Architectural Sciences

1. Introductory notions: basic concepts of mechanics, physical quantities, dimensional equations, vectors, and elements of linear algebra. 2. Discrete mechanical systems and rigid beams: notion of a rigid body. 2.1 Kinematics: definitions and assumptions; linearized kinematics for the rigid body and for systems of rigid bodies; kinematic performance of constraints; kinematic analysis of the constrained rigid body and of systems; kinematic matrix and kinematic classification. 2.2 Statics: definitions; forces, moments, and systems of forces; cardinal equations of statics; static performance of constraints; static analysis of the constrained rigid body and of systems of rigid bodies; static matrix and static classification. 2.3 Static–kinematic duality: Principle of Virtual Work. 3. The structural beam element: 3.1 Stress resultants: variation laws of stress resultants and construction of the corresponding diagrams for isostatic beam systems. 3.2 Trusses: definitions, classification, method of joints, Ritter’s method of sections. 4. One-dimensional elastic beams: 4.1 Kinematics: geometry, displacements and strains, implicit congruence equations, the kinematic problem for the planar beam. 4.2 Statics: indefinite equilibrium equations, the static problem for the planar beam. 4.3 Static–kinematic duality: Principle of Virtual Work, general displacement formula. 4.4 Constitutive material behavior: uniaxial tests, elastic behavior, plastic behavior, response to thermal variations, constitutive law of the elastic beam. 4.5 The elastic problem: Euler–Bernoulli beam, equation of the elastic line, solution of hyperstatic systems using the displacement method. 5. Geometry of areas: area, centroid, static and inertia moments, principal moments of inertia, special cases. 6. Elastic instability. Two weeks prior to the start of classes, access to the course’s Google Classroom site will be made available. This platform, in addition to providing all relevant information about the course, will be used to share teaching materials and to communicate with students.

Prior knowledge of the topics covered in the first-year course Istituzioni di Matematica I is required. In particular, students are expected to have a solid understanding of matrices and vectors, operations involving matrices and vectors, elements of linear algebra, and systems of linear equations. At the beginning of the course, a review of the main mathematical tools necessary for addressing the topics will be provided, so that students may fill any specific or general gaps in their background.

Il docente alla fine di ogni lezione fornirà delle dispense sugli argomenti trattati. Per un approfondimento degli argomenti trattati si riportano sotto dei possibili libri. - D. Capecchi, M. De Angelis, V. Sepe, Cinematica Piana dei Corpi Rigidi, CISU, Roma, 2005. - D. Capecchi, M. De Angelis, L. Sorrentino, Statica Piana dei Corpi Rigidi, CISU, Roma, 2008. - D. Capecchi, Teoria Tecnica della Trave Deformabile, CISU, Roma, 2007. Alternativamente ai tre libri riportati sopra: - Scienza Delle Costruzioni, Paolo Casini e Marcello Vasta, CittàStudi, 2008. - Statica - Un'introduzione alla meccanica delle strutture, Davide Bernardini, CittàStudi, 2009. (link sotto una versione draft)

Attendance is not compulsory. However, the highest possible level of participation is strongly encouraged.

The examination consists of a practical component, to be carried out in written form, and a theoretical component, to be taken partly in written form and partly orally, or entirely in oral form. Towards the end of October or during the first week of November, students may take the first mid-term examination (esonero) on Topics 1 and 2 listed in the “Program” section. The esonero consists of both a practical and a theoretical test, both in written form. Students who obtain a grade of at least 18/30 in both the practical and theoretical parts will be exempted from Topics 1 and 2 in subsequent examinations. On the last day of classes, it will be possible to take the second mid-term examination (only for those who have successfully completed the first mid-term examination in the practical part) on the remaining topics (practical part in written form), or to repeat/take the first esonero. Students who successfully complete both mid-term examinations will be required to take only an oral examination on the remaining topics during the official winter examination sessions. Students who successfully complete only the first mid-term examination will be required, during the official examination sessions, to take a written practical test and an oral theoretical test. Finally, students who do not pass or do not take the mid-term examinations may sit for the full examination during the official sessions, consisting of a written practical test and an oral theoretical test. Upon completion of all examinations, a separate grade will be assigned for the practical component and for the theoretical component. Both grades, expressed out of 30, will be calculated as the weighted average of the marks obtained in the first part (weight 0.4) and the second part (weight 0.6) of the program. The final grade will be the arithmetic mean of the overall marks achieved in the practical and theoretical components. Candidates who achieve a final grade of 30/30 may, at the discretion of the examiner, be awarded cum laude through additional questions and/or exercises. The assessment methods for non-attending students do not differ from those for attending students. The content of the practical tests consists of types of exercises that will be extensively covered in class, with numerous examples made available on Classroom. The theoretical tests consist of questions and proofs related to the topics addressed during the lectures. The assessment methods described above may be subject to change, which will in any case be discussed and agreed upon in class.

Under construction

Teaching will take place exclusively in person, except in cases where classrooms are unavailable due to graduation sessions or other institutional needs. Google Meet and Zoom may be used for office hours. Lectures will be primarily based on the use of the blackboard by the instructor for the explanation of topics. Theoretical presentations will be followed by practical sessions dedicated to exercises. Both the theoretical explanations and, in particular, the exercise sessions will be characterized by a high level of collective interaction. Students will also be invited, on a voluntary basis, to present and solve exercises previously prepared at home.

1. Introductory notions: basic concepts of mechanics, physical quantities, dimensional equations, vectors, elements of linear algebra. 2. Discrete mechanical systems and rigid beams: Notion of rigid body. 2.1 Kinematics: definition and hypothesis, linearized kinematics for rigid body and rigid body systems, kinematic performance of constraints, kinematic analysis of the constrained rigid body and systems, kinematic matrix and kinematic classification. 2.2 Statics: definition, forces, moments, systems of forces, cardinal equations of statics, performance statics of constraints, static analysis of the constrained rigid body and systems of rigid bodies, static matrix e static classification. 2.3 Static-kinematic duality: Theorem of virtual works. 3. The beam structural element: 3.1 Resultant forces: computation of the characteristics of the stress and skecthof the relative diagram for systems of isostatic beams. 3.2 The Trusses: Definitions, classification, node method, Ritter section method. 4. One-dimensional elastic beams: 4.1 Kinematics: geometry, displacements and deformations, implicit equations of congruence, the kinematic problem for the plane beam. 4.2 Statics: indefinite equilibrium equations, the static problem for the beam in the plane. 4.3 Static-kinematic duality: virtual works theorem, general formula of the displacement. 4.4 Constituent material: uniaxial tests, elastic behavior, plastic behavior, response to thermal variations, constitutive bond of the elastic beam. 4.5 The elastic problem: Euler-Bernoulli beam, equation of the elastic line, solution of hyperstatic systems with the displacement method. 5. Geometry of the areas: area, center of gravity, static and inertia moments, main moments of inertia, notable cases. 6. Elastic instability. Access to the course's Google Classroom site will be made available two weeks before the start of the lessons. This site will not only provide all the information related to the course but will also be used to share study materials and communicate with the students.

Knowledge of the topics covered in the course of Institutions of Mathematics I in the first year. In particular, consolidated knowledge of matrices and vectors, operations between matrices and vectors, elements of linear algebra and systems of linear equations are required. At the beginning of the course will be made references to the main mathematical tools necessary for the treatment of the topics in such a way that attending students can fill specific or general gaps.

The teacher at the end of each lesson will provide some notes on the illustrated topics. For an in-depth study of the topics covered, below are some possible books. D. Capecchi, M. De Angelis, V. Sepe, Cinematica Piana dei Corpi Rigidi, CISU, Roma, 2005. D. Capecchi, M. De Angelis, L. Sorrentino, Statica Piana dei Corpi Rigidi, CISU, Roma, 2008. D. Capecchi, Teoria Tecnica della Trave Deformabile, CISU, Roma, 2007. Alternatively to the three books above: Scienza Delle Costruzioni, Paolo Casini and Marcello Vasta, CittàStudi, 2008.

In presence and by remote.

Attendance to the course is not mandatory. However, the greatest possible attendance is required.

The exam consists of a practical part to be performed in written form and a theoretical part to be performed in part in written form and in part in oral form, or entirely in oral form. Around the end of october or the first week of November, students can take a first partial test (exemption) on topics 1 and 2 listed in the tab "Program". The test consists of a practical test and a theretical test both to be executed in written form. Who achieves a grade of at least 18/30 in the practical test and the theoretical test, respectively, will be exempted from topics 1 and 2 in subsequent tests. On the last day of class it is possible to take the second partial test (only those who have successfully taken the first partial test on the practical part) on the remaining topics (practical part in written form) or repeat/perform the first partial test. Those who successfully take both partial tests will have to take only one oral test on the remaining topics. Those who successfully take only the first partial test must take a written practical test and an oral theoretical test on the official exam dates. Finally, for those who do not pass or do not perform the exemptions it is possible to take the entire exam on official dates by taking a written practical test and an oral theoretical test. After completing all the assessments, a grade will be assigned for the practical part and another for the theoretical part. Both scores, out of thirty, will be calculated as a weighted average of the grades obtained in the first part (weight 0.4) and the second part (weight 0.6) of the program. The final grade will be the arithmetic average of the total scores obtained in the practical and theoretical parts. Candidates who achieve a final grade of 30/30 will have the discretionary opportunity to earn honors through additional questions and/or exercises. The assessment methods for non-attending students do not differ from those for attending students. The contents of the practical tests consist in exercises that will be widely treated in class and of which many examples will be provided on the Classroom website. The theoretical tests consist of questions and demonstrations related to the topics that will be treated in the lessons. The methods of evaluation described above may be subject to changes that will be discussed and agreed in the classroom.

Teaching will take place exclusively in person, except in cases where classrooms are unavailable due to graduation sessions or other institutional events. Google Meet and Zoom platforms may be used for consultations. Lectures will primarily involve the instructor using the chalkboard to explain topics. The theoretical discussion will be followed by a practical part where exercises are performed. Both the theoretical explanations and especially the exercise sessions will be characterized by strong collective interaction. Students will also be asked to voluntarily complete exercises prepared at home.