Structural Analysis 1

Salah Khalfallah is Professor at the National Polytechnic School of Constantine (ENPC), Algeria. He teaches Continuum Mechanics, Mechanical Vibrations and Finite Element Methods. His research is focused on the analysis of the nonlinear behavior of structures, the dynamics of soil–structure interactions and, since his transfer to the ENPC, biomechanics.

• Preface xiChapter 1. Introduction to Structural Analysis 11.1. Introduction 11.2. Concept of a structure 21.3. Structural analysis 21.4. History of structural analysis 31.5. Classification of structures 41.5.1. Plane trusses 41.5.2. Beams 61.5.3. Frames 71.5.4. Crossbeams 81.5.5. Arches 81.6. Static indeterminacy of structures 81.6.1. Trusses 91.6.2. Beam and frames 111.7. Sign convention 141.8. Conclusion 151.9. Problems 16Chapter 2. Actions on Structures 212.1. Loads 212.2. Permanent loads 222.3. Live loads 232.4. Snow loads 262.5. Wind loads 292.6. Seismic loads 402.7. Thermal loads 472.8. Hydrostatic loads and land thrust 482.9. Conclusion 492.10. Problems 49Chapter 3. External Analysis of Plane Structures 553.1. External equilibrium of structures 553.2. External and internal actions 573.2.1. External actions 583.2.2. Internal actions 583.3. Types of plane structure supports 593.4. Static determinacy, static indeterminacy and structural stability 593.4.1. External analysis 593.4.2. Internal analysis 613.5. Calculation of support reactions 633.6. Superposition principle 713.7. Matrix formulation 723.8. Concept of displacement 763.9. Concept of work 773.10. Principle of virtual work 803.11. Calculation of reactions by the virtual work method 813.12. Conclusion 843.13. Problems 85Chapter 4. Analysis of Trusses 914.1. Definition of a truss 914.2. Hypothesis of analysis 924.3. Sign convention and representation of internal forces 934.4. Degree of static indeterminacy and stability of trusses 944.4.1. External analysis 944.4.2. Internal analysis 954.5. Analysis methods of trusses 964.5.1. Method of joint equilibrium 974.5.2. Method of sections 1004.5.3. Matrix method 1044.5.4. Graphic or Cremona method 1094.6. Composite trusses 1114.7. Complex trusses 1184.8. Space trusses 1204.8.1. Space truss analysis 1214.9. Conclusion 1274.10. Problems 127Chapter 5. Internal Analysis of Beams and Frames 1355.1. Normal force, shear force and bending moment 1355.2. Sign convention 1375.3. Beam analysis procedure 1385.4. Diagrams of internal actions 1435.5. Relationship between loading, shear force and bending moment 1465.6. Static determinacy, static indeterminacy and instability of beams and frames 1475.7. Plane frame analysis procedure 1485.8. Conclusion 1605.9. Problems 160Chapter 6. Deflections of Elastic Beams: Energy Methods 1676.1. Elastic deflection of beams 1676.2. Calculation of deflections 1696.2.1. Method of the differential equation of the elastic line 1696.2.2. Direct integration method 1736.2.3. Moment-area method. 1766.2.4. Conjugate beam method 1816.3. Superposition principle 1856.4. Conclusion 1886.5. Problems 189Chapter 7. Structural Deflections: Energy Methods 1937.1. Work of external actions 1937.2. Internal or strain energy 2007.3. Principle of energy conservation 2047.4. Principle of virtual work 2087.4.1. Method of virtual work: trusses 2117.4.2. Method of virtual work: beams 2177.4.3. Method of virtual work: frames 2257.5. Conservation of energy and strain energy 2317.6. Castigliano’s theorem 2317.6.1. Displacement theorem statement 2327.6.2. Slope theorem statement 2327.6.3. Application of Castigliano’s theorem to truss analysis 2347.6.4. Using Castigliano’s theorem to analyze beams and frames 2367.7. Maxwell–Betti law 2417.8. Conclusion 2457.9. Problems 246Chapter 8. Cable Analysis 2538.1. Introduction 2538.2. Mechanical characteristics of cables 2548.3. Hypothesis of cable analysis 2558.4. Cable analysis 2558.4.1. Cables subject to concentrated force 2558.4.2. Cables subject to distributed forces 2638.4.3. Cables subject to any force 2728.5. Cables with an inflection point outside the cable 2758.6. Suspension bridges 2808.7. Conclusion 2838.8. Problems 284Chapter 9. Analysis of Arches 2899.1. Introduction 2899.2. Three-hinged arch 2909.2.1. Semicircular arch under concentrated load 2919.2.2. Semicircular arch under uniformly distributed load 2999.2.3. Parabolic arch under concentrated load 3029.2.4. Parabolic arch under uniformly distributed load 3099.2.5. Semicircular arch with support settlements 3149.3. Bi-hinged arch 3199.4. Conclusion 3239.5. Problems 323Chapter 10. Influence Lines 32910.1. Introduction 32910.2. Influence line definition 33010.3. Influence lines of a beam using the equilibrium method 33010.3.1. Influence lines of a support reaction 33110.3.2. Influence line of a shear force 33210.3.3. Influence line of a bending moment 33310.4. Influence lines of a frame using the equilibrium method 33810.4.1. Influence line of support reaction VA 33910.5. Analysis steps 34410.6. Influence lines of trusses 35310.7. Influence lines using the Muller–Breslau principle 35610.7.1. Influence lines of a support reaction 35610.7.2. Influence line of a shear force 36010.7.3. Influence line of a bending moment 36610.9. Conclusion 37510.10. Problems 376Appendices 381Bibliography 383Index 387