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MOOC Massive Open Online Courses (Ακαδημαϊκό έτος 2014/2015)

Scienza delle Costruzioni


Πιστώσεις: 9
Γλώσσα περιεχομένου:Γαλλικά
Περιγραφή μαθήματος
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.).
Προϋποθέσεις
To pass the exam of Structural mechanics it is necessary also to pass the exam of statics and dynamics of mechanical systems.
Στόχοι
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.
Πρόγραμμα
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
Βιβλίο
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
Εργασίες
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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