The course integrates the students' basic knowledge acquired during the Bachelor degree with fundamental aspects for the analysis and the design of repairing interventions of existing structures. Particular attention will be paid to the study of masonry buildings, as they mainly characterize the existing historical-architectural heritage, deepening the static behavior of structures such as towers, bridges, arches, vaults and domes. Structural failures will be interpreted on masonry structures for an effective planning of consolidation interventions, without however neglecting the intervention techniques on steel and reinforced concrete load-bearing structures. The course also involves the use of a commercial finite element software for the analysis of structural architecture examples directed to identify and understand peculiarities and critical issues of existing structures.

The course aims at providing the student the theoretical basis and the practical tools to critically address the structural analysis of existing structures (masonry, reinforced concrete and steel) and the design of repairing and strengthening interventions. Through guided exercises, the students acquire the ability to apply the methods of structural verification in order to evaluate the degree of structural safety of existing buildings.

Fundamentals of statics and mechanics of structures, fundamental notions about the verification of structural elements in steel and reinforced concrete.

Fundamentals of statics: graphic statics, funicular polygon, line of thrust Introduction to masonry: typological aspects and classification, materials, constitutive laws Arches: typological aspects, study of the rigid and the elastic arch Vaults and domes: typological aspects of vaults and domes, historical development; double curvature vaults; vaults of revolution; membranes and thin shells Study of existing masonry bridges Study of existing masonry towers Fundamentals of dynamics and seismic behavior of structures Criteria for the seismic design of reinforced concrete and steel structures, analysis of failure case histories Presentation and discussion of the current Italian standard for the design of structures Stability issues of existing structures, static instability in masonry walls, repairing and strengthening techniques Structural monitoring techniques for existing buildings Fundamentals of the finite element method: one-, two- and three-dimensional elements Use of a finite element method software for the design and verification of structures Assisted design project: the students analyze a case study with the support of the professor, by carrying out the analysis of the structural response by varying the input data (structural optimization) and developing the structural repairing intervention.

Approximately two third of the lectures are dedicated to the presentation of the theoretical basis for the analysis and testing of existing structures, whereas one third is dedicated to learn the use of practical tools and present practical applications of the methods. In this latter part, a project is assigned to the students, to be developed in groups, under the supervision and assistance of the professor.

Classnotes Ballio, G., Mazzolani, F. M. (1987) Strutture in acciaio sistemi strutturali - sicurezza e carichi - materiale - unioni e collegamenti - resistenza e stabilità, Hoepli, Milano Bathe K.-J. (1996) Finite Element Procedures, Prentice Hall Benvenuto, E. (1981) La Scienza delle Costruzioni ed il suo Sviluppo Storico, Sansoni, Firenze. Carpinteri A. (1997) Structural Mechanics: a unified approach, Chapman & Hall, London Como M. (2017) Statics of historic masonry constructions, Springer Fardis M.N. (2009) Seismic Design, Assessment and Retrofitting of Concrete Buildings, Springer Olivito R.S. (2009) Statica e stabilità delle costruzioni murarie, Pitagora, Bologna Mariani, M. (2006) Trattato sul consolidamento e restauro degli edifici in muratura, Voll. 1 e 2, DEI, Roma Nuove norme tecniche per le costruzioni, D.M. 17 gennaio 2018

Modalità di esame: Prova orale obbligatoria; Prova scritta su carta con videosorveglianza dei docenti; Elaborato progettuale in gruppo;

Aim of the exam is to ascertain that the student has assimilated all the presented topics and is able to apply theories and methods for the analysis of existing structures and the design of repairing and strengthening interventions. The exam is composed by a written test and the oral presentation of the report of a group project. The final written test consists of a paper-based written exam with open queries and exercises, with video surveillance by professors. It is intended to evaluate the comprehension of the background theory. It lasts about 90 minutes. It contributes to the definition of the final mark with a weight of 20/30. The oral examination is done remotely. It is intended to assess the full understanding of the topics covered by the group project assignments, and to verify the effective contribution of the student. It contributes to the definition of the final mark with a weight of 10/30.

Modalità di esame: Prova scritta (in aula); Prova orale obbligatoria; Prova scritta su carta con videosorveglianza dei docenti; Elaborato progettuale in gruppo;

Aim of the exam is to ascertain that the student has assimilated all the presented topics and is able to apply theories and methods for the analysis of existing structures and the design of repairing and strengthening interventions. The exam is composed by a written test and the oral presentation of the report of a group project. The onsite written examination consists of open queries and exercises. The online written test consists of a paper-based written exam with open queries and exercises, with video surveillance by professors. The written test, in both modalities, is intended to evaluate the comprehension of the background theory. It lasts about 90 minutes. It contributes to the definition of the final mark with a weight of 20/30. The oral examination is done either onsite or remotely. It is intended to assess the full understanding of the topics covered by the group project assignments, and to verify the effective contribution of the student. It contributes to the definition of the final mark with a weight of 10/30.