Cover -- Title Page -- Copyright -- Contents -- Preface -- Chapter 1 Matrix Algebra -- 1.1 Definitions -- 1.2 Addition and Subtraction -- 1.3 Multiplication -- 1.4 Determinant -- 1.5 Inverse Matrix -- 1.6 Counting Rules -- 1.7 Systems of Equations -- 1.7.1 Systems of Equations with Only Unknown Components in the Vector a -- 1.7.2 Systems of Equations with Known and Unknown Components in the Vector a -- 1.7.3 Eigenvalue Problems -- Exercises -- Chapter 2 Systems of Connected Springs -- 2.1 Spring Relations -- 2.2 Spring Element -- 2.3 Systems of Springs -- Exercises
Chapter 3 Bars and Trusses -- 3.1 The Differential Equation for Bar Action -- 3.1.1 Definitions -- 3.1.2 The Material Level -- 3.1.3 The Cross-Section Level -- 3.1.4 Bar Action -- 3.2 Bar Element -- 3.2.1 Definitions -- 3.2.2 Solving the Differential Equation -- 3.2.3 From Local to Global Coordinates -- 3.3 Trusses -- Exercises -- Chapter 4 Beams and Frames -- 4.1 The Differential Equation for Beam Action -- 4.1.1 Definitions -- 4.1.2 The Material Level -- 4.1.3 The Cross-Section Level -- 4.1.4 Beam Action -- 4.2 Beam Element -- 4.2.1 Definitions
4.2.2 Solving the Differential Equation for Beam Action -- 4.2.3 Beam Element with Six Degrees of Freedom -- 4.2.4 From Local to Global Directions -- 4.3 Frames -- Exercises -- Chapter 5 Modelling at the System Level -- 5.1 Symmetry Properties -- 5.2 The Structure and the System of Equations -- 5.2.1 The Deformations and Displacements of the System -- 5.2.2 The Forces and Equilibria of the System -- 5.2.3 The Stiffness of the System -- 5.3 Structural Design and Simplified Manual Calculations -- 5.3.1 Characterising Structures -- 5.3.2 Axial and Bending Stiffness
5.3.3 Reducing the Number of Degrees of Freedom -- 5.3.4 Manual Calculation Using Elementary Cases -- Exercises -- Chapter 6 Flexible Supports -- 6.1 Flexible Supports at Nodes -- 6.2 Foundation on Flexible Support -- 6.2.1 The Constitutive Relations of the Connection Point -- 6.2.2 The Constitutive Relation of the Base Surface -- 6.2.3 Constitutive Relation for the Support Point of the Structure -- 6.3 Bar with Axial Springs -- 6.3.1 The Differential Equation for Bar Action with Axial Springs -- 6.3.2 Bar Element -- 6.4 Beam on Elastic Spring Foundation
6.4.1 The Differential Equation for Beam Action with Transverse Springs -- 6.4.2 Beam Element -- Exercises -- Chapter 7 Three-Dimensional Structures -- 7.1 Three-Dimensional Bar Element -- 7.2 Three-Dimensional Trusses -- 7.3 The Differential Equation for Torsional Action -- 7.3.1 Definitions -- 7.3.2 The Material Level -- 7.3.3 The Cross-Section Level -- 7.3.4 Torsional Action -- 7.4 Three-Dimensional Beam Element -- 7.4.1 Element for Torsional Action -- 7.4.2 Beam Element with 12 Degrees of Freedom -- 7.4.3 From Local to Global Directions -- 7.5 Three-Dimensional Frames -- Exercises
