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 2019
- Offered
- 2020/21
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa integrata
RATIONAL MECHANICS
| Code | GP003211 |
|---|---|
| CFU | 5 |
| Teacher | Giuseppe Saccomandi |
| Teachers |
|
| Hours |
|
| Learning activities | Base |
| Area | Discipline matematiche per l'architettura |
| Academic discipline | MAT/07 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | Italian |
| Contents | Classical Mechanics of Points and Rigid-Bodies with special emphasise on Statics |
| Reference texts | Biscari, P., Ruggeri, T., Saccomandi, G., & Vianello, M. (2015). Meccanica razionale (Vol. 93). Springer. |
| Educational objectives | The ability to solve problems about the statics of free and constrained systems. |
| Prerequisites | Calculus and general Physics. |
| Teaching methods | Classical |
| Other information | None |
| Learning verification modality | Written and oral examination |
| Extended program | Geometry, trigonometry and vector algebra: vector algebra in three dimensions using different bases, length, addition and multiplication of vectors, inner product and cross product. The properties of the inner product and the vector product, geometric and physical interpretations, rules of differentiation for vector functions, differentiation of coordinates and basis vectors in different coordinate systems. Curves, area elements, volume elements. Applications of statics and geometry: force, torque. The kinematics of particles in different coordinate systems, cartesian-, normal and tangential- as well as polar coordinates. The dynamics of particles: force, linear momentum, impulse, torque, angular momentum, angular impulse, Newton's laws. Particle systems, center of mass, Euler's law for the movement of the the center of mass. Mass flows, the rocket equation. Work and energy. Energy relations. Gradient. Accelerated reference frames. The development of the mechanics. Kepler's laws. Short introduction to oscillatory motion. Models for the motion of objects with applications. |
STATICS
| Code | GP003210 |
|---|---|
| CFU | 5 |
| Teacher | Emanuela Speranzini |
| Teachers |
|
| 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 -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 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: -types of support -types of loads -statically determinate beams: linear axis beams and curved beams -cinematic behaviour, static behaviour -equilibrium equations -diagrams of the axial force, shear force and bending moment |