The current trend of building more streamlined structures has made stability analysis a subject of extreme importance. It is mostly a safety issue because Stability loss could result in an unimaginable catastrophe. Written by two authors with a combined 80 years of professional and academic experience, the objective of Stability of Structures: Principles and Applications is to provide engineers and architects with a firm grasp of the fundamentals and principles that are essential to performing effective stability analysts.
Concise and readable, this guide presents stability analysis within the context of elementary nonlinear flexural analysis, providing a strong foundation for incorporating theory into everyday practice. The first chapter introduces the buckling of columns. It begins with the linear elastic theory and proceeds to include the effects of large deformations and inelastic behavior. In Chapter 2 various approximate methods are illustrated along with the fundamentals of energy methods. The chapter concludes by introducing several special topics, some advanced, that are useful in understanding the physical resistance mechanisms and consistent and rigorous mathematical analysis. Chapters 3 and 4 cover buckling of beam-columns. Chapter 5 presents torsion in structures in some detail, which is one of the least well understood subjects in the entire spectrum of structural mechanics. Strictly speaking, torsion itself does not belong to a topic in structural stability, but needs to be covered to some extent for a better understanding of buckling accompanied with torsional behavior. Chapters 6 and 7 consider stability of framed structures in conjunction with torsional behavior of structures. Chapters 8 to 10 consider buckling of plate elements, cylindrical shells, and general shells. Although the book is primarily devoted to analysis, rudimentary design aspects are discussed.
1. 1.1. Introduction 2. 1.2. Neutral Equilibrium 3. 1.3. Euler Load 4. 1.4. Differential Equations of Beam-Columns 5. 1.5. Effects of Boundary Conditions on the Column Strength 6. 1.6. Introduction to Calculus of Variations 7. 1.7. Derivation of Beam-Column GDE Using Finite Strain 8. 1.8. Galerkin Method 9. 1.9. Continuous Beam-Columns Resting on Elastic Supports 10. 1.10. Elastic Buckling of Columns Subjected to Distributed Axial Loads 11. 1.11. Large Deflection Theory (The Elastica) 12. 1.12. Eccentrically Loaded Columns—Secant Formula 13. 1.13. Inelastic Buckling of Straight Column 14. 1.14. Metric System of Units 15. Chapter 2. Special Topics in Elastic Stability of Columns 16. 2.1. Energy Methods 17. 2.2. Stability Criteria 18. 2.3. Rayleigh-Ritz Method 19. 2.4. The Rayleigh Quotient 20. 2.5. Energy Method Applied to Columns Subjected to Distributed Axial Loads 21. 2.6. Elastically Supported Beam-Columns 22. 2.7. Differential Equation Method 23. 2.8. Methods of Successive Approximation 24. 2.9. Matrix Method 25. 2.10. Free Vibration of Columns Under Compressive Loads 26. 2.11. Buckling by a Nonconservative Load 27. 2.12. Self-Adjoint Boundary Value Problems 28. Chapter 3. Beam-Columns 29. 3.1. Transversely Loaded Beam Subjected to Axial Compression 30. 3.2. Beam-Columns with Concentrated Lateral Loads 31. 3.3. Beam-Columns with Distributed Lateral Loads 32. 3.4. Effect of Axial Force on Bending Stiffness 33. 3.5. Ultimate Strength of Beam-Columns 34. 3.6. Design of Beam-Columns 35. Chapter 4. Continuous Beams and Rigid Frames 36. 4.1. Introduction 37. 4.2. Continuous Beams 38. 4.3. Buckling Modes of Frames 39. 4.4. Critical Loads of Frames 40. 4.5. Stability of Frames by Matrix Analysis 41. 4.6. Second-Order Analysis of a Frame by Slope-Deflection Equations 42. 4.7. Effect of Primary Bending and Plasticity on the Behavior of Frames 43. 4.8. Stability Design of Frames 44. Chapter 5. Torsion in Structures 45. 5.1. Introduction 46. 5.2. Uniform Torsion and St. Venant Theory 47. 5.3. Membrane Analogy 48. 5.4. Twisting of Thin Rectangular Bars 49. 5.5. Torsion in the Inelastic Range 50. 5.6. Torsion in Closed Thin-Walled Cross Sections 51. 5.7. Nonuniform Torsion of W Shapes 52. 5.8. Nonuniform Torsion of Thin-Walled Open Cross Sections 53. 5.9. Cross-Section Properties 54. Chapter 6. Torsional and Flexural-Torsional Buckling 55. 6.1. Introduction 56. 6.2. Strain Energy of Torsion 57. 6.3. Torsional and Flexural-Torsional Buckling of Columns 58. 6.4. Torsional and Flexural-Torsional Buckling under Thrust and End Moments 59. Chapter 7. Lateral-Torsional Buckling 60. 7.1. Introduction 61. 7.2. Differential Equations for Lateral-Torsional Buckling 62. 7.3. Generalization of Governing Differential Equations 63. 7.4. Lateral-Torsional Buckling for Various Loading and Boundary Conditions 64. 7.5. Application of Bessel Function to Lateral-Torsional Buckling Problems 65. 7.6. Lateral-Torsional Buckling by Energy Method 66. 7.7. Design Simplification for Lateral-Torsional Buckling 67. Chapter 8. Buckling of Plate Elements 68. 8.1. Introduction 69. 8.2. Differential Equation of Plate Buckling 70. 8.3. Linear Equations 71. 8.4. Application of Plate Stability Equation 72. 8.5. Energy Methods 73. 8.6. Design Provisions for Local Buckling of Compression Elements 74. 8.7. Inelastic Buckling of Plate Elements 75. 8.8. Failure of Plate Elements 76. Chapter 9. Buckling of Thin Cylindrical Shell Elements 77. 9.1. Introduction 78. 9.2. Large-Deflection Equations (Donnell Type) 79. 9.3. Energy Method 80. 9.4. Linear Stability Equations (Donnell Type) 81. 9.5. Applications of Linear Buckling Equations 82. 9.6. Failure of Cylindrical Shells 83. 9.7. Postbuckling of Cylindrical Shells 84. Chapter 10. Buckling of General Shell Elements 85. 10.1. Introduction 86. 10.2. Nonlinear Equilibrium Equations 87. 10.3. Linear Stability Equations (Donnell Type) 88. 10.4. Applications 89. Author Index 90. Subject Index
The current trend of building more streamlined structures has made stability analysis a subject of extreme importance. It is mostly a safety issue because Stability loss could result in an unimaginable catastrophe. Written by two authors with a combined 80 years of professional and academic experience, the objective of Stability of Structures: Principles and Applications is to provide engineers and architects with a firm grasp of the fundamentals and principles that are essential to performing effective stability analysts.
Concise and readable, this guide presents stability analysis within the context of elementary nonlinear flexural analysis, providing a strong foundation for incorporating theory into everyday practice. The first chapter introduces the buckling of columns. It begins with the linear elastic theory and proceeds to include the effects of large deformations and inelastic behavior. In Chapter 2 various approximate methods are illustrated along with the fundamentals of energy methods. The chapter concludes by introducing several special topics, some advanced, that are useful in understanding the physical resistance mechanisms and consistent and rigorous mathematical analysis. Chapters 3 and 4 cover buckling of beam-columns. Chapter 5 presents torsion in structures in some detail, which is one of the least well understood subjects in the entire spectrum of structural mechanics. Strictly speaking, torsion itself does not belong to a topic in structural stability, but needs to be covered to some extent for a better understanding of buckling accompanied with torsional behavior. Chapters 6 and 7 consider stability of framed structures in conjunction with torsional behavior of structures. Chapters 8 to 10 consider buckling of plate elements, cylindrical shells, and general shells. Although the book is primarily devoted to analysis, rudimentary design aspects are discussed.
1. 1.1. Introduction 2. 1.2. Neutral Equilibrium 3. 1.3. Euler Load 4. 1.4. Differential Equations of Beam-Columns 5. 1.5. Effects of Boundary Conditions on the Column Strength 6. 1.6. Introduction to Calculus of Variations 7. 1.7. Derivation of Beam-Column GDE Using Finite Strain 8. 1.8. Galerkin Method 9. 1.9. Continuous Beam-Columns Resting on Elastic Supports 10. 1.10. Elastic Buckling of Columns Subjected to Distributed Axial Loads 11. 1.11. Large Deflection Theory (The Elastica) 12. 1.12. Eccentrically Loaded Columns—Secant Formula 13. 1.13. Inelastic Buckling of Straight Column 14. 1.14. Metric System of Units 15. Chapter 2. Special Topics in Elastic Stability of Columns 16. 2.1. Energy Methods 17. 2.2. Stability Criteria 18. 2.3. Rayleigh-Ritz Method 19. 2.4. The Rayleigh Quotient 20. 2.5. Energy Method Applied to Columns Subjected to Distributed Axial Loads 21. 2.6. Elastically Supported Beam-Columns 22. 2.7. Differential Equation Method 23. 2.8. Methods of Successive Approximation 24. 2.9. Matrix Method 25. 2.10. Free Vibration of Columns Under Compressive Loads 26. 2.11. Buckling by a Nonconservative Load 27. 2.12. Self-Adjoint Boundary Value Problems 28. Chapter 3. Beam-Columns 29. 3.1. Transversely Loaded Beam Subjected to Axial Compression 30. 3.2. Beam-Columns with Concentrated Lateral Loads 31. 3.3. Beam-Columns with Distributed Lateral Loads 32. 3.4. Effect of Axial Force on Bending Stiffness 33. 3.5. Ultimate Strength of Beam-Columns 34. 3.6. Design of Beam-Columns 35. Chapter 4. Continuous Beams and Rigid Frames 36. 4.1. Introduction 37. 4.2. Continuous Beams 38. 4.3. Buckling Modes of Frames 39. 4.4. Critical Loads of Frames 40. 4.5. Stability of Frames by Matrix Analysis 41. 4.6. Second-Order Analysis of a Frame by Slope-Deflection Equations 42. 4.7. Effect of Primary Bending and Plasticity on the Behavior of Frames 43. 4.8. Stability Design of Frames 44. Chapter 5. Torsion in Structures 45. 5.1. Introduction 46. 5.2. Uniform Torsion and St. Venant Theory 47. 5.3. Membrane Analogy 48. 5.4. Twisting of Thin Rectangular Bars 49. 5.5. Torsion in the Inelastic Range 50. 5.6. Torsion in Closed Thin-Walled Cross Sections 51. 5.7. Nonuniform Torsion of W Shapes 52. 5.8. Nonuniform Torsion of Thin-Walled Open Cross Sections 53. 5.9. Cross-Section Properties 54. Chapter 6. Torsional and Flexural-Torsional Buckling 55. 6.1. Introduction 56. 6.2. Strain Energy of Torsion 57. 6.3. Torsional and Flexural-Torsional Buckling of Columns 58. 6.4. Torsional and Flexural-Torsional Buckling under Thrust and End Moments 59. Chapter 7. Lateral-Torsional Buckling 60. 7.1. Introduction 61. 7.2. Differential Equations for Lateral-Torsional Buckling 62. 7.3. Generalization of Governing Differential Equations 63. 7.4. Lateral-Torsional Buckling for Various Loading and Boundary Conditions 64. 7.5. Application of Bessel Function to Lateral-Torsional Buckling Problems 65. 7.6. Lateral-Torsional Buckling by Energy Method 66. 7.7. Design Simplification for Lateral-Torsional Buckling 67. Chapter 8. Buckling of Plate Elements 68. 8.1. Introduction 69. 8.2. Differential Equation of Plate Buckling 70. 8.3. Linear Equations 71. 8.4. Application of Plate Stability Equation 72. 8.5. Energy Methods 73. 8.6. Design Provisions for Local Buckling of Compression Elements 74. 8.7. Inelastic Buckling of Plate Elements 75. 8.8. Failure of Plate Elements 76. Chapter 9. Buckling of Thin Cylindrical Shell Elements 77. 9.1. Introduction 78. 9.2. Large-Deflection Equations (Donnell Type) 79. 9.3. Energy Method 80. 9.4. Linear Stability Equations (Donnell Type) 81. 9.5. Applications of Linear Buckling Equations 82. 9.6. Failure of Cylindrical Shells 83. 9.7. Postbuckling of Cylindrical Shells 84. Chapter 10. Buckling of General Shell Elements 85. 10.1. Introduction 86. 10.2. Nonlinear Equilibrium Equations 87. 10.3. Linear Stability Equations (Donnell Type) 88. 10.4. Applications 89. Author Index 90. Subject Index
