( english version )
Advanced structural mechanics ( 6 CFU )
Prof. Sabrina Vantadori
          E-mail. sabrina.vantadori@unipr.it

Finalità
To present basic concepts and tools for structural design, with reference to the theory of one-dimensional structures (cables and beams) and two-dimensional structures (plates and shells).

Programma
(1) Composition of coplanar forces
Resultant of coplanar forces : the funicular polygon
- Theorem of Culmann
- The funicular polygon for three points
Resultant of distributed coplanar forces: the funicular curve
- Equation of the funicular curve for a given distributed loading

(2) Static response of cables
- Introduction
- Cables under significant tension
- Cables under low tension

(3) The influence lines for statically determinate elastic frames (beam systems)
- Fundamentals
- Use of the influence lines

(4) Plane stress and plane strain states
Plane stress state
- Formulation: Stress function or Airy function
- Simple cases related to rectangular plates
- Cantilever beam with a rectangular cross section
- Supported beam with a rectangular cross section
Plane strain state
- Formulation

Plane stress and stain state for solids of revolution
- Formulation
- Thick cylindrical vessel
- Circular hole in a plate subjected to tension
- Concentrated force acting on the edge of an elastic half-plane

(5) Bending of plates
Le piastre di forma qualsiasi
- Fundamentals: the Sophie Germain-Lagrange hypothesis
- Components of displacements, strains, stresses; internal reaction characteristics
- Differential equation of the elastic surface (or differential equation of Germain-Lagrange)
- Boundary conditions
- Moments with reference to a point
- Finite difference method: approximate solutions for rectangular plates

Rectangular plate simply supported to the boundary
- Navier solution
- Lévy solution

Circular axisymmetric plate
- Circular plate simply supported to the boundary
- Circular plate fixed to the boundary

(6) Shells of revolution
- Introduction
- Gli sforzi interni nelle lastre curve di rivoluzione: membrane regime
- Gli sforzi interni nelle lastre curve di rivoluzione: bending regime

Attività d'esercitazione
Theory supported by exercises.

Modalità d'esame
Oral examination.

Propedeuticità
Analisi A-B, Analisi C, Geometria, Meccanica Razionale, Scienza delle Costruzioni A-B (Structural Mechanics A-B).

Testi consigliati
O.Belluzzi “Scienza delle Costruzioni” Vol.I e Vol.III, Zanichelli, Bologna.
Al.Carpinteri “Scienza delle Costruzioni” Vol.II, Pitagora Editrice, Bologna.
L. Corradi dell’Acqua “Meccanica delle strutture” Vol.I e Vol.II, McGraw-Hill, Milano.
E. Giangreco. Teoria e Tecnica delle Costruzioni. Vol.III, Liguori Editore, Napoli.
P. Pozzati. Teoria e Tecnica delle Strutture. Vol.II, UTET, Torino.
E.Viola“ Esercitazioni di Scienza delle Costruzioni/1. Pitagora Editrice, Bologna.

 
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