Structural Analysis Fourth Edition SI Edition PDF

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Summary

CONVERSIONS BETWEEN U.S. CUSTOMARY UNITS AND SI UNITS (Continued) Times conversion factor U.S. Customary unit Equals SI unit Accurate Practical Moment of inertia (area) inch to fourth power in.4 416,231 416,000 millimeter to fourth power mm4 inch to fourth power in.4 0.416231 ⫻ 10⫺6 0.416 ⫻ 10⫺6 me...

Description

CONVERSIONS BETWEEN U.S. CUSTOMARY UNITS AND SI UNITS (Continued)

Times conversion factor U.S. Customary unit

Equals SI unit

Moment of inertia (area) inch to fourth power

in.4

inch to fourth power

in.4

Accurate

Practical

416,231

416,000

0.416231 

106

millimeter to fourth power meter to fourth power

mm4 m4

kilogram meter squared

kg·m2

watt (J/s or N·m/s) watt watt

W W W

47.9 6890 47.9 6.89

pascal (N/m2) pascal kilopascal megapascal

Pa Pa kPa MPa

16,400 16.4  106

millimeter to third power meter to third power

mm3 m3

meter per second meter per second meter per second kilometer per hour

m/s m/s m/s km/h

cubic meter cubic meter cubic centimeter (cc) liter cubic meter

m3 m3 cm3 L m3

0.416  106

Moment of inertia (mass) slug foot squared

slug-ft2

1.35582

1.36

Power foot-pound per second foot-pound per minute horsepower (550 ft-lb/s)

ft-lb/s ft-lb/min hp

1.35582 0.0225970 745.701

1.36 0.0226 746

Pressure; stress pound per square foot pound per square inch kip per square foot kip per square inch

psf psi ksf ksi

Section modulus inch to third power inch to third power

in.3 in.3

Velocity (linear) foot per second inch per second mile per hour mile per hour

ft/s in./s mph mph

Volume cubic foot cubic inch cubic inch gallon (231 in.3) gallon (231 in.3)

ft3 in.3 in.3 gal. gal.

47.8803 6894.76 47.8803 6.89476 16,387.1 16.3871  106 0.3048* 0.0254* 0.44704* 1.609344* 0.0283168 16.3871  106 16.3871 3.78541 0.00378541

0.305 0.0254 0.447 1.61 0.0283 16.4  106 16.4 3.79 0.00379

*An asterisk denotes an exact conversion factor Note: To convert from SI units to USCS units, divide by the conversion factor

Temperature Conversion Formulas

5 T(°C)   [T(°F)  32]  T(K)  273.15 9 5 T(K)   [T(°F)  32]  273.15  T(°C)  273.15 9 9 9 T(°F)   T(°C)  32   T(K)  459.67 5 5

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Structural Analysis Fourth Edition, SI

Aslam Kassimali Southern Illinois University—Carbondale SI Edition prepared by Amit Prashant, Indian Institute of Technology, Kanpur

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Structural Analysis, Fourth Edition, SI Aslam Kassimali SI Edition prepared by Amit Prashant Publisher: Christopher M. Shortt Senior Developmental Editor: Hilda Gowans Acquisitions Editor, SI Edition: Swati Meherishi

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Printed in the United States of America 1 2 3 4 5 6 7 13 12 11 10 09

IN MEMORY OF AMI

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Contents

Preface to the SI Edition Preface xiv

xiii

PART ONE INTRODUCTION TO STRUCTURAL ANALYSIS AND LOADS 1

1

2

Introduction to Structural Analysis

Loads on Structures

3 1.1 1.2 1.3 1.4

Historical Background 4 Role of Structural Analysis in Structural Engineering Projects 6 Classification of Structures 7 Analytical Models 12 Summary 16

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 E¤ects 37 Load Combinations 37 Summary 38 Problems 39

17

vii

viii

Contents

PART TWO

3

4

ANALYSIS OF STATICALLY DETERMINATE STRUCTURES 41

Equilibrium and Support Reactions

Plane and Space Trusses

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 47 Computation of Reactions 60 Principle of Superposition 78 Reactions of Simply Supported Structures Using Proportions 79 Summary 80 Problems 82

4.1 4.2

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 100 Analysis of Plane Trusses by the Method of Joints 106 Analysis of Plane Trusses by the Method of Sections 121 Analysis of Compound Trusses 128 Complex Trusses 133 Space Trusses 134 Summary 144 Problems 145

89

4.3 4.4 4.5 4.6 4.7 4.8 4.9

5

Beams and Frames: Shear and Bending Moment 5.1 5.2 5.3 5.4 5.5

160

Axial Force, Shear, and Bending Moment 161 Shear and Bending Moment Diagrams 167 Qualitative Deflected Shapes 172 Relationships between Loads, Shears, and Bending Moments 173 Static Determinacy, Indeterminacy and Instability of Plane Frames 195

Contents

5.6

6

Deflections of Beams: Geometric Methods 6.1 6.2 6.3 6.4 6.5 6.6

7

8

Analysis of Plane Frames 201 Summary 215 Problems 217

226 Di¤erential Equation for Beam Deflection 227 Direct Integration Method 230 Superposition Method 233 Moment-Area Method 234 Bending Moment Diagrams by Parts 248 Conjugate-Beam Method 253 Summary 269 Problems 269

Deflections of Trusses, Beams, and Frames: Work–Energy Methods

Influence Lines

275

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8

Work 276 Principle of Virtual Work 278 Deflections of Trusses by the Virtual Work Method 282 Deflections of Beams by the Virtual Work Method 293 Deflections of Frames by the Virtual Work Method 301 Conservation of Energy and Strain Energy 312 Castigliano’s Second Theorem 316 Betti’s Law and Maxwell’s Law of Reciprocal Deflections 325 Summary 326 Problems 328

8.1

Influence Lines for Beams and Frames by Equilibrium Method 338 Mu¨ller-Breslau’s Principle and Qualitative Influence Lines 353 Influence Lines for Girders with Floor Systems 367 Influence Lines for Trusses 377 Influence Lines for Deflections 389 Summary 392 Problems 393

337

8.2 8.3 8.4 8.5

ix

x

9

Contents

Application of Influence Lines

401 9.1 9.2 9.3 9.4

10

Analysis of Symmetric Structures

425 10.1 10.2 10.3 10.4

PART THREE

11

Symmetric Structures 426 Symmetric and Antisymmetric Components of Loadings 432 Behavior of Symmetric Structures under Symmetric and Antisymmetric Loadings 443 Procedure for Analysis of Symmetric Structures 447 Summary 455 Problems 456

ANALYSIS OF STATICALLY INDETERMINATE STRUCTURES 459

Introduction to Statically Indeterminate Structures 11.1 11.2

12

Response at a Particular Location Due to a Single Moving Concentrated Load 401 Response at a Particular Location Due to a Uniformly Distributed Live Load 403 Response at a Particular Location Due to a Series of Moving Concentrated Loads 408 Absolute Maximum Response 415 Summary 421 Problems 422

461

Advantages and Disadvantages of Indeterminate Structures 462 Analysis of Indeterminate Structures 465 Summary 470

Approximate Analysis of Rectangular Building Frames 12.1 12.2 12.3 12.4

471

Assumptions for Approximate Analysis 472 Analysis for Vertical Loads 475 Analysis for Lateral Loads—Portal Method 481 Analysis for Lateral Loads—Cantilever Method 497 Summary 504 Problems 505

Contents

13

Method of Consistent Deformations—Force Method 13.1 13.2 13.3 13.4

14

16

17

Structures with Single Degree of Indeterminacy 509 Internal Forces and Moments as Redundants 531 Structures with Multiple Degrees of Indeterminacy 544 Support Settlements, Temperature Changes and Fabrication Errors 568 Summary 577 Problems 578

Three-Moment Equation and the Method of Least Work 14.1 14.2 14.3

15

508

Derivation of Three-Moment Equation 587 Application of Three-Moment Equation 592 Method of Least Work 599 Summary 606 Problems 607

Influence Lines for Statically Indeterminate Structures

Slope-Deflection Method

586

609

15.1 15.2

Influence Lines for Beams and Trusses 610 Qualitative Influence Lines by Mu¨ller-Breslau’s Principle 627 Summary 631 Problems 632

16.1 16.2 16.3 16.4 16.5

Slope-Deflection Equations 636 Basic Concept of the Slope-Deflection Method 644 Analysis of Continuous Beams 651 Analysis of Frames without Sidesway 673 Analysis of Frames with Sidesway 681 Summary 702 Problems 702

17.1 17.2 17.3

Definitions and Terminology 708 Basic Concept of the Moment-Distribution Method 717 Analysis of Continuous Beams 725

635

Moment-Distribution Method

707

xi

xii

Contents

17.4 17.5

18

Introduction to Matrix Structural Analysis 18.1 18.2 18.3 18.4 18.5 18.6

Analysis of Frames without Sidesway 741 Analysis of Frames with Sidesway 744 Summary 761 Problems 762

767 Analytical Model 768 Member Sti¤ness Relations in Local Coordinates 772 Coordinate Transformations 780 Member Sti¤ness Relations in Global Coordinates 786 Structure Sti¤ness Relations 787 Procedure for Analysis 795 Summary 813 Problems 814

Appendix A

Areas and Centroids of Geometric Shapes

Appendix B

Review of Matrix Algebra

821 B.1 B.2 B.3 B.4

Appendix C

Computer Software

817

Definition of a Matrix 821 Types of Matrices 822 Matrix Operations 824 Solution of Simultaneous Equations by the Gauss-Jordan Method 831 Problems 835

837 Starting the Computer Software Inputting Data 837 Results of the Analysis 844 Problems 849 Bibliography 851 Answers to Selected Problems 853 Index 863

837

Preface to the SI Edition

This edition of Structural Analysis has been adapted to incorporate the International System of Units (Le Syste`me International d’Unite´s or SI) throughout the book. Amit Prashant wishes to acknowledge the contributions made by his colleagues, Arindam Dey, and Kaustubh Dasgupta to this SI Edition.

Le Syste`me International d’Unite´s The United States Customary System (USCS) of units uses FPS (foot-poundsecond) units (also called English or Imperial units). SI units are primarily the units of the MKS (meter-kilogram-second) system. However, CGS (centimetergram-second) units are often accepted as SI units, especially in textbooks.

Using SI Units in this Book In this book, we have used both MKS and CGS units. USCS units or FPS units used in the US Edition of the book have been converted to SI units throughout the text and problems. However, in case of data sourced from handbooks, government standards, and product manuals, it is not only extremely di‰cult to convert all values to SI, it also encroaches upon the intellectual property of the source. Also, some quantities such as the ASTM grain size number and Jominy distances are generally computed in FPS units and would lose their relevance if converted to SI. Some data in figures, tables, examples, and references, therefore, remains in FPS units. For readers unfamiliar with the relationship between the FPS and the SI systems, conversion tables have been provided inside the front and back covers of the book. To solve problems that require the use of sourced data, the sourced values can be converted from FPS units to SI units just before they are to be used in a calculation. To obtain standardized quantities and manufacturers’ data in SI units, the readers may contact the appropriate government agencies or authorities in their countries/regions.

Instructor Resources A Printed Instructor’s Solution Manual in SI units is available on request. An electronic version of the Instructor’s Solutions Manual, and PowerPoint slides of the figures from the SI text are available through www.cengage.com/engineering. The readers’ feedback on this SI Edition will be highly appreciated and will help us improve subsequent editions. The Publishers xiii

Preface

The objective of this book is to 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 beams, trusses, and rigid frames. It also presents an introduction to the matrix analysis of structures. The book is divided into three parts. Part One presents a general introduction to the subject of structural engineering. It includes a chapter devoted entirely to the topic of loads because attention to this important topic is generally lacking in many civil engineering curricula. Part Two, consisting of Chapters 3 through 10, covers the analysis of statically determinate beams, trusses, and rigid frames. The chapters on deflections (Chapters 6 and 7) are placed before those on influence lines (Chapters 8 and 9), so that influence lines for deflections can be included in the latter chapters. This part also contains a chapter on the analysis of symmetric structures (Chapter 10). Part Three of the book, Chapters 11 through 18, covers the analysis of statically indeterminate structures. The format of the book is flexible to enable instructors to emphasize topics that are consistent with the goals of the course. Each chapter of the book begins with an introductory section defining its objective and ends with a summary section outlining its salient features. An important general feature of the book is the inclusion of step-by-step procedures for analysis to enable students to make an easier transition from theory to problem solving. Numerous solved examples are provided to illustrate the application of the fundamental concepts. A computer program for analyzing plane framed structures is available on the publisher’s website www.cengage.com/engineering. This interactive software can be used to simulate a variety of structural and loading configurations and to determine cause versus e¤ect relationships between loading and various structural parameters, thereby enhancing the students’ understanding of the behavior of structures. The software shows deflected shapes of structures to enhance students’ xiv

Preface

xv

understanding of structural response due to various types of loadings. It can also include the e¤ects of support settlements, temperature changes, and fabrication errors in the analysis. A solutions manual, containing complete solutions to over 600 text exercises, is also available for the instructor.

A NOTE ON THE REVISED EDITION In this fourth edition, while the major features of the third editon have been retained, over 15 percent of the problems from the previous edition have been replaced with new ones. The chapter on loads has been revised to meet the provisions of the ASCE 7-05 Standard, and the treatment of the structures with internal hinges has been expanded in Chapter 3. The computer software has been upgraded to make it compatible with the latest versions of Microsoft Windows. Finally, most of the photographs have been replaced with new ones, and the page layout of the book has been redesigned to enhance clarity.

ACKNOWLEDGMENTS I wish to express my thanks to Christopher Carson and Hilda Gowans of Cengage Learning for their constant support and encouragement throughout this project, and to Rose Kernan for all her help during the production phase. The comments and suggestions for improvement from colleagues and students who have used previous editions are gratefully acknowledged. All of their suggestions were carefully considered, and implemented whenever possible. Thanks are due to the following reviewers for their careful reviews of the manuscripts of the various editions, and for their constructive suggestions: Ayo Abatan Virginia Polytechnic Institute and State University Riyad S. Aboutaha Georgia Institute of Technology Osama Abudayyeh Western Michigan University

Thomas T. Baber University of Virginia Gordon B. Batson Clarkson University George E. Blandford University of Kentucky

xvi

Preface

Ramon F. Borges Penn State/Altoona College

Eugene B. Loverich Northern Arizona University

Kenneth E. Buttry University of Wisconsin

L. D. Lutes Texas A&M University David Mazurek US Coast Guard Academy

Steve C. S. Cai Louisiana State University William F. Carroll University of Central Florida Malcolm A. Cutchins Auburn University Jack H. Emanuel University of Missouri—Rolla Fouad Fanous Iowa State University Leon Feign Fairfield University Robert Fleischman University of Notre Dame George Kostyrko California State University E. W. Larson California State University/ Northridge

Ahmad Namini University of Miami Arturo E. Schultz North Carolina State University Kassim Tarhin...