1.1 Introduction to Matrix Methods of Structural Analysis; 1.2 Framed Structures; 1.3 Cartesian Coordinate System; 1.4 Coordinate Systems for Forces and Displacements; 1.5 Nodes and Elements; 1.6 Nodal Degrees of Freedom; 1.7 Global and Local Coordinate System; 1.8 Specification of Geometry of the Structure; 1.9 Equivalent Nodal Loads; 1.10 Kinematic and Static Indeterminacy; 1.10.1 Degree of Kinematic Indeterminacy (DKI); 1.10.2 Degree of Static Indeterminacy (DSI). 1.11 Methods of Structural Analysis1.11.1 Equilibrium Equations; 1.11.2 Compatibility of Displacements; 1.11.3 Force-Displacement Relations; 1.11.4 Flexibility and Stiffness Method of Analysis; Problems; 2. Flexibility and Stiffness: Characteristics of Structures; 2.1 Introduction; 2.2 Force-Displacement Relation of a Structure; 2.2.1 Structures with Single Coordinate; 2.2.2 Structures with Multiple Coordinates; 2.2.2.1 Flexibility Matrix; 2.2.2.2 Stiffness Matrix; 2.2.3 Development of Flexibility and Stiffness Matrices; 2.2.4 Properties of Flexibility and Stiffness Matrix. 2.3 Work and Energy2.3.1 Work W; 2.3.2 Complementary Work W*; 2.3.3 Strain Energy U; 2.3.4 Complementary Strain Energy U*; 2.3.5 Law of Conservation of Energy; 2.4 Symmetry of Flexibility and Stiffness Matrices; 2.5 Relation between Stiffness and Flexibility Coefficients and Strain Energy; Problems; 3. Flexibility Method; 3.1 Introduction; 3.2 Coordinates for Forces and Displacements; 3.2.1 Global Coordinates: Action and Redundant Coordinates; 3.2.2 Local Coordinates; 3.2.2.1 Types of Elements; 3.2.2.2 Element Force and Element Displacement Vectors. 3.3 Equilibrium Equations and Force Transformation Matrix3.3.1 Development of Force Transformation Matrix; 3.3.2 Statically Determinate Structure; 3.3.3 Statically Indeterminate Structure; 3.4 Force-Displacement Relations; 3.4.1 For an Element; 3.4.2 For the Unassembled Structure; 3.4.3 For the Structure; 3.5 Compatibility Conditions; 3.6 Structure Flexibility Matrix; 3.6.1 Flexibility Matrix of a Statically Determinate Structure; 3.6.2 Flexibility Matrix of a Statically Indeterminate Structure; 3.6.3 Relation between [F[sub(AX)]] and [F[sub(XA)]]. 3.7 Transformations Used in Flexibility Method3.8 Analysis of Statically Determinate Structure; 3.8.1 Structures Subjected to Element Loads; 3.9 Analysis of Statically Indeterminate Structures; 3.9.1 Analysis of Structures Subjected to Element Loads; 3.10 Analysis of Trusses Having Thermal Changes and Fabrication Errors; Problem; 4. Stiffness Method; 4.1 Introduction; 4.2 Coordinates for Displacements and Forces; 4.2.1 Global Coordinates: Active and Restrained Coordinates; 4.2.2 Local Coordinates; 4.2.2.1 Elements, Coordinates, and Stiffness Matrix. 4.2.2.2 Basic End Actions, Displacements, and Stiffness Matrix.
This book deals with matrix methods of structural analysis for linearly elastic framed structures. It starts with background of matrix analysis of structures followed by procedure to develop force-displacement relation for a given structure using flexibility and stiffness coefficients. The remaining text deals with the analysis of framed structures using flexibility, stiffness and direct stiffness methods. Simple programs using MATLAB for the analysis of structures are included in the appendix. Key Features Explores matrix methods of structural analysis for linearly elastic framed structures Introduces key concepts in the development of stiffness and flexibility matrices Discusses concepts like action and redundant coordinates (in flexibility method) and active and restrained coordinates (in stiffness method) Helps reader understand the background behind the structural analysis programs Contains solved examples and MATLAB codes.