Course teached as: B028591 - SCIENZA DELLE COSTRUZIONI 3-years First Cycle Degree (DM 270/04) in CIVIL, BUILDING AND ENVIRONMENTAL ENGINEERING Curriculum CIVILE
Teaching Language
Italian
Course Content
The aim of the Course is that to furnish a general methodology to analyze the statics of the sistems of beams (truss and framed structures), using the De Saint Venant model. Some aspects of the elastic stability of such structures and of the strenght of materials are also given. The language is that used in mathematics and in the continuum mechanics.
Slides PDF of the lessons are available on-line in the Moodle ambient of the course. Recordings of the lessons of the previous course (2021-2022) are also available. Books useful to improve the knowledge of the matter are listed below.
a) Fundamentals books (in Italian):
1. C. Borri, M. Betti, E. Marino. Lectures on Solid Mechanics, Firenze, FUP, 2008.
2. L. Galano, P.M. Mariano. Eserciziario di Meccanica delle strutture. Roma, CompoMat, 2011.
3. R. Baldacci. Scienza delle costruzioni, Torino, Vol. I (UTET, 1970), Vol. II (UTET, 1976).
b) Further books (in Italian):
4. P.M. Mariano, L. Galano, Fondamenti di Meccanica dei Solidi, Ed. Bollati Boringhieri, Torino, ISBN: 978-88-339-5893-4.
5. O. Belluzzi. Scienza delle costruzioni, Bologna, Zanichelli, 1970.
6. E. Benvenuto. La Scienza delle Costruzioni ed il suo sviluppo storico. Sansoni, 1981.
7. E. Viola. Scienza delle costruzioni, Bologna, Pitagora, 1992.
8. R. Camiciotti, A. Cecchi. Esercizi di Scienze delle Costruzioni, Firenze, Morelli, 1992.
9. L.C. Dell'Acqua. Meccanica delle strutture, Milano, McGraw-Hill libri Italia, 1992.
10. L. Gambarotta, L. Nunziante, A. Tralli. Scienza delle costruzioni, Milano, McGraw-Hill, 2003.
11. F. Angotti, A. Borri. Lezioni di scienza delle costruzioni, Roma, DEI, 2005.
Learning Objectives
The student will learn to resolve the hysostatic beam systems and carried out the safety verifications. The main principles concern the structural mechanics, the continuum mechanics, the elasticity, the aequilibrium stability.
Referring to Dublin 1 (knowledge and understanding) the student have to acquire the theoretical knowledges (proved during the examination) concerning the modelling of the systems of beams and the linear elasticity.
Referring to Dublin 2 (applying knowledge and understanding) the student have to acquire ability in applicatrion to real cases of the theoric concepts, for example the solution of truss systems, the calculus of displacements and the others main tppic of the program.
Referring to Dublin 2 (making judgements) the student have to acquire a self capacity of judgement in the more approriate choice of the method to resolve a problem in relation to the main topics treated in the Course.
Prerequisites
Follow the didactic organization. Important requirements to understand the lessons are good knowledgements of the main topics of the Courses of Mathematic Analysis I and II, Geometry, Physics I and II and Continuum Mechanics.
Teaching Methods
Lessons in the classroom. Explanation of esercises in the classroom on the different topics of the Course.
Further information
See the Moodle ambient (e-learning) activated for this Course and eventually see the same ambient related to the previous versions of the Course (in particular the previous version i.e. 2021-2022).
Type of Assessment
The exam consists in two parts: a written test and a oral examination. Both the tests have to be passed from the student.
a) Written test. The test can be passed by two different modes:
First mode.
The student can partecipate to the two intermediate tests during the period of the lessons (the second tests can also be fixed soon after the conclusion of the Course). These tests are reserved to the students following the lessons. Each test has a duration of about two hours. The average votation obtained in the two tests needs to be equal or greater of 18/30. In every case the student needs to obtain a minimum evaluation of 12/30 in each test. Both the tests needs to be sustained in the same year and in case in which a student passes these tests they maintain the validity to give access to the oral examination up to the begin of the Course of the following year. The students cannot use mobile phones during the tests and can read only published books not manuscript papers.
Second mode.
The student can sustain the written test in all the exam sessions in calendar. The test has a duration of about three hours and it is generally composed of 3 exercises regarding all the topics of the Course. The test is passed if the votation is greater or equal to 18/30. The validity to give access to the oral examination is limited to the oral test following the written part (after few days). The students cannot use mobile phones during the test and can read only published books not manuscript papers. If a student delived the elaborate automatically expired the validity of the previous tests eventually passed with the first mode.
b) Oral examination. This test consists in a interview to be sustained in one of the dates in calendar after have passed the written test. If a student passed the written test in the first mode can sustain two times the oral examination. After two failures the written test have to be repeated (some exceptions are possible according each time with the Professor). The interview regards all the topics of the Course (theory and exercises). If the votation of tye written tets is greater or equal to 25/30 the oral interview will be rather simple regarding only the theory and not the execises, in some particular cases the Professor could confirm the votation of the written test (in this case the student has to agree). The interview is passed with a votation of al least 18/30. The final votation of the exam will be based on both the tests (written and oral) with prevalence of the oral colloquium.
Sometimes the Professor can prolungate the oral session in two or more days (the so called post-sessions of the same exam). Generally will not be fixed dates beyond those in the official calendar of the School.
The written test is useful to verify: i) understanding the problems examined in the Course (Dublin 1), ii) capacity in applying the thoretical knowledgements (Dublin 2) ability in the choice of the correct method to resolve a problem among the different alternativers (Dublin 3), iv) ability in communication skills (Dublin v) capacity in learning the basic topics of the Course, learning skills (Dublin 5).
The oral examination is useful to verify: i) the level of knowlesdge acquired in the lessons (Dublin 1), ii) the reached level in exposing, for example, the methods to resolve the plane trussed systems or the solution of the De Saint Venant's problem (Dublin 2), iii) autonomy in judgement (Dublin 3) in the choice of the most correct approach to resolve a problem considering the simplified hypotheses, the physical meaning of the single quantities and the obtained level of approximation of the results. Further scopes of the oral examination are: capacity of explain to the Professor the topics requested in the proposed questions (Dublin 4) and capacity in learning the theoretical aspects of the Course (Dublin 5).
Course program
A. ELASTIC CONTINUUM MECHANICS
Constitutive laws (elastic solids) and energetic theorems.
Hooke's law: hyperlelastic and linear elastic materials; hisotrophy. Lamè moduli (Young modulus and Poisson ratio). Principal axes of stress and strrain. Elastic problem in the Navier and Beltrami-Michell formulations. Deformation energy. Clapeyron and Betti theorems. Castigliano theorem. Kirchhoff theorem. The superposition of the effects principle.
Theorem of the virtual work in the direct and the inverse formulations, vorious cases.
De Saint Venant's problem. Body, loads, contraints and stress state. Inner forces, the De Saint Venant's principle.
Particular cases:
• Axial force alone, main results.
• Simple bending: main results.
• Axial force and bending: main results.
• Torque and shear, Bredt and Jourawsky formulae.
B. ELASTIC BEAM MECHANICS
Static of beams and more complex system of beams. Hysostatic systems.
External loads and relative models, the inner forces.
External and internal constraints, statics and kynematics of the systems of beams. Calculus of the constraint reactions. Inner forced diagrams, equilibrium equations. Calculus of displacements and rotations in particulr point of a beam (simple cases). The Thymoshenko and the Bernoully beams, differential equations and boundary conditions.
Hysostatic truss systems.
Calculus of the axial forces in the members, equilibrium of the nodes, method of the Ritter's sections. Dispacements of the nodes by the TVW.
Geometry of areas. The lessons are referred to plane areas.
Barycenter, static moments, second order moments, the Huygens-Steiner's theorem. The inertia tensor. The central ellypse of inertial (Culmann) and associated properties. Bulk of inertia.
C. STRENGTH OF MATERIALS
Fundamentals theories. Crisis, strength and safety conditions. Allowable stresses criterion. Von Mises criterio, particular cases. Other criteria (Galileo, Navier, Tresca, Beltrami.
D. ELASTIC STABILITY
Critical load; structures with cioncentrated elasticity and the Eulero's lamina. Eulero's formula. Safety check. Beam slenderness.
During the lessons will be developed some exercises related to the main topics.
Sustainable Development Goals 2030
This Course is part of the ONU 2030 agenda related to the Sustinable Development.