Unit RATIONAL AND STATISTICAL MECHANICS
- Course
- Building engineering and architecture
- Study-unit Code
- GP003199
- Curriculum
- In all curricula
- Teacher
- Emanuela Speranzini
- CFU
- 10
- Course Regulation
- Coorte 2018
- Offered
- 2019/20
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa integrata
RATIONAL MECHANICS
| Code | GP003211 |
|---|---|
| CFU | 5 |
| Teacher | Maria Cesarina Salvatori |
| Teachers |
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| Hours |
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| Learning activities | Base |
| Area | Discipline matematiche per l'architettura |
| Academic discipline | MAT/07 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | Italian |
| Contents | Vectorial Calculus. The Kinematic of Rigid Body Relative Kinematics. Constrained Systems. Centre of Mass. Moment of Inertia. Force, Work, Potential. Laws of Mechanics. Statics. Dynamics. Lagrange Equations. |
| Reference texts | T. Ruggeri: Richiami di Calcolo Vettoriale e Matriciale. - Pitagora Editrice Bologna. P. Biscari, T. Ruggeri, G. Saccomandi, M.Vianello : Meccanica Razionale. - Spinger. |
| Educational objectives | The goal of this course is to provide the students with an introduction to the statics and the dynamics of the rigid body as well as of the holonomic systems using the principle of virtual work and the Lagrange Equations respectively . |
| Prerequisites | Calculus level I and II, geometry I. |
| Teaching methods | Lectures on all subjects of the course and Exercices in the classroom. |
| Other information | Yor are recommanded to attend the lectures. The lectures will be held at the department at in Via Goffredo Duranti 06125 Perugia. A tutor is available by appointment at mariacesarina.salvatori@unipg.it |
| Learning verification modality | The oral examination consists on an interview about 2/3 arguments treated during the course. This allows to verify the ability of knowledge and understanding, the ability to apply the acquired skills, the ability to display and learn. Operating time up to 30-40 minutes. |
| Extended program | Vectorial Calculus: dot product, cross product, scalar triple product, vectorial triple product. Applied vectors. Moment of a vector about a point. Moment of a vector about an axis. Couples. Equivalence of systems of vectors. The Kinematic of the Rigid Body: rigid configurations. Euler angles. Angular velocity. Poisson's formulas. Rigid motion. Mozzi's Theorem. Relative Kinematics: Galileo's Theorem. Coriolis Theorem. Constrained Systems: virtual constraints, virtual displacement and virtual velocity. Rigid virtual displacement. Holonomic constraints. Degrres of freedom. Configurations space. Centre of Mass. Moment of Inertia. Force, Work, Potential: elementary work. Work of a force moving along a curve. Work of a system of forces acting on a rigid body. Conservative forces. Laws of Mechanics: Princilples of Mechanics. Statics: Equation of statics, Equilibrium positions of a rigid body and of an holonomic system. The priciple of virtual works. The dynamics of the rigid body. |
STATICS
| Code | GP003210 |
|---|---|
| CFU | 5 |
| Teacher | Emanuela Speranzini |
| Teachers |
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| Hours |
|
| Learning activities | Caratterizzante |
| Area | Analisi e progettazione strutturale per l'architettura |
| Academic discipline | ICAR/08 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | Italian |
| Contents | Rigid body. Beams and systems of beams with straight axis and curved-axis. -cinematic behaviour, static behaviour -equilibrium equations -graphic methods for the equilibrium of beams -diagrams of the axial force, shear force and bending moment. Truss beams. Principe of virtual work for rigid body. |
| Reference texts | Main book:“Statica –Fondamenti di meccanica strutturale” E. Guarenti, F. Buccino, E. Garavaglia, G. Novati, - Mac Graw Hill. Other suggested books: “Lezioni di Scienza delle Costruzioni”, G. Menditto, - Pitagora “Esercitazioni di Scienza delle Costruzioni”, E. Viola – Pitagora – vol.1 |
| Educational objectives | The main objective is to give students the basis for dealing with the study the structural systems which consist of straight and curved axis beams, in static equilibrium. The student will acquire theoretical and practical knowledge for the resolution of isostatic structures. The main skill will be the analysis of kinematic and static behavior of one-dimensional systems, the determination of the internal forces (axial force, shear force, and bending moment). |
| Prerequisites | The knowledge acquired at Analysis I, Physics and Geometry courses is necessary. |
| Teaching methods | Theoretical and practical lectures. Classroom exercises are planned so that students can check the level of learning they have achieved. |
| Learning verification modality | A written exam concerning the resolution of an isostatic structure (in the time of 2 hours) and a subsequent oral test on all the topics covered in the course. It is necessary to reach the vote of 18/30 for admission to the oral test. The completeness of the answer, the argumentative rigor and the ownership of language will be assessed. |
| Extended program | Rigid body. Finite and infinitesimal rigid displacements. Beams and systems of beams with straight axis and curved-axis: -types of support -types of loads -statically determinate beams: linear axis beams and curved beams -cinematic behaviour, static behaviour -equilibrium equations -graphic methods for the equilibrium of beams -diagrams of the axial force, shear force and bending moment |