, 106–122, 138–140 least work, 601608 matrix stiÔness, 769817 moment-distribution, 709768 portal, 483499 sections, 122–128, 140–141, 168 slope-deflection, 637–708 Mohr, Otto, 5, 255 Moment: bending, 162–168 Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Licensed to: iChapters User Index Moment (cont.) carryover, 713 diagrams, 168–173, 178–196, 202–217, 250–254, 537 fixed-end, 559, 642–645, 718–719 Moment-area method, 236–249 Moment diagrams, 168–173, 250–254 construction, 178–196, 202–217 by parts, 250–254 by simple-beam parts, 537 for statically indeterminate structures, 195–196 Moment distribution method, 709–768 basic concept, 719–727 for continuous beams, 727–743 definitions and terminology, 710–719 for frames without sidesway, 743–745 for frames with sidesway, 746–763 sign convention, 710 Moving loads, 339–340, 403–424 Muller-Breslau, Heinrich, 5, 355 Muller-Breslau principle, 355–360, 613 for statically determinate structures, 355– 360 for statically indeterminate structures, 629–633 Multistory frames, 690, 699–703, 762–763 Navier, L M., Newton, Isaac, Nonprismatic beam, 754–757 Null matrix, 824 Order of matrix, 822 Parker truss, 92 Plane structure, 13–15 Plane truss, 89–135 Point of inflection, 171 Portal method, 483–499 Pratt truss, 92, 93 Primary structure, 510 Principle: conservation of energy, 314 least work, 602 superposition, 78, 404, 411 virtual displacements for rigid bodies, 280–281 virtual forces for deformable bodies, 282–284 virtual work, 280 Purlin, 91 Qualitative deflected shapes, 173–174 Qualitative influence lines, 360, 629–633 Reactions, 47 for plane structures, 47–49 for space trusses, 136–138 using proportions, 78–79 Redundancies, 464–466 Redundants, 199, 510 Reflection, 428–429 Roof truss, 91, 93 Row matrix, 822 Sections, method of, 122–128, 140–141 Settlements, see Support settlements Shear diagrams, 168–173 construction, 178–196 for statically indeterminate structures, 195–196 Shear force, 162–168 diagrams, 168–173, 178–180, 202–217 relation to load, 175–178 sign convention, 163–165 Sidesway analysis, 683–703, 746–763 Simple trusses, 96, 136 Simultaneous equations, 831–835 Singularity functions, 232 Slabs, 11, 19–20 Slope deflection equations, 638–646 Slope deflection method, 637–708 for continuous beams, 653–674 for frames without sidesway, 675–683 for frames with sidesway, 683–703 sign convention, 638 Snow loads, 32–35 Soil pressure, 37 Space structures, 13 Space trusses, 135–145 Square matrix, 822–823 Stability, 47–50, 54, 95–100 Statically determinate structures, 41 Statically indeterminate structures, 463–472 advantages and disadvantages, 464–467 analysis, 469–471, 510–610, 637–817 influence lines, 611–636 methods of analysis, 471–472 Static determinacy, 47–58 external for plane structures, 50–54 of frames, 196–202 of internally stable structures, 50–54 of internally unstable structures, 54–58 of plane trusses, 101–106 of space trusses, 138 Static indeterminacy, 47–58 external for plane structures, 50–58 of frames, 196202 of trusses, 101106, 138 Static instability, 4758 StiÔness: bending, 710–715 coe‰cients, 777 joint, 716 matrices, 769–817 member, 711 methods, 471472, 637817 StiÔness coecients, 777 Strain energy, 314317 of beams, 316 of frames, 317 of trusses, 315 Stringers, 13–14, 369 Structural analysis, 3–6 863 Structural engineering project, 6–7 Structures: analytical model of, 12–16, 770–774 bending, 11 classification, 7–11 compression, 9–10 equilibrium of, 43–46 framed, 11 kinematically determinate, 648 plane 1315 primary, 510 shear, 10 space, 13, 4346 stiÔness relations, 789797 symmetric, 428434, 445458 tension, Structure stiÔness matrix, 789797 Superposition principle, 78 Supports, 16, 47–49, 136–138 plane structures, 47–49 space trusses, 136–138 Support settlements, 466, 570–579, 667– 672, 681–683, 739–743 Symmetric loads, 434–457 Symmetric matrix, 823 Symmetric structures, 428–434, 445458 Symmetry, 427458 Temperature eÔects, 37, 285286, 466467, 570579 Tetrahedron, 135136 Tezcan, S S., 795 Thermal eÔects, 37 Three-force structures, 46 Three-hinged arch, 70, 119–122 Three-moment equation, 588–601 application, 594–601 derivation, 589–594 Tra‰c loads, 21–24 Transformation matrix, 784–787 Transpose of matrix, 829–830 Tributary area, 20 Truss deflections, 284–295, 318–327 Castigliano’s second theorem, 318–327 virtual work method, 284–295 Trusses, 10, 89–160 assumptions for analysis, 91–95 basic truss element, 95–96, 135–136 bridge, 13, 92 complex, 134–135 compound, 91, 97, 129–134 degree of static indeterminacy, 103 equations of condition, 100–101 ideal, 93 influence lines, 379391 internal stability, 9798 member stiÔness, 781, 788789 plane, 89–135 roof, 91, 93 simple, 91, 96, 136 space, 91, 135–145 statically determinate, 89–160 Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part 864 Index Trusses (cont.) statically indeterminate, 510–610, 769– 817 static determinacy, 101–106, 138 types, 92–93, 95–97 Turner, M T., Two-force structures, 46 Unit matrix, 823 Unit weights, 19 Virtual displacements, principle, 280–281, 357 Virtual forces, principle, 282–284 Virtual work, 280 method, 284–314 principle, 280–284 Virtual work method, 284–314 for beams, 295–304 for frames, 304–314 for trusses, 284–295 Variable loads, 339–340 Warren truss, 92, 93, 114 Wilson, A C., 499 Wilson, E L., Wind loads, 24–32 Wind speed map, 26 Winkler, E., 340 Work, 278–279 virtual, 280 Young’s modulus of elasticity, 230 Zero-force members, 111–113, 140 Zienkiewicz, O C., Copyright 2005 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part ... PART ONE INTRODUCTION TO STRUCTURAL ANALYSIS AND LOADS Introduction to Structural Analysis 1.1 1.2 1.3 1.4 xiii Historical Background Role of Structural Analysis in Structural Engineering Projects... Indeterminacy, and Instability of Plane Trusses 101 Analysis of Plane Trusses by the Method of Joints 106 Analysis of Plane Trusses by the Method of Sections 122 Analysis of Compound Trusses 129 Complex... develop an understanding of the basic principles of structural analysis Emphasizing the intuitive classical approach, Structural Analysis covers the analysis of statically determinate and indeterminate