FONDAMENTI DI MECCANICA E STATICA

The module of Statics aims at delivering students the basic knowledge of the mechanics of structures, in view of the future courses of Mechanics of Structures and Design of Structures.

In particular, as shown below in the contents of the course, after dealing with the basic topics regarding the equilibrium, the statics and kinematics of rigid bodies, several plane structural typologies subjected to forces were analyzed (beams, frames, articulated systems, arches).

Such structures will be classified, characterized on the basis of a kinematic analysis, and the reactions and the force on the structure will be obtained.

Finally, a part of the course will be devoted to topics which will be applied in future courses with reference to the stress and strain analyses. In particular, the geometric properties of plane figures will be inferred.

The required prerequisites are the knowledge of mathematical concepts already delivered during the first year of the course, and within the module of physics of the same course. Other concepts, already faced in the module physics are restated within a different light, e.g. vectors. Some courses of the first year are preparatory for the course.

Polygon of forces, decomposition of a force along two assigned directions, definition of moment, resultant force and moment of a system of forces, equivalent system of forces, central axis, funicular polygon.

2.Cardinal equations of the statics (A. Greco, Scienza delle Costruzioni, Aracne Editrice, 2012)

Definition of rigid body; the principles of dynamics; equilibrium with respect to translation and rotation, graphic method, analytical and graphic applications.

3.Statics and kinematics of restrained rigid bodies (A. Greco, Scienza delle Costruzioni, Aracne Editrice, 2012)

Definition of restraint; static and kinematic characterization of external restraints; kinematics of rigid bodies; absolute centre of rotation; statically determined, statically indetermined and ill-conditioned systems; graphic and analytical evaluation of reactions for statically determined rigid bodies, uniaxial problems, bi-dimensional problems, forces, indefinite equilibrium equations, static and kinematic characterization of internal restraints, articulated systems, internal reactions, equilibrium of articulated systems, graphic method, symmetric systems, kinematic analysis of articulated systems, virtual displacement, relative centre of rotation, kinematic chains, Chasles and Kennedy's theorems, static-kinematic duality, virtual work principle for rigid bodies, computation of reaction and forces with the virtual work principle, applications.

4.Statically determined structural typologies (A. Greco, Scienza delle Costruzioni, Aracne Editrice, 2012)

Truss systems; node equilibrium method, Ritter's section method, il metodo dell’equilibrio ai nodi; il metodo della sezione di Ritter; Gerber beams, arches, physical reality and structural modelling.

5.Geometry of areas (see the website of the course)

Center of gravity of discrete and continuous systems, graphic and analytical assessment, static moment, moment of inertia, Huygens's theorem, principal axes of inertia, central ellipse of inertia, pole and anipole with respect to the central ellipse of inertial, central core or inertia, application to common sections.

1) J.L. Meriam, L.G. Kraige Statics (7th edition), Wiley

2) A. Greco, Scienza delle Costruzioni, Aracne Editrice, 2012

3) E. Viola. Esercitazioni di scienza delle costruzioni – vol.1: strutture isostatiche e geometria delle masse. Pitagora, 1977.

The prerequisites required to students are the basic notions of mathematical analysis, already acquired during the first year of studies.

Attendance is strongly recommended.

The main topics of the course are the following.
1) Physical quantities, their measurement and related errors.
2) Vector calculus.
3) Kinematics of the mass point.
4) Concept of momentum.
5) The forces.
6) Angular momentum.
7) Conservation principles.
8) Modeling (extremely simplified) of some physical phenomena of applicative interest.

Any university-level physics text.
The teacher will provide students with copies of their notes dictated during classes. The teacher will also provide notes with typical exercises which will also be presented in the classroom.

The exam consists in a simple written assignment (3 exercises, one of them being on the part of the course relating to vector calculus and mandatory for passing the exam), subsequently (unless exempted at the discretion of the teacher and with the agreement of the student) an oral test may be carried out which will aim to better ascertain the understanding of the topics covered in the course. The grade for the Physics module is overall for the written and oral parts.