Purpose of the course is to present the fundamental concepts of static and dynamic stability of long-span and high-rise structures. In the introductory part of the course, the basic subjects of the buckling instability are presented for rectilinear elastic beams, frames, plates, and shells. The second part of the program is devoted to roofing and bridge structures, with particular emphasis on the phenomena of snap-through and flutter, respectively. In the third and last part of the program, statics, dynamics, and stability of tall buildings are dealt with, with particular emphasis on the structural behaviour of closed and open thin-walled vertical elements (external tubes and internal cores). Vlasov theory is widely recalled as a completion of Saint Venant torsion theory. The historical development of the different structural typologies (roofing structures, bridges, tall buildings) is also illustrated in the course with the related stability aspects.

The course has the scope of providing to the students all the conceptual elements and the tools, which are necessary to face the stability problems, in both the static and dynamic regimes, and in the cases of slender, thin, or shallow structures.

Fundamental notions from the basic mathematical courses (Analysis 1 and 2, Geometry, Analytical Mechanics, Numerical Methods: Solution of ordinary and partial differential equations, eigenvalue/eigenvector problems; Statics, kinematics and dynamics of rigid bodies) and engineering courses (Structural Mechanics, Theory of Structures: Study of isostatic and statically indeterminate structures; Static, kinematic, and constitutive equations for beams, arches, plates, shells, Finite Element Method) are required.

The program of the course is subdivided into the following topics: (1) Buckling of discrete mechanical systems: Rigid bars with elastic springs; Matrix of geometric stiffness (2) Buckling of rectilinear elastic beams: Euler problem; Different kinematic and static boundary conditions; Buckling of plane frames (3) Buckling of elastic plates and lateral-torsional instability (Prandtl problem) (4) Buckling of elastic rings and thin cylinders subjected to normal external pressure; Buckling of elastic arches and shells subjected to vertical loads (5) Roofing shell or space structures: Historical and typological aspects; Shallowness and snap-through instability (6) Long-span bridges: Arch, cable-stayed, suspension typologies; Historical aspects (7) Dynamics and stability: Conservative loads; Interaction between resonance and buckling (8) Dynamics and stability: Nonconservative follower loads; Aero-elastic instability (Flutter) (9) High-rise buildings: Historical and typological aspects; General Algorithm (10) Torsion of thin-walled open-section cores: Vlasov theory (11) Distribution of the external actions between the different vertical elements: Capurso‘s method (12) Dynamics and stability of high-rise buildings

The theoretical classes are followed by practical exercises carried out in the Computational Laboratories. In such practical classes, numerical methods are applied for the solution of the problems already treated from an analytical point of view during the theoretical classes. Commercial finite element codes as well as software developed ad-hoc within the research activity are provided by the teacher.

All the slides shown during the lectures are available for regularly registered students on the course website. Books: - A. Carpinteri, “Structural Mechanics: A Unified Approach”, Chapman & Hall, London, 1997. - A. Carpinteri, “Advanced Structural Mechanics”, CRC Press, New York, 2017. - D.P. Billington, “The Tower and the Bridge: The New Art of Structural Engineering”, Princeton University Press, Princeton, 1985.

Modalità di esame: Prova orale obbligatoria;

Exam: Compulsory oral exam;

... The exam consists in an oral interview, during which the student replies to scientific questions. In this way, the level of preparation of the student is carefully assessed on both the theoretical and the practical aspects.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.

Modalità di esame: Prova orale obbligatoria;

The exam consists in an oral interview, during which the student replies to scientific questions. In this way, the level of preparation of the student is carefully assessed on both the theoretical and the practical aspects.

Modalità di esame: Prova orale obbligatoria;

The exam consists in an oral interview, during which the student replies to scientific questions. In this way, the level of preparation of the student is carefully assessed on both the theoretical and the practical aspects.