CONTENTS Preface v 1.Introduction 1 1.1 Introductory Remarks 1 1.2 Idealisations and Assumptions 1 1.3 Conditions of Equilibrium 6 1.4 Compatibility Conditions 7 1.5 Statically Determinate and Indeterminate Structures 7 1.6 Simple and Compound Systems 7 1.7 Linear and Non-linear Systems 8 2.Deflection of determinate beams using moment area and conjugate beam methods9 2.1 Introduction 9 2.2 Moment Area Theorems 9 2.3 Derivation of Moment Area Theorems 11 2.4 Sign Convention in the Moment Area Method Applied to Beams 12 2.5 Conjugate Beam Theorems 23 2.6 Conjugate Beams 25 2.7 Conjugate Beam Method 27 Exercises 39 3.Deflection of beams and rigid frames by energy methods43 3.1 Introduction 43 3.2 Strain Energy and Complementary Energy 43 3.3 Strain Energy Due to Bending 46 3.4 Deflection by Strain Energy Method 47 3.5 Virtual Work 52 3.6 Unit Load Method 56 3.7 The Unit Load Method-Application to Beam Deflections 58 3.8 Castigliano's Theorems 69 3.9 Finding Deflection Using Castigliano's Method 71 3.10 Other Useful Theorems 79 Exercises 82 4.Deflections of pin-jointed plane frames85 4.1 Introduction 85 4.2 Unit load Method 86 4.3 Deflections Due to Lack of Fit and Temperature Changes 102 Exercises 109 5. Moving loads and influence lines for beams 113 5.1 Introduction 113 5.2 Influence Line Diagram 113 5.3 Influence Line Diagrams for Simply Supported Beams 114 5.4 Influence Line Diagrams for Cantilever Beams 116 5.5 Influence Line Diagrams for Overhanging Beams 118 5.6 Influence Line Diagrams for Double Overhanging Beams 122 5.7 Influence Line Diagrams in a Balanced Cantilever Beam 124 5.8 Influence Line Diagrams for Girders Supporting Floor Beams 127 5.9 Use of Influence Line Diagrams 130 5.10Maximum S.F and B.M Values Due to Moving Loads 133 Exercises155 6. Influence lines for bridge trusses 157 6.1 Introduction 157 6.2 Method of Finding Influence Line Diagrams 158 Exercises 184 7. Three hinged arches 187 7.1 Introduction 187 7.2 Three Hinged Arches 188 7.3 Analysis for Static Loads 191 7.4Bending Moment Diagrams 204 7.5Influence Line Diagrams 207 7.6Maximum Bending Moment Diagrams 212 Exercises 225 8. Cables and suspension bridges 227 8.1 Introduction 227 8.2 Equilibrium of Cable 228 8.3 Cable Subjected to Concentrated Loads 229 8.4 Cable Subjected to a Uniformly Distributed Load 232 8.5 Cable with Ends at Different Levels 235 8.6 Forces on Anchor Cables and Towers 238 8.7 Effect of Temperature on Cable 246 8.8 Suspension Bridge with Three Hinged Stiffening Girder 249 8.9 Influence Lines and Rolling Loads 254 8.10 Maximum Moment Diagrams 266 8.11 Maximum Shear Force Diagram 267 8.12 Suspension Cable with Two Hinged Stiffening Girder 272 Exercises 276 9. Introduction to analysis of indeterminate structures279 9.1Introduction 279 9.2Degree of Indeterminacy 279 9.3Determining Degree of Indeterminacy 280 9.4Methods of Analysis 287 10.Analysis of pin-connected indeterminate frames by consistent deformation method289 10.1Frames with External Indeterminacy 289 10.2Stresses Due to Errors in Length of a Member 306 10.3 Temperature Stresses 312 Exercises 316 11. Analysis of indeterminate beams and rigid frames by consistent deformation method319 11.1Introduction 319 11.2 Propped Cantilevers 319 11.3 Fixed Beams 327 11.4 Analysis of Continuous Beams 342 11.5 Analysis of Frames 351 Exercises 359 12. Three moment equation363 12.1 Introduction 363 12.2 Derivation of Three Moment Equations 363 12.3 Application of Three Moment Equation 365 12.4 Application of Three Moment Equation to Problems with Fixed End 378 Exercises 382 Appendix: Analysis of Pin-Jointed Plane Frames 385 Index 425