Matrix analysis of structures

Abstract

1. INTRODUCTION Historical Background / Classical, Matrix, and Finite-Element Methods of Structural Analysis / Flexibility and Stiffness Methods / Classification of Framed Structures / Analytical Models / Fundamental Relationships for Structural Analysis / Linear versus Nonlinear Analysis / Software / Summary 2. MATRIX ALGEBRA Definition of a Matrix / Types of Matrices / Matrix Operations / Gauss-Jordan Elimination Method / Summary / Problems 3. PLANE TRUSSES Global and Local Coordinate Systems / Degrees of Freedom / Member Stiffness Relations in the Local Coordinate System / Finite-Element Formulation Using Virtual Work / Coordinate Transformations / Member Stiffness Relations in the Global Coordinate System / Structure Stiffness Relations / Procedure for Analysis / Summary / Problems 4. COMPUTER PROGRAM FOR ANALYSIS OF PLAIN TRUSSES Data Input / Assignment of Structure Coordinate Numbers / Generation of the Structure Stiffness Matrix / Formation of the Joint Load Vector / Solution for Joint Displacements / Calculation of Member Forces and Support Reactions / Summary / Problems 5. BEAMS Analytical Model / Member Stiffness Relations / Finite-Element Formation Using Virtual Work / Member Fixed-End Forces Due to Loads / Structure Stiffness Relations / Structure Fixed-Joint Forces and Equivalent Joint Loads / Procedure for Analysis / Computer Programs / Summary / Problems 6. PLANE FRAMES Analytical Model / Member Stiffness Relations in the Local Coordinate System / Coordinate Transformations / Member Stiffness Relations in the Global Coordinate System / Structure Stiffness Relations / Procedure for Analysis / Computer Program / Summary / Problems 7. MEMBER RELEASES AND SECONDARY EFFECTS Member Releases in Plane Frames and Beams / Computer Implementation of Analysis for Member Releases / Support Displacements / Computer Implementation of Support Displacement Effects / Temperature Changes and Fabrication Errors / Summary / Problems 8. THREE-DIMENSIONAL FRAMED STRUCTURES Space Trusses / Grids / Space Frames / Summary / Problems 9. SPECIAL TOPICS AND MODELING TECHNIQUES The Structure Stiffness Matrix Including Restrained Coordinates-An Alternative Formulation of the Stiffness Method / Approximate Matrix Analysis of Rectangular Building Frames / Condensation of Degrees of Freedom, and Substructuring / Inclined Roller Supports / Offset Connections / Shear Deformations / Nonprismatic Members / Solution of Large Systems of Stiffness Equations / Summary / Problems / APPENDICES / A. Computer Software / B. Flexibility Method / BIBLIOGRAPHY / ANSWERS TO SELECTED PROBLEMS / INDEX / TABLE OF FIXED-END MOMENTS