# STATICS

Academic year and teacher
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Versione italiana
2022/2023
Teacher
RAFFAELLA RIZZONI
Credits
6
Didactic period
Secondo Semestre
SSD
ICAR/08

#### Training objectives

The course introduces the basic concepts of the Structural Engineering, such as the determination of reactions, internal forces and deflections under static load conditions.
In particular, the course is intended to develop the ability to calculate internal forces and moments, to analyze the stress state of critical cross-sections and to calculate displacements and rotations at points of interest in a structure.

The principal objective of the course consists in providing the basis of the analysis of the state of stress in beams, systems of beams and continuous media.

The main acquired knowledge will be:

- modeling of planar rectilinear beams and of systems of beams,

- modeling of deformable elastic beams under the assumptions of the linearized theory,

- Cauchy’s theory for continuous media,

- the method of Mohr’s circle,

- the problem of the equilibrium of a continuous body,

- the fundamental loading cases of extension, bending, torsion, and flexure.

The basic acquired abilities (capacity of applying the acquired knowledge) will be:

- the analysis of the equilibrium problem of planar rectilinear beams and of systems of beams,

- the determination of reaction forces and internal stress in beams and in systems of beams statically determined,

- the calculation of displacements and rotations in system of beam in the presence of loads, distorsions and thermal loads,

- the graphic determination of principal stresses and their directions (for states of plane stress),

- the analysis of the stress state in critical cross-sections.

#### Prerequisites

Knowledge of basic elements of geometry, algebra and trigonometry usually taught in the high schools are mandatory together with the following concepts provided by the courses of “Analisi matematica (Mathematical Analysis)”, “Geometria e algebra (Geometry and Algebra)”, “Fisica generale I (General Physics I)” and “Meccanica razionale (Rational Mechanics)”: differential and integral calculus for functions of several variables, basic concepts of linear algebra, statics of a rigid body and geometry of masses.

#### Course programme

Subjects covered include:
- analisys of simple beams, continuous beams, frames, and trusses, both statically determinate (isostatic) and indeterminate (hyperstatic);
- the equation of the elastica;
- external and internal forces in continuum mechanics, balance of forces, the Cauchy stress tensor;
- Saint-Venant's theory for beams: centred axial force, flexure (bending moment), biaxial flexure, eccentric axial force, torsion, bending and shearing force.

#### Didactic methods

The course will include classroom lectures,
exercises and additional tutoring activities.
If necessary, the course and the tutoring activities could be delivered completely online, through video lessons shared on the Classroom platform and weekly meetings with Google Meet for clarifications and explanations about the video lessons.

#### Learning assessment procedures

The examination is divided into two parts, taking place on two different days.
The first part is a written test consisting of two assignments (maximum score for each assignement is 15/30): the first assignment is the internal stress determination of a statically determinate structure and its sizing; the second assignment is the stress analysis in a cross-section subjected to one of the fundamental loading cases of extension, bending, torsion, and flexure. Time at the student's disposal to complete the written test: 2 hours. The minimum passing grade is 18/30.

The second part consists in an oral exam, where the ability of linking different theoretical subjects related to the course content is evaluated. In case of crowded exam sessions, for organizational reasons the oral exam could be conducted in writing: in this case, the time available to answer the question is 30 minutes.

The final grade is the average of the grades obtained in the two parts. The minimum passing grade is 18/30.

#### Reference texts

Nunziante L., Gambarotta L., Tralli A., - Scienza delle Costruzioni - McGraw-Hill – 2013

Belluzzi O. - Scienza delle costruzioni - Zanichelli – 1989

Capurso M. - Lezioni di scienza delle costruzioni - Pitagora – 1971

Bigoni D., Di Tommaso A., Gei M., Laudiero F., Zaccaria D. - Geometria delle masse - Progetto Leonardo Bologna – 1995

Luongo A., Paolone A. - Scienza delle costruzioni - Casa Editrice Ambrosiana – 2004

Shigley J. E., Budynas R., Nisbett J.K., Progetto e Costruzione di Macchine - McGraw-Hill - 2014.

Angeli P., De Bona F. – Fondamenti di calcolo strutturale meccanico – Forum Edizioni – 2015.