Preface. About the author. Introduction : Preliminary remarks. Classification of structural elements. Structural types. External loading and constraint reactions. Numerical models. Geometry of areas: Introduction.
Laws of transformation of the position vector. Laws of transformation of the static moment vector. Laws of transformation of the moments of inertia tensor. Principal axes and moments of inertia. Mohr's circle. Areas presenting symmetry. Elementary areas. Thin-walled sections.
Examples of calculation. Kinematics and statics of rigid systems: Introduction. Degrees of freedom of a mechanical system. Kinematic definition of plane constraints. Algebraic study of rigid systems. Graphical study of kinematics of systems having one degree of freedom. Cardinal equations of statistics. Static definition of plane constraints.
Algebraic study of statics of rigid systems. Static-kinematic duality. Determination of constraint reactions: Introduction. Auxiliary equations. Principle of Virtual Work. Graphical method. Line of pressure. Internal beam reactions: Introduction.
Indefinite equations of equilibrium for plane beams. Diagrams of characteristics of internal reaction: direct method and graphical method. Determination of characteristics of internal reaction via the Principle of Virtual Work. Statically determinate beam systems: Introduction. remarks. Gerber beams. Trusses. Three-hinged arches and closed-frame structures.
Analysis of strain and stress : Introduction. Strain tensor. Dilations and shearing strains. Law of transformation of the strain tensor for rotations of the reference system. Principal directions of strain. Equations of compatibility. Stress tensor. Law of transformation of the stress tensor for rotations of the reference system.
Principal directions of stress. Plane stress condition. Theory of elasticity: Introduction. Indefinite equations of equilibrium. Static-kinematic duality. Principle of virtual work. Elastic constitutive law. Linear elasticity.
The problem of a linear elastic body. Clapeyron's Theorem. Isotropy. Strength, ductility, fracture energy. Strength criteria. The Saint Venant problem: Introduction. Fundamental hypotheses. Centred axial force.
Flexure. Eccentric axial force and biaxial flexure. Torsion in beams of circular cross section. Torsion in beams of generic cross section. Torsion in open thin-walled sections. Torsion in closed thin-walled sections. Combined shearing and torsional loading. Shearing force.
Biaxial shearing force. Thin-walled cross sections subjected to shear. Beam stength analysis. Beams and plates in flexure: Introduction. Technical theory of beams. Beams with rectilinear axes. Plane beams with curvilinear axes. Differential equation of the elastic line.
Notable displacements and rotations of elementary schemes. Composition of rotations and displacements. Beam on elastic foundation. Dynamics of deflected beams. Plates in flexure. Sophie Germain equation. Shells with double curvature. Finite Element Method : Introduction.
Single-degree-of-freedom system. Principle of Minimum of Total Potential Energy. Ritz-Galerkin method. Principle of Virtual Work. Kinematic boundary conditiions. Dynamics of elastic solids. Structural symmetry : Introduction. Beam systems with axial symmetry.
Beam systems with axial skew-symmetry. Beam systems with polar symmetry. Beam systems with polar skew-symmetry. Non-symmetrically loaded shells of revolution. Symmetrically loaded shells of revolution. Membranes and thin shells. Circular plates. Cylindrical shells.
Cylindrical vessels with bottoms subjected to internal pressure. Three-dimensional solids of revolution. Statically indeterminate structures: method of forces : Introduction. Axial indeterminacy. Elementary statically indeterminate schemes. Elastic.