Learning objectives
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).
Prerequisites
Analisi A-B, Analisi C, Geometria, Meccanica Razionale, Scienza delle Costruzioni A-B (Structural Mechanics A-B).
Course unit content
<p> (1) Composition of coplanar forces <br />
Resultant of coplanar forces : the funicular polygon <br />
- Theorem of Culmann <br />
- The funicular polygon for three points <br />
Resultant of distributed coplanar forces: the funicular curve <br />
- Equation of the funicular curve for a given distributed loading <br />
<br />
(2) Static response of cables <br />
- Introduction <br />
- Cables under significant tension <br />
- Cables under low tension <br />
<br />
(3) The influence lines for statically determinate elastic frames (beam systems) <br />
- Fundamentals <br />
- Use of the influence lines <br />
<br />
(4) Plane stress and plane strain states <br />
Plane stress state <br />
- Formulation: Stress function or Airy function <br />
- Simple cases related to rectangular plates <br />
- Cantilever beam with a rectangular cross section <br />
- Supported beam with a rectangular cross section <br />
Plane strain state <br />
- Formulation <br />
<br />
Plane stress and stain state for solids of revolution <br />
- Formulation <br />
- Thick cylindrical vessel <br />
- Circular hole in a plate subjected to tension <br />
- Concentrated force acting on the edge of an elastic half-plane <br />
<br />
(5) Bending of plates <br />
Le piastre di forma qualsiasi <br />
- Fundamentals: the Sophie Germain-Lagrange hypothesis <br />
- Components of displacements, strains, stresses; internal reaction characteristics <br />
- Differential equation of the elastic surface (or differential equation of Germain-Lagrange) <br />
- Boundary conditions <br />
- Moments with reference to a point <br />
- Finite difference method: approximate solutions for rectangular plates <br />
<br />
Rectangular plate simply supported to the boundary <br />
- Navier solution <br />
- Lévy solution <br />
<br />
Circular axisymmetric plate <br />
- Circular plate simply supported to the boundary <br />
- Circular plate fixed to the boundary <br />
<br />
(6) Shells of revolution <br />
- Introduction <br />
- Gli sforzi interni nelle lastre curve di rivoluzione: membrane regime <br />
- Gli sforzi interni nelle lastre curve di rivoluzione: bending regime <br />
</p>
<p>Theory supported by exercises.</p>
Full programme
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Bibliography
O.Belluzzi “Scienza delle Costruzioni” Vol.I e Vol.III, Zanichelli, Bologna. <br />
Al.Carpinteri “Scienza delle Costruzioni” Vol.II, Pitagora Editrice, Bologna. <br />
L. Corradi dell’Acqua “Meccanica delle strutture” Vol.I e Vol.II, McGraw-Hill, Milano. <br />
E. Giangreco. Teoria e Tecnica delle Costruzioni. Vol.III, Liguori Editore, Napoli. <br />
P. Pozzati. Teoria e Tecnica delle Strutture. Vol.II, UTET, Torino. <br />
E.Viola“ Esercitazioni di Scienza delle Costruzioni/1. Pitagora Editrice, Bologna. <br />
Teaching methods
Oral examination.
Assessment methods and criteria
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Other information
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