STRUCTURAL ANALYSIS Using Classical and Matrix Methods Fourth Edition Jack C. McCormac Clemson University 8 O 7 2 O O 7 John Wiley and Sons, Inc.
Table of Contents DEDICATION PREFACE xiii vii PART ONE: STATICALLY DETERMINATE STRUCTURES CHAPTER I Introduction 3 1.1 Structural Analysis and Design 3 1.2 History of Structural Analysis 4 1.3 Basic Principles of Structural Analysis 7 1.4 Structural Components and Systems 8 1.5 Structural Forces 9 1.6 Structural Idealization (Line Diagrams) 11 1.7 Calculation Accuracy 13 1.8 Checks on Problems 13 1.9 Impact of Computers on Structural Analysis 14 CHAPTER 2 Structural Loads 16 2.1 Introduction 16 2.2 Structural Safety 17 2.3 Specifications and Building Codes 17 2.4 Types of Structural Loads 20 2.5 Dead Loads 20 2.6 Live Loads 21 2.7 Live Load Impact Factors 23 2.8 Live Loads on Roofs 23 2.9 Rain Loads 24 2.10 Wind Loads 26 2.11 Simplified ASCE Procedure for Estimating Wind Loads 29 XIX
XX TABLE OF CONTENTS 2.12 Detailed ASCE Procedure for Estimating Wind Loads 31 2.13 Seismic Loads 32 2.14 Equivalent Lateral Force Procedure for Estimating Seismic Loads 34 2.15 Snow Loads 37 2.16 Other Loads 40 2.17 Problems for Solution 41 CHAPTER 3 System Loading and Behavior 43 3.1 Introduction 43 3.2 Tributary Areas 44 3.3 Influence Areas 48 3.4 Live Load Reduction 48 3.5 Loading Conditions for Allowable Stress Design 50 3.6 Loading Conditions for Strength Design 52 3.7 Concept of the Force Envelope 55 3.8 Problems for Solution 56 CHAPTER 4 Reactions 57 4.1 Equilibrium 57 4.2 Moving Bodies 57 4.3 Calculation of Unknowns 58 4.4 Types of Support 59 4.5 Stability, Determinacy, and Indeterminacy 61 4.6 Unstable Equilibrium and Geometric Instability 64 4.7 Sign Convention 65 4.8 Free-Body Diagrams 66 4.9 Horizontal and Vertical Components 67 4.10 Reactions by Proportions 67 4.11 Reactions Calculated by Equations of Statics 68 4.12 Principle of Superposition 71 4.13 The Simple Cantilever 72 4.14 Cantilevered Structures 73 4.15 Reaction Calculations for Cantilevered Structures 75 4.16 Arches 77 4.17 Three-Hinged Arches 78 4.18 Uses of Arches and Cantilevered Structures 83 4.19 Cables 83 4.20 Problems for Solution 88 CHAPTER 5 Shearing Force and Bending Moment 95 5.1 Introduction 95 5.2 Shear Diagrams 97 5.3 Moment Diagrams 98
TABLE OF CONTENTS xxi 5.4 Relations Among Loads, Shearing Forces, and Bending Moments 98 5.5 Moment Diagrams Drawn from Shear Diagrams 99 5.6 Shear and Moment Diagrams for Statically Determinate Frames 106 5.7 Shearing Force and Bending Moment Equations 110 5.8 Problems for Solution 112 CHAPTER 6 Introduction to Plane Trusses I 17 6.1 Introduction 117 6.2 Assumptions for Truss Analysis 118 6.3 Truss Notation 119 6.4 Roof Trusses 120 6.5 Bridge Trusses 121 6.6 Arrangement of Truss Members 122 6.7 Statical Determinacy of Trusses 123 6.8 Methods of Analysis and Conventions 127 6.9 Method of Joints 129 6.10 Computer Analysis of Statically Determinate Trusses 134 6.11 Example Computer Problem 135 6.12 Problems for Solution 138 CHAPTER 7 Plane Trusses, Continued 143 7.1 Analysis by the Method of Sections 143 7.2 Application of the Method of Sections 144 7.3 Method of Shears 151 7.4 Zero-Force Members 153 7.5 When Assumptions Are Not Correct 155 7.6 Simple, Compound, and Complex Trusses 156 7.7 The Zero-Load Test 157 7.8 Stability 159 7.9 Equations of Condition 161 7.10 Problems for Solution 162 CHAPTER 8 Three-Dimensional or Space Trusses 168 8.1 Introduction 168 8.2 Basic Principles 168 8.3 Equations of Static Equilibrium 169 8.4 Stability of Space Trusses 171 8.5 Special Theorems Applying to Space Trusses 171 8.6 Types of Support 172 8.7 Illustrative Examples 173 8.8 Solution Using Simultaneous Equations 178 8.9 Example Problem with SABLE32 180 8.10 Problems for Solution 182
XXii TABLE OF CONTENTS CHAPTER 9 Influence Lines for Beams 185 9.1 Introduction 185 9.2 The Influence Line Defined 185 9.3 Influence Lines for Simple Beam Reactions 186 9.4 Influence Lines for Simple Beam Shearing Forces 187 9.5 Influence Lines for Simple Beam Moments 188 9.6 Qualitative Influence Lines 189 9.7 Uses of Influence Lines; Concentrated Loads 194 9.8 Uses of Influence Lines; Uniform Loads 195 9.9 Common Simple Beam Formulas from Influence Lines 196 9.10 Determining Maximum Loading Effects Using Influence Lines 197 9.11 Maximum Loading Effects Using Beam Curvature 198 9.12 Impact Loading 199 9.13 Problems for Solution 201 CHAPTER 10 Truss Influence Lines and Moving Loads 204 10.1 Influence Lines for Trusses 204 10.2 Arrangement of Bridge Floor Systems 204 10.3 Influence Lines for Truss Reactions 206 10.4 Influence Lines for Member Forces of Parallel-Chord Trusses 206 10.5 Influence Lines for Members Forces of Nonparallel Chord Trusses 208 10.6 Influence Lines for K Truss 210 10.7 Determination of Maximum Forces 211 10.8 Counters in Bridge Trusses 213 10.9 Live Loads for Highway Bridges 215 10.10 Live Loads for Railway Bridges 219 10.11 Maximum Values for Moving Loads 220 10.12 Problems for Solution 223 CHAPTER 11 Deflections and Angle Changes Using Geometric Methods 225 11.1 Introduction 225 11.2 Sketching Deformed Shapes of Structures 225 11.3 Reasons for Computing Deflections 230 11.4 The Moment-Area Theorems 232 11.5 Application of the Moment-Area Theorems 234 11.6 Analysis of Fixed-End Beams 241 11.7 Maxwell's Law of Reciprocal Deflections 243 11.8 Problems for Solution 245 CHAPTER 12 Deflections and Angle Changes Using Geometric Methods Continued 241 12.1 The Method of Elastic Weights 248 12.2 Application of the Method of Elastic Weights 249 12.3 Limitations of the Elastic-Weight Method 254 12.4 Conjugate-Beam Method 255
TABLE OF CONTENTS xxiii 12.5 Summary of Conjugate Beams 257 12.6 Equilibrium 257 12.7 Summary of Beam Relations 258 12.8 Application of the Conjugate Method to Beams 258 12.9 Long Term Deflections 260 12.10 Application of the Conjugate Method to Frames 261 12.11 Problems for Solution 261 CHAPTER 13 Deflection and Angle Changes Using Energy Methods 264 13.1 Introduction to Energy Methods 264 13.2 Conservation of Energy Principle 264 13.3 Virtual Work or Complementary Virtual Work Method 265 13.4 Truss Deflections by Virtual Work 267 13.5 Application of Virtual Work to Trusses 269 13.6 Deflections of Beams and Frames by Virtual Work 273 13.7 Example Problems for Beams and Frames 274 13.8 Rotations or Angle Changes by Virtual Work 281 13.9 Introduction to Castigliano's Theorems 283 13.10 Castigliano's Second Theorem 284 13.11 Problems for Solution 289 PART TWO! STATICALLY INDETERMINATE STRUCTURES Classical Methods CHAPTER 14 Introduction to Statically Indeterminate Structures 297 14.1 Introduction 297 14.2 Continuous Structures 298 14.3 Advantages of Statically Indeterminate Structures 300 14.4 Disadvantages of Statically Indeterminate Structures 302 14.5 Methods of Analyzing Statically Indeterminate Structures 302 14.6 Looking Ahead 304 CHAPTER 15 Force Methods of Analyzing Statically Indeterminate Structures 305 15.1 Beams and Frames with One Redundant 305 15.2 Beams and Frames with Two or More Redundants 314 15.3 Support Settlement 316 15.4 Problems for Solution 320 CHAPTER 16 Force Methods for Analyzing Statically Indeterminate Structures Continued 322 16.1 Analysis of Externally Redundant Trusses 322 16.2 Analysis of Internally Redundant Trusses 326
XXiv TABLE OF CONTENTS 16.3 Analysis of Trusses Redundant Internally and Externally 329 16.4 Temperature Changes, Shrinkage, Fabrication Errors, and So On 330 16.5 Castigliano's First Theorem 332 16.6 Analysis Using Computers 341 16.7 Problems for Solution 342 CHAPTER 17 Influence Lines for Statically Indeterminate Structures 347 17.1 Influence Lines for Statically Indeterminate Beams 347 17.2 Qualitative Influence Lines 353 17.3 Influence Lines for Statically Indeterminate Trusses 356 17.4 Problems for Solution 360 CHAPTER 18 Slope Deflection: A Displacement Method of Analysis 363 18.1 Introduction 363 18.2 Derivation of Slope-Deflection Equations 363 18.3 Application of Slope Deflection to Continuous Beams 366 18.4 Continuous Beams with Simple Ends 369 18.5 Miscellaneous Items Concerning Continuous Beams 371 18.6 Analysis of Beams with Support Settlement 372 18.7 Analysis of Frames No Sidesway 374 18.8 Analysis of Frames with Sidesway 376 18.9 Analysis of Frames with Sloping Legs 382 18.10 Problems for Solution 382 PART THREE: STATICALLY INDETERMINATE STRUCTURES Common Methods in Current Practice CHAPTER 19 Approximate Analysis of Statically Indeterminate Structures 389 19.1 Introduction 389 19.2 Trusses with Two Diagonals in Each Panel 390 19.3 Continuous Beams 391 19.4 Analysis of Building Frames for Vertical Loads 395 19.5 Analysis of Portal Frames 398 19.6 Analysis of Building Frames for Lateral Loads 400 19.7 Approximate Analyses of Frame Compared to "Exact" Analysis by SABLE32 407 19.8 Moment Distribution 408 19.9 Analysis of Vierendeel "Trusses" 408 19.10 Problems for Solution 410 CHAPTER 20 Moment Distribution for Beams 413 20.1 Introduction 413 20.2 Basic Relations 415
TABLE OF CONTENTS XXV 20.3 Definitions 417 20.4 Sign Convention 419 20.5 Application of Moment Distribution 419 20.6 Modification of Stiffness for Simple Ends 424 20.7 Shearing Force and Bending Moment Diagrams 425 20.8 Computer Solution with SABLE32 428 20.9 Problems for Solution 430 CHAPTER 21 Moment Distribution for Frames 433 21.1 Frames with Sidesway Prevented 433 21.2 Frames with Sidesway 435 21.3 Sidesway Moments 437 21.4 Frames with Sloping Legs 447 21.5 Multistory Frames 451 21.6 Computer Analysis of Frame 455 21.7 Problems for Solution 457 CHAPTER 22 Introduction to Matrix Methods 461 22.1 Structural Analysis Using the Computer 461 22.2 Matrix Methods 461 22.3 Review of Matrix Algebra 462 22.4 Force and Displacement Methods of Analysis 462 22.5 Introduction to the Force or Flexibility Method 463 22.6 Problems for Solution 468 CHAPTER 23 Fundamentals of the Displacement or Stiffness Method 470 23.1 Introduction 470 23.2 General Relationships 470 23.3 Stiffness Equations for Axial Force Members 472 23.4 Stiffness Equations for Flexural Members 478 23.5 Stiffness Matrix for Combined Axial and Flexural Members 487 23.6 Characteristics of Stiffness Matrices 489 23.7 Relation Between Stiffness and Flexibility Matrices 490 23.8 Problems for Solution 492 CHAPTER 24 Stiffness Matrices for Inclined Members 494 24.1 General 494 24.2 Axial Force Members 494 24.3 Flexural Members 500 24.4 Loading Between Nodes 510 24.5 Problems for Solution 515
XXVI TABLE OF CONTENTS CHAPTER 25 Additional Matrix Procedures 518 25.1 General 518 25.2 Addition of Stiffness Equations 518 25.3 Stiffness Matrices for Inclined Members 520 25.4 Stiffness Equations for Structures with Enforced Displacements 523 25.5 Stiffness Equations for Structures with Members Experiencing Temperature Changes 524 25.6 Stiffness Equations for Structures Whose Members Have Incorrect Lengths 526 25.7 Applications of Matrix Partitioning 526 25.8 Condensation 527 25.9 Band Width of Stiffness Matrices for General Structures 528 25.10 Problems for Solution 531 APPENDICES APPENDIX A The Catenary Equation 533 APPENDIX B Matrix Algebra 538 B.I Introduction 538 B.2 Matrix Definitions and Properties 538 B.3 Special Matrix Types 539 B.4 Determinant of a Square Matrix 540 B.5 Adjoint Matrix 541 B.6 Matrix Arithmetic 542 B.7 Gauss's Method for Solving Simultaneous Equations 547 B.8 Special Topics 548 APPENDIX C Wind, Seismic, and Snow Load Tables and Figures 553 APPENDIX D Computer Analysis of Various Structures Using SAP2000 565 D. 1 Introduction 565 D.2 Analysis of Plane Trusses 565 D.3 Analysis of Space Trusses 567 D.4 Analysis of Statically Indeterminate Plane Trusses 568 D.5 Analysis of Composite Structures 570 D.6 Analysis of Continuous Beams and Frames 571 Glossary 573 Index 579