Matrix Analysis Framed Structures

1 Basic Concepts of Structural Analysis.- 1.1 Introduction.- 1.2 Types of Framed Structures.- 1.3 Deformations in Framed Structures.- 1.4 Actions and Displacements.- 1.5 Equilibrium.- 1.6 Compatibility.- 1.7 Static and Kinematic Indeterminacy.- 1.8 Structural Mobilities.- 1.9 Principle of Superposition.- 1.10 Action and Displacement Equations.- 1.11 Flexibility and Stiffness Matrices.- 1.12 Equivalent Joint Loads.- 1.13 Energy Concepts.- 1.14 Virtual Work.- References.- Problems.- 2 Fundamentals of the Flexibility Method.- 2.1 Introduction.- 2.2 Flexibility Method.- 2.3 Examples.- 2.4 Temperature Changes, Prestrains, and Support Displacements.- 2.5 Joint Displacements, Member End-Actions, and Support Reactions.- 2.6 Flexibilities of Prismatic Members.- 2.7 Formalization of the Flexibility Method.- Problems.- 3 Fundamentals of the Stiffness Method.- 3.1 Introduction.- 3.2 Stiffness Method.- 3.3 Examples.- 3.4 Temperature Changes, Prestrains and Support Displacements.- 3.5 Stiffness of Prismatic Members.- 3.6 Formalization of the Stiffness Method.- Problems.- 4 Computer-Oriented Direct Stiffness Method.- 4.1 Introduction.- 4.2 Direct Stiffness Method.- 4.3 Complete Member Stiffness Matrices.- 4.4 Formation of Joint Stiffness Matrix.- 4.5 Formation of Load Vector.- 4.6 Rearrangement of Stiffness and Load Arrays.- 4.7 Calculation of Results.- 4.8 Analysis of Continuous Beams.- 4.9 Example.- 4.10 Plane Truss Member Stiffnesses.- 4.11 Analysis of Plane Trusses.- 4.12 Example.- 4.13 Rotation of Axes in Two Dimensions.- 4.14 Application to Plane Truss Members.- 4.15 Rotation of Axes in Three Dimensions.- 4.16 Plane Frame Member Stiffnesses.- 4.17 Analysis of Plane Frames.- 4.18 Example.- 4.19 Grid Member Stiffnesses.- 4.20 Analysis of Grids.- 4.21 Space Truss Member Stiffnesses.- 4.22 Selection of Space Truss Member Axes.- 4.23 Analysis of Space Trusses.- 4.24 Space Frame Member Stiffnesses.- 4.25 Analysis of Space Frames.- Problems.- 5 Computer Programs for Framed Structures.- 5.1 Introduction.- 5.2 FORTRAN Programming and Flow Charts.- 5.3 Program Notation.- 5.4 Preparation of Data.- 5.5 Description of Programs.- 5.6 Continuous Beam Program.- 5.7 Plane Truss Program.- 5.8 Plane Frame Program.- 5.9 Grid Program.- 5.10 Space Truss Program.- 5.11 Space Frame Program.- 5.12 Combined Program for Framed Structures.- References.- 6 Additional Topics for the Stiffness Method.- 6.1 Introduction.- 6.2 Rectangular Framing.- 6.3 Symmetric and Repeated Structures.- 6.4 Loads Between Joints.- 6.5 Automatic Dead Load Analysis.- 6.6 Temperature Changes and Prestrains.- 6.7 Support Displacements.- 6.8 Oblique Supports.- 6.9 Elastic Supports.- 6.10 Translation of Axes.- 6.11 Member Stiffnesses and Fixed-End Actions from Flexibilities.- 6.12 Nonprismatic Members.- 6.13 Curved Members.- 6.14 Releases in Members.- 6.15 Elastic Connections.- 6.16 Shearing Deformations.- 6.17 Offset Connections.- 6.18 Axial-Flexural Interactions.- 6.19 Axial Constraints in Frames.- References.- Problems.- 7 Finite-Element Method for Framed Structures.- 7.1 Introduction.- 7.2 Stresses and Strains in Continua.- 7.3 Virtual-Work Basis of Finite-Element Method.- 7.4 One-Dimensional Elements.- 7.5 Application to Framed Structures.- References.- General References.- Notation.- Appendix A. Displacements of Framed Structures.- A.1 Stresses and Deformations in Slender Members.- A.2 Displacements by the Unit-Load Method.- A.3 Displacements of Beams.- A.4 Integrals of Products for Computing Displacements.- References.- Appendix B. End-Actions for Restrained Members.- Appendix C. Properties of Sections.- Appendix D. Computer Routines for Solving Equations.- D.1 Factorization Method for Symmetric Matrices.- D.2 Subprogram FACTOR.- D.3 Subprogram SOLVER.- D.4 Subprogram BANFAC.- D.5 Subprogram BANSOL.- References.- Appendix E. Solution without Rearrangement.- Answers to Problems.- Order Form for Diskette.