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Salah KHALFALLAH, National Polytechnic School of Constantine, Algeria.

Preface ix

Chapter 1. Introduction to Statically Indeterminate Structural Analysis 1

1.1. Introduction 1

1.2. External static indeterminacy 2

1.3. Internal static indeterminacy 5

1.3.1. Truss structures 5

1.3.2. Beam and frame structures 7

1.3.3. Crossbeams 9

1.4. Kinematic static indeterminacy 11

1.5. Statically indeterminate structural analysis methods 15

1.6. Superposition principle 16

1.7. Advantages and disadvantages of statically indeterminate structures 17

1.7.1. Advantages of statically indeterminate structures 18

1.7.2. Disadvantages of statically indeterminate structures 19

1.8. Conclusion 21

1.9. Problems 21

Chapter 2. Method of Three Moments 25

2.1. Simple beams 25

2.2. Continuous beam 37

2.3. Applying Clapeyron's theorem 43

2.3.1. Beam with two spans 44

2.3.2. Beam with support settlements 46

2.3.3. Beam with cantilever 49

2.4. Focus method 51

2.4.1. Left focus method 52

2.4.2. Right focus method 54

2.4.3. Focus method with loaded bays 57

2.5. Conclusion 63

2.6. Problems 63

Chapter 3. Method of Forces 67

3.1. Beam with one degree of static indeterminacy 67

3.2. Beam with many degrees of static indeterminacy 72

3.3. Continuous beam with support settlements 77

3.4. Analysis of a beam with two degrees of static indeterminacy 80

3.5. Analysis of a beam subjected to a moment 84

3.6. Analysis of frames 87

3.6.1. Frame with two degrees of static indeterminacy 87

3.6.2. Frame with cantilever 93

3.6.3. Frame with many degrees of static indeterminacy 100

3.6.4. Frame with oblique bars 106

3.7. Analysis of truss 113

3.7.1. Internally statically indeterminate truss 114

3.7.2. Externally statically indeterminate truss 121

3.7.3. Internally and externally statically indeterminate truss 125

3.8. Conclusion 129

3.9. Problems 130

Chapter 4. Slope-Deflection Method 137

4.1. Relationship between deflections and transmitted moments 137

4.2. Fixed-end moments 141

4.2.1. Bi-hinged beam 141

4.2.2. Simply supported beam 142

4.3 Rigidity factor and transmission coefficient 142

4.4. Beam analysis 148

4.4.1. Single span beam 148

4.4.2. Continuous beam 150

4.4.3. Continuous beam with cantilever 153

4.4.4. Beam with support settlements 156

4.4.5. Beam subjected to a moment 160

4.5. Analysis of frames 164

4.5.1. Frame without sidesway 164

4.5.2. Frames with sidesway 182

4.6. Conclusion 208

4.7. Problems 208

Chapter 5. Moment-Distribution Method 213

5.1. Hypotheses of the moment-distribution method 213

5.2. Presentation of the moment-distribution method 214

5.2.1. Distribution of a moment around a rigid joint 214

5.2.2. Distribution procedure 216

5.3. Continuous beam analysis 219

5.3.1. Beam with support settlement 220

5.3.2. Beam with cantilever 224

5.3.3. Beam subjected to a moment 227

5.4. Analysis of frames 229

5.4.1. Frame without sidesway 229

5.4.2. Frame with sidesway 234

5.5. Conclusion 264

5.6. Problems 265

Chapter 6. Influence Lines of Statically Indeterminate Structures 271

6.1. Introduction 271

6.2. Influence lines of beams 272

6.2.1. Beam with one degree of static indeterminacy 272

6.2.2. Beam with two degrees of static indeterminacy 279

6.3. Influence lines of frames 286

6.4. Influence lines of trusses 290

6.4.1. Internally statically indeterminate truss 292

6.4.2. Externally statically indeterminate truss 300

6.5. Conclusion 304

6.6. Problems 304

Chapter 7. Statically Indeterminate Arch Analysis 309

7.1. Introduction 309

7.2. Classification of arches 310

7.3. Semicircular arch under concentrated load 311

7.4. Parabolic arch under concentrated load 321

7.5. Semicircular arch under distributed load 326

7.6. Parabolic arch under distributed load 331

7.7. Semicircular arch fixed under concentrated load 337

7.8. Statically indeterminate tied arch 345

7.9. Arch with many degrees of freedom 350

7.10. Influence lines of statically indeterminate arch 356

7.10.1. Influence lines of bi-hinged arch 356

7.10.2. Influence line of fixed-end arch 360

7.11. Conclusion 364

7.12. Problems 365

Appendix 371

Bibliography 375

Index 379