STATICS
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- Versione italiana
- Academic year
- 2018/2019
- 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 principle of virtual works for beams;
- 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. Learning assessment procedures
- The examination is divided into two parts, taking place on two different days.
The first part consists of a written exercise on the internal stress determination of a statically determinate structure and on the calculation of displacements or rotations also in the presence of distorsions or thermal loads.
The second part consists in a written exercise on
the stress analysis in a cross-section subjectto one of the fundamental loading cases of extension, bending, torsion, and flexure and in an oral section, where the ability of linking different theoretical subjects related to the course content is evaluated.
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.
