Divided into 12 chapters, Matrix Methods for Advanced Structural Analysis begins with an
introduction to the analysis of structures (fundamental concepts and basic steps of structural
analysis, primary structural members and their modeling, brief historical overview of methods
of static analysis, programming principles, and suggestions for the rational use of computer
programs). This is followed by the principal steps of the Direct Stiffness Method including plane
trusses, plane framed structures, space trusses, and space framed structures. The case of
plane or space framed structure, including possible rigid elements at their beam ends (rigid
joints) is discussed in detail.
Other topics discussed in this reference include the procedure for analyzing beams with internal
releases (partial connection of beam elements) and elastic hinges, as well as the alternative
handling of internal releases by modifying the element stiffness matrix. Furthermore, the
Method of Substructures is demonstrated for the solution of large-scale models in terms of the
associated number of degrees of freedom.
1. Chapter One Introduction to Matrix Methods of Structural Analysis - p. 1 2. Chapter Two Plane Trusses - p. 17 3. Keywords: - p. 17 4. 2.1 Introduction - p. 17 5. 2.2 Overview of the Plane Truss - p. 22 6. 2.3 Vectors of End-Actions of Plane Truss Element - p. 23 7. 2.4 End-Translation Vectors of Plane Truss Element - p. 25 8. 2.5 Transformation Matrix of Plane Truss Element - p. 26 9. 2.6 Total Local Stiffness Matrix of Plane Truss Element - p. 31 10. 2.7 Total Global Stiffness Matrix of Plane Truss Element - p. 34 11. 2.8 Vectors of Nodal-Forces and Nodal-Translations of Plane Truss - p. 38 12. 2.9 Global Stiffness Matrix of Plane Trusses - p. 40 13. 2.10 Modification of Global Stiffness Matrix Due to Support Conditions—Reordering Matrix - p. 47 14. 2.11 Modification of Global Stiffness Matrix of a Plane Truss Due to Inclined and Elastic Supports - p. 54 15. 2.12 Plane Truss Subjected to Member Loading - p. 65 16. 2.13 Stress Resultants of Plane Truss Members - p. 74 17. Chapter Three Plane Frames - p. 77 18. Keywords - p. 77 19. 3.1 Introduction - p. 77 20. 3.2 Overview of the Plane Frame - p. 80 21. 3.3 Vectors of End-Actions of Plane Frame Element - p. 82 22. 3.4 End-Displacement Vector of Plane Frame Element - p. 84 23. 3.5 Transformation Matrix of Plane Frame Element - p. 86 24. 3.6 Total Local Stiffness Matrix of Plane Frame Element - p. 90 25. 3.7 Total Global Stiffness Matrix of Plane Frame Element - p. 94 26. 3.8 Vectors of Nodal-Forces and Nodal-Displacements of Plane Frame - p. 97 27. 3.9 Global Stiffness Matrix of Plane Frames - p. 100 28. 3.10 Modification of Global Stiffness Matrix Due to Support Conditions—Reordering Matrix - p. 106 29. 3.11 Modification of Global Stiffness Matrix of a Plane Frame Due to Inclined And Elastic Supports - p. 113 30. 3.12 Plane Frame Subjected to Member Loading - p. 126 31. 3.13 Stress Resultants of Plane Frame Members - p. 136 32. Chapter Four Spatial Trusses - p. 139 33. Chapter Five Spatial Frames - p. 167 34. Keywords: - p. 167 35. 5.1 Introduction - p. 167 36. 5.2 Overview of Spatial Frames - p. 167 37. 5.3 Vectors of End-Actions and End-Displacements of Spatial Frame Element - p. 170 38. 5.4 Transformation Matrix of Spatial Frame Element - p. 174 39. 5.5 Local Stiffness Matrix of Spatial Frame Element - p. 189 40. 5.6 Global Stiffness Matrix of Spatial Frame Element - p. 196 41. 5.7 Vectors of Nodal-Actions and Nodal-Displacements of Spatial Frame - p. 199 42. 5.8 Global Stiffness Matrix of Spatial Frame - p. 201 43. 5.9 Modification of Global Stiffness Matrix of Spatial Frame Due to Support Conditions—Reordering Matrix - p. 205 44. 5.10 Internal Actions of Spatial Frame Members - p. 210 45. 5.11 Application—Analysis of Grid Structure - p. 211 46. Chapter Six Rigid Joints - p. 227 47. Chapter Seven Internal Releases—Method of Combined Nodes - p. 257 48. Chapter Eight Internal Hinges—Modified Stiffness Matrix Method - p. 281 49. Chapter Nine Static Condensation Method - p. 299 50. Chapter Ten Elements of Variable Cross Section - p. 333 51. Chapter Eleven The Method of Substructures - p. 359 52. Chapter Twelve Programming of Direct Stiffness Method—PFrameMatlab Program - p. 401 53. Appendix A—Tensor Calculus - p. 425 54. References - p. 443 55. Index - p. 445
Divided into 12 chapters, Matrix Methods for Advanced Structural Analysis begins with an
introduction to the analysis of structures (fundamental concepts and basic steps of structural
analysis, primary structural members and their modeling, brief historical overview of methods
of static analysis, programming principles, and suggestions for the rational use of computer
programs). This is followed by the principal steps of the Direct Stiffness Method including plane
trusses, plane framed structures, space trusses, and space framed structures. The case of
plane or space framed structure, including possible rigid elements at their beam ends (rigid
joints) is discussed in detail.
Other topics discussed in this reference include the procedure for analyzing beams with internal
releases (partial connection of beam elements) and elastic hinges, as well as the alternative
handling of internal releases by modifying the element stiffness matrix. Furthermore, the
Method of Substructures is demonstrated for the solution of large-scale models in terms of the
associated number of degrees of freedom.
1. Chapter One Introduction to Matrix Methods of Structural Analysis - p. 1 2. Chapter Two Plane Trusses - p. 17 3. Keywords: - p. 17 4. 2.1 Introduction - p. 17 5. 2.2 Overview of the Plane Truss - p. 22 6. 2.3 Vectors of End-Actions of Plane Truss Element - p. 23 7. 2.4 End-Translation Vectors of Plane Truss Element - p. 25 8. 2.5 Transformation Matrix of Plane Truss Element - p. 26 9. 2.6 Total Local Stiffness Matrix of Plane Truss Element - p. 31 10. 2.7 Total Global Stiffness Matrix of Plane Truss Element - p. 34 11. 2.8 Vectors of Nodal-Forces and Nodal-Translations of Plane Truss - p. 38 12. 2.9 Global Stiffness Matrix of Plane Trusses - p. 40 13. 2.10 Modification of Global Stiffness Matrix Due to Support Conditions—Reordering Matrix - p. 47 14. 2.11 Modification of Global Stiffness Matrix of a Plane Truss Due to Inclined and Elastic Supports - p. 54 15. 2.12 Plane Truss Subjected to Member Loading - p. 65 16. 2.13 Stress Resultants of Plane Truss Members - p. 74 17. Chapter Three Plane Frames - p. 77 18. Keywords - p. 77 19. 3.1 Introduction - p. 77 20. 3.2 Overview of the Plane Frame - p. 80 21. 3.3 Vectors of End-Actions of Plane Frame Element - p. 82 22. 3.4 End-Displacement Vector of Plane Frame Element - p. 84 23. 3.5 Transformation Matrix of Plane Frame Element - p. 86 24. 3.6 Total Local Stiffness Matrix of Plane Frame Element - p. 90 25. 3.7 Total Global Stiffness Matrix of Plane Frame Element - p. 94 26. 3.8 Vectors of Nodal-Forces and Nodal-Displacements of Plane Frame - p. 97 27. 3.9 Global Stiffness Matrix of Plane Frames - p. 100 28. 3.10 Modification of Global Stiffness Matrix Due to Support Conditions—Reordering Matrix - p. 106 29. 3.11 Modification of Global Stiffness Matrix of a Plane Frame Due to Inclined And Elastic Supports - p. 113 30. 3.12 Plane Frame Subjected to Member Loading - p. 126 31. 3.13 Stress Resultants of Plane Frame Members - p. 136 32. Chapter Four Spatial Trusses - p. 139 33. Chapter Five Spatial Frames - p. 167 34. Keywords: - p. 167 35. 5.1 Introduction - p. 167 36. 5.2 Overview of Spatial Frames - p. 167 37. 5.3 Vectors of End-Actions and End-Displacements of Spatial Frame Element - p. 170 38. 5.4 Transformation Matrix of Spatial Frame Element - p. 174 39. 5.5 Local Stiffness Matrix of Spatial Frame Element - p. 189 40. 5.6 Global Stiffness Matrix of Spatial Frame Element - p. 196 41. 5.7 Vectors of Nodal-Actions and Nodal-Displacements of Spatial Frame - p. 199 42. 5.8 Global Stiffness Matrix of Spatial Frame - p. 201 43. 5.9 Modification of Global Stiffness Matrix of Spatial Frame Due to Support Conditions—Reordering Matrix - p. 205 44. 5.10 Internal Actions of Spatial Frame Members - p. 210 45. 5.11 Application—Analysis of Grid Structure - p. 211 46. Chapter Six Rigid Joints - p. 227 47. Chapter Seven Internal Releases—Method of Combined Nodes - p. 257 48. Chapter Eight Internal Hinges—Modified Stiffness Matrix Method - p. 281 49. Chapter Nine Static Condensation Method - p. 299 50. Chapter Ten Elements of Variable Cross Section - p. 333 51. Chapter Eleven The Method of Substructures - p. 359 52. Chapter Twelve Programming of Direct Stiffness Method—PFrameMatlab Program - p. 401 53. Appendix A—Tensor Calculus - p. 425 54. References - p. 443 55. Index - p. 445
