STRUCTURAL ANALYSIS Using Classical and Matrix Methods

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1 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.

2 Table of Contents DEDICATION PREFACE xiii vii PART ONE: STATICALLY DETERMINATE STRUCTURES CHAPTER I Introduction Structural Analysis and Design History of Structural Analysis Basic Principles of Structural Analysis Structural Components and Systems Structural Forces Structural Idealization (Line Diagrams) Calculation Accuracy Checks on Problems Impact of Computers on Structural Analysis 14 CHAPTER 2 Structural Loads Introduction Structural Safety Specifications and Building Codes Types of Structural Loads Dead Loads Live Loads Live Load Impact Factors Live Loads on Roofs Rain Loads Wind Loads Simplified ASCE Procedure for Estimating Wind Loads 29 XIX

3 XX TABLE OF CONTENTS 2.12 Detailed ASCE Procedure for Estimating Wind Loads Seismic Loads Equivalent Lateral Force Procedure for Estimating Seismic Loads Snow Loads Other Loads Problems for Solution 41 CHAPTER 3 System Loading and Behavior Introduction Tributary Areas Influence Areas Live Load Reduction Loading Conditions for Allowable Stress Design Loading Conditions for Strength Design Concept of the Force Envelope Problems for Solution 56 CHAPTER 4 Reactions Equilibrium Moving Bodies Calculation of Unknowns Types of Support Stability, Determinacy, and Indeterminacy Unstable Equilibrium and Geometric Instability Sign Convention Free-Body Diagrams Horizontal and Vertical Components Reactions by Proportions Reactions Calculated by Equations of Statics Principle of Superposition The Simple Cantilever Cantilevered Structures Reaction Calculations for Cantilevered Structures Arches Three-Hinged Arches Uses of Arches and Cantilevered Structures Cables Problems for Solution 88 CHAPTER 5 Shearing Force and Bending Moment Introduction Shear Diagrams Moment Diagrams 98

4 TABLE OF CONTENTS xxi 5.4 Relations Among Loads, Shearing Forces, and Bending Moments Moment Diagrams Drawn from Shear Diagrams Shear and Moment Diagrams for Statically Determinate Frames Shearing Force and Bending Moment Equations Problems for Solution 112 CHAPTER 6 Introduction to Plane Trusses I Introduction Assumptions for Truss Analysis Truss Notation Roof Trusses Bridge Trusses Arrangement of Truss Members Statical Determinacy of Trusses Methods of Analysis and Conventions Method of Joints Computer Analysis of Statically Determinate Trusses Example Computer Problem Problems for Solution 138 CHAPTER 7 Plane Trusses, Continued Analysis by the Method of Sections Application of the Method of Sections Method of Shears Zero-Force Members When Assumptions Are Not Correct Simple, Compound, and Complex Trusses The Zero-Load Test Stability Equations of Condition Problems for Solution 162 CHAPTER 8 Three-Dimensional or Space Trusses Introduction Basic Principles Equations of Static Equilibrium Stability of Space Trusses Special Theorems Applying to Space Trusses Types of Support Illustrative Examples Solution Using Simultaneous Equations Example Problem with SABLE Problems for Solution 182

5 XXii TABLE OF CONTENTS CHAPTER 9 Influence Lines for Beams Introduction The Influence Line Defined Influence Lines for Simple Beam Reactions Influence Lines for Simple Beam Shearing Forces Influence Lines for Simple Beam Moments Qualitative Influence Lines Uses of Influence Lines; Concentrated Loads Uses of Influence Lines; Uniform Loads Common Simple Beam Formulas from Influence Lines Determining Maximum Loading Effects Using Influence Lines Maximum Loading Effects Using Beam Curvature Impact Loading Problems for Solution 201 CHAPTER 10 Truss Influence Lines and Moving Loads Influence Lines for Trusses Arrangement of Bridge Floor Systems Influence Lines for Truss Reactions Influence Lines for Member Forces of Parallel-Chord Trusses Influence Lines for Members Forces of Nonparallel Chord Trusses Influence Lines for K Truss Determination of Maximum Forces Counters in Bridge Trusses Live Loads for Highway Bridges Live Loads for Railway Bridges Maximum Values for Moving Loads Problems for Solution 223 CHAPTER 11 Deflections and Angle Changes Using Geometric Methods Introduction Sketching Deformed Shapes of Structures Reasons for Computing Deflections The Moment-Area Theorems Application of the Moment-Area Theorems Analysis of Fixed-End Beams Maxwell's Law of Reciprocal Deflections Problems for Solution 245 CHAPTER 12 Deflections and Angle Changes Using Geometric Methods Continued The Method of Elastic Weights Application of the Method of Elastic Weights Limitations of the Elastic-Weight Method Conjugate-Beam Method 255

6 TABLE OF CONTENTS xxiii 12.5 Summary of Conjugate Beams Equilibrium Summary of Beam Relations Application of the Conjugate Method to Beams Long Term Deflections Application of the Conjugate Method to Frames Problems for Solution 261 CHAPTER 13 Deflection and Angle Changes Using Energy Methods Introduction to Energy Methods Conservation of Energy Principle Virtual Work or Complementary Virtual Work Method Truss Deflections by Virtual Work Application of Virtual Work to Trusses Deflections of Beams and Frames by Virtual Work Example Problems for Beams and Frames Rotations or Angle Changes by Virtual Work Introduction to Castigliano's Theorems Castigliano's Second Theorem Problems for Solution 289 PART TWO! STATICALLY INDETERMINATE STRUCTURES Classical Methods CHAPTER 14 Introduction to Statically Indeterminate Structures Introduction Continuous Structures Advantages of Statically Indeterminate Structures Disadvantages of Statically Indeterminate Structures Methods of Analyzing Statically Indeterminate Structures Looking Ahead 304 CHAPTER 15 Force Methods of Analyzing Statically Indeterminate Structures Beams and Frames with One Redundant Beams and Frames with Two or More Redundants Support Settlement Problems for Solution 320 CHAPTER 16 Force Methods for Analyzing Statically Indeterminate Structures Continued Analysis of Externally Redundant Trusses Analysis of Internally Redundant Trusses 326

7 XXiv TABLE OF CONTENTS 16.3 Analysis of Trusses Redundant Internally and Externally Temperature Changes, Shrinkage, Fabrication Errors, and So On Castigliano's First Theorem Analysis Using Computers Problems for Solution 342 CHAPTER 17 Influence Lines for Statically Indeterminate Structures Influence Lines for Statically Indeterminate Beams Qualitative Influence Lines Influence Lines for Statically Indeterminate Trusses Problems for Solution 360 CHAPTER 18 Slope Deflection: A Displacement Method of Analysis Introduction Derivation of Slope-Deflection Equations Application of Slope Deflection to Continuous Beams Continuous Beams with Simple Ends Miscellaneous Items Concerning Continuous Beams Analysis of Beams with Support Settlement Analysis of Frames No Sidesway Analysis of Frames with Sidesway Analysis of Frames with Sloping Legs Problems for Solution 382 PART THREE: STATICALLY INDETERMINATE STRUCTURES Common Methods in Current Practice CHAPTER 19 Approximate Analysis of Statically Indeterminate Structures Introduction Trusses with Two Diagonals in Each Panel Continuous Beams Analysis of Building Frames for Vertical Loads Analysis of Portal Frames Analysis of Building Frames for Lateral Loads Approximate Analyses of Frame Compared to "Exact" Analysis by SABLE Moment Distribution Analysis of Vierendeel "Trusses" Problems for Solution 410 CHAPTER 20 Moment Distribution for Beams Introduction Basic Relations 415

8 TABLE OF CONTENTS XXV 20.3 Definitions Sign Convention Application of Moment Distribution Modification of Stiffness for Simple Ends Shearing Force and Bending Moment Diagrams Computer Solution with SABLE Problems for Solution 430 CHAPTER 21 Moment Distribution for Frames Frames with Sidesway Prevented Frames with Sidesway Sidesway Moments Frames with Sloping Legs Multistory Frames Computer Analysis of Frame Problems for Solution 457 CHAPTER 22 Introduction to Matrix Methods Structural Analysis Using the Computer Matrix Methods Review of Matrix Algebra Force and Displacement Methods of Analysis Introduction to the Force or Flexibility Method Problems for Solution 468 CHAPTER 23 Fundamentals of the Displacement or Stiffness Method Introduction General Relationships Stiffness Equations for Axial Force Members Stiffness Equations for Flexural Members Stiffness Matrix for Combined Axial and Flexural Members Characteristics of Stiffness Matrices Relation Between Stiffness and Flexibility Matrices Problems for Solution 492 CHAPTER 24 Stiffness Matrices for Inclined Members General Axial Force Members Flexural Members Loading Between Nodes Problems for Solution 515

9 XXVI TABLE OF CONTENTS CHAPTER 25 Additional Matrix Procedures General Addition of Stiffness Equations Stiffness Matrices for Inclined Members Stiffness Equations for Structures with Enforced Displacements Stiffness Equations for Structures with Members Experiencing Temperature Changes Stiffness Equations for Structures Whose Members Have Incorrect Lengths Applications of Matrix Partitioning Condensation Band Width of Stiffness Matrices for General Structures 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 SAP 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

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