Integrated Matrix Analysis of Structures Theory and Computation

7. 2 Element Stiffness Matrix of a Space Truss Local Coordinates 221 7. 3 Transformation of the Element Stiffness Matrix 223 7. 4 Element Axial Force 224 7. 5 Assemblage ofthe System Stiffness Matrix 225 7. 6 Problems 236 8 STATIC CONDENSATION AND SUBSTRUCTURING 8. 1 Introduction 239 8. 2 Static Condensation 239 8. 3 Substructuring 244 8. 4 Problems 259 9 INTRODUCTION TO FINITE ELEMENT MEmOD 9. 1 Introduction 261 9. 2 Plane Elasticity Problems 262 9. 3 Plate Bending 285 9. 4 Rectangular Finite Element for Plate Bending 285 9. 5 Problems 298 APPENDIX I Equivalent Nodal Forces 301 APPENDIXll Displacement Functions for Fixed-End Beams 305 GLOSSARY 309 SELECTED BmLIOGRAPHY 317 INDEX 319 ix Preface This is the first volume of a series of integrated textbooks for the analysis and design of structures. The series is projected to include a first volume in Matrix Structural Analysis to be followed by volumes in Structural Dynamics and Earthquake Engineering as well as other volumes dealing with specialized or advanced topics in the analysis and design of structures. An important objective in the preparation of these volumes is to integrate and unify the presentation using common notation, symbols and general format. Furthermore, all of these volumes will be using the same structural computer program, SAP2000, developed and maintained by Computers and Structures, Inc. , Berkeley, California.

1 Beams: Analytical Methodology.- 1.1 Introduction.- 1.2 Elements, Nodes and Nodal Coordinates.- 1.3 Shape Functions and Stiffness Coefficients.- 1.4 Element Stiffness Matrix.- 1.5 Assembly of the System Stiffness Matrix.- 1.6 System Force Vector.- 1.7 System Nodal Displacements and Support Reactions.- 1.8 Element End Forces.- 1.9 End Releases in Beam Elements.- 1.10 Support Displacements.- 1.11 Element Displacement Functions.- 1.12 Shear Force and Bending Moment Functions.- 1.13 The Temperature Effect.- 1.14 Elastic Supports.- 1.15 Analytical Problems.- 1.16 Practice Problems.- 2 Beams: Computer Applications.- 2.1 Computer Program.- 2.2 Problems.- 3 Plane Frames.- 3.1 Introduction.- 3.2 Stiffness Coefficients for Axial Forces.- 3.3 Displacement Functions for Axially Loaded Beams.- 3.4 Element Stiffness Matrix for Plane Frame Elements.- 3.5 Coordinate Transformation.- 3.6 Equivalent Nodal Force for an Axially Loaded Beam Element.- 3.7 Element End Forces.- 3.8 Inclined Roller Supports.- 3.9 Analytical Problems.- 3.10 Practice Problems.- 4 Grid Frames.- 4.1 Introduction.- 4.2 Torsional Effects.- 4.3 Stiffness Matrix for a Grid Element.- 4.4 Transformation of Coordinates.- 4.5 Analysis of Grid Frames.- 4.6 Problems.- 5 Space Frames.- 5.1 Introduction.- 5.2 Element Stiffness Matrix.- 5.3 Transformation of Coordinates.- 5.4 Reduced System Stiffness Equation.- 5.5 Analytical Problems.- 5.6 Practice Problems.- 6 Plane Trusses.- 6.1 Introduction.- 6.2 Element Stiffness Matrix in Local Coordinates.- 6.3 Transformation of Coordinates.- 6.4 Element Stiffness Matrix in Global Coordinates.- 6.5 Assemblage of System Stiffness Matrix.- 6.6 End-Forces for an Element of a Truss.- 6.7 Problems.- 7 Space Trusses.- 7.1 Introduction.- 7.2 Element Stiffness Matrix of a Space Truss Local Coordinates.- 7.3 Transformation of the Element Stiffness Matrix.- 7.4 Element Axial Force.- 7.5 Assemblage of the System Stiffness Matrix.- 7.6 Problems.- 8 Static Condensation and Substructuring.- 8.1 Introduction.- 8.2 Static Condensation.- 8.3 Substructuring.- 8.4 Problems.- 9 Introduction to Finite Element Method.- 9.1 Introduction.- 9.2 Plane Elasticity Problems.- 9.3 Plate Bending.- 9.4 Rectangular Finite Element for Plate Bending.- 9.5 Problems.- Appendix I Equivalent Nodal Forces.- Appendix II Displacement Functions for Fixed-End Beams.- Selected Bibliography.