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Description du cours |
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Structural mechanics is that discipline that deals with the physical-mathematical models and experimental studies that describe the static and the dynamic behavior of structures and their components (structural elements) under the effect of various actions (external forces, temperature variations, earthquakes etc.). |
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Connaissances requises |
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To pass the exam of Structural mechanics it is necessary also to pass the exam of statics and dynamics of mechanical systems. |
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Objectifs |
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The overriding purpose of the course of structural mechanics is to develop a mindset that will lead to operational recognize, formulate and solve structural problems. |
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Programme |
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Geometry of areas
Laws of transformation of the position vector, of static moment vector and of moment of inertia tensor
Principal axes and moments of inertia
Mohr's circIe
Thin-walled sections
Kinematics and statics of rigid beam systems
Degrees of freedom of a mechanical system
Kinematic and static definition of pIane constraints
Algebraic study of kinematics of rigid beam systems
Graphical study of kinematics of systems having one degree of freedom
Equations of statics
Algebraic study of statics of rigid beam systems
Static-kinematic duality
Determination of constraint reactions
Auxiliary equations
Principle of Virtual Work
Graphical method
Line of pressure:differential equation
Line of pressure: examples
Graphical study of kinematics
Theorems of kinematic chains
Method of kinematic chains for internal reactions
Statically determinate beam systems
Gerber beams
Force and funicular polygons. Ropes and cables
Three-hinged arches
Closed-frame structures
Trusses
Internal beam reactions
Indefinite equations of equilibrium for plane beams
Diagrams of characteristics of internal reaction: direct method and graphical method
Construction of the parabola for bending moments and lines of pressure.
Determination of characteristics of internal reaction via the Principle of Virtual Work
Analysis of strain
Starting hypotheses (displacement field)
Infinitesimal strain tensor
Law of transformation of the strain tensor for rotations of the reference system
Principal directions of strain
Equations of compatibility
Logarithmic strain
Analysis of stress
Stress tensor
Cosserat's Stress tensor
Cauchy tetrahedron
Law of transformation of the stress tensor for rotations of the reference system
Principal directions of stress
Plane stress condition
Mohr's Circle for Stress Analysis
Principle of Virtual Work for a deformable body
Stress and strain vectors. Differential operators
Indefinite equations of equilibrium
Static-kinematic duality
Simplified schemes for the calculation of the internal work
Demonstration of Principle of Virtual Work using Gauss-Green's theorem
Theory of elasticity
Elastic constitutive law and nonlinear elasticity
Linear elastic potential
The problem of a linear elastic body
Superposition principle
Clapeyron's Theorem and Betti's Reciprocal Theorem
Theorem of unicity of the solution (Kirchhoff)
Elastic law for isotropic materials
Strength criteria for ductile and fragile materials
Maximum stress and maximum strain criteria
Strength criteria for ductile materials: Tresca and Von Mises
Strength criteria for fragile materials: Mohr-Coulomb
Triaxial and biaxial expressions for the strength criteria
The Saint Venant problem
Fundamental hypotheses
Centered axial force
Pure and biaxial bending
Eccentric axial force and central core of inertia
No tension materials (masonry)
Shear force
Biaxial shear force
Torsion in beams of circular and generic cross sections
Thin-walled cross sections subjected to shear and torsion
Beam strength analysis
Instability of elastic equilibrium
Second order effects and bifurcation of the equilibrium
Euler critical buckling load
Different boundary conditions
Types of post-critical behaviour
Technical theory of beams
Static-kinematic duality for the straight beams
Differential equation of the elastic line
Notable displacements and rotations in elementary schemes
Statically indeterminate structures: method of forces
Direct method: congruence equations
Continuous beams
Plane frames
Structural symmetry
Inelastic constraints: theory and examples
Elastic constraints: theory and examples
Thermal distortions: theory and examples
Principle of Virtual Work for the solution of beam systems
Application of the principle to elastic beams
Determination of elastic displacements in statically determinate structures
Resolution of structures having one or more degrees of static indeterminacy
Muller-Breslau's equations- influence coefficients |
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Textes |
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The texts for reference to follow the video lectures are as follows
•A. Carpinteri, Scienza delle Costruzioni. Vol.I-II, Pitagora editrice.
•A. Sollazzo et al., Scienza delle Costruzioni. Vol.I-II-III, Edizioni UTET.
•F. dell’Isola, L. Placidi, Esercizi e complementi di Scienza delle costruzioni. Vol.I. Matrici cinematiche e strutture isostatiche. Società editrice Esculapio, 2012.
Even the following texts are advisables
•U. Andreaus, Scienza delle Costruzioni. Vol. I, III, IV Editrice Esculapio.
•A. Bichara, - F. dell’Isola, Elementi di algebra tensoriale con applicazioni alla meccanica dei solidi. Editore: Esculapio |
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Entraînements |
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Classification of structures. Calculation of isostatic structures, determined and over-determined structures, calculation of stresses and principal stresses, calculation of the principal directions, calculation of axial and tangential forces in sections, calculation of the elastic line. |
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Professeur |
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Bernardino Chiaia
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Enseignant vidéo |
Prof.
Ali Kezmane
- Université Mouloud Mammeri Tizi-Ouzou (Algeria)
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Liste des leçons |
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Ali Kezmane
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Ali Kezmane
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Ali Kezmane
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Ali Kezmane
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Ali Kezmane
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Ali Kezmane
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Ali Kezmane
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Ali Kezmane
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Ali Kezmane
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Ali Kezmane
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Ali Kezmane
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Ali Kezmane
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Ali Kezmane
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Ali Kezmane
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Ali Kezmane
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Ali Kezmane
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