Il Duomo di Milano : analisi dello stato di conservazione dell'abside

In the course of the master degree "Project and protection of the built heritage", for the thesis it was chosen to study with some degree of deepening, an architectural good of great value, such as the Milan Cathedral. In particular, it was chosen to understand the static structure of the Duomo's Bishop, the oldest part of the building and not particularly thorough in recent studies relating to this building, of such remarkable artistic and symbolic significance in the city in which it resides. The paper presented here intends to link different aspects: historical, architectural, geometric, structural, past damage, and predicting future damage. Here, in order to achieve the stated purpose, in particular, we strive in the static discipline to understand the observable degradations and disadvantages. Starting from the historical analysis, the construction of the building began in 1386 following the style of the Gothic bloom, but the events that characterized its construction are not limited to the chronology of events but also include formal debates on the most appropriate geometries A canvas cathedral important. Afterwards, a new three-dimensional digital geometric model, functional for static calculations, was rebuilt. Having only two-dimensional plants and sections generously provided by the Venerable Factory, it had to be derived from the geometries of the essential logical relationships. During this phase, problems of representation, such as those of the Gothic cruising times, were solved through a digital modeling program, without the aid of a laser pad. The method set out in the second chapter allows you to solve the problem more quickly and economically, with an approximation error that can be neglected. The method of limit analysis followed in the third chapter captures essential aspects of the structural typology and has the value of the synthesis view from the results. The developments of the limit analysis in the study of collapse states and collapse mechanisms also take into account the tendency to rigid particle kinematics and system mechanisms, which are related to observable cracks. The limits of the method are in the reduced attention given to two aspects: strength and deformability. Resistance can be studied with more modern methods of construction science and technique, displacements and deformations of the deformable continuous important for slim structures are also subject to more in-depth studies. Finally, the method does not address problems of degradation of materials and viscous sliding phenomena (creeps), the elaborate is therefore the basis for a wider future intervention. The whole process of analysis is an algorithm, a procedure that tries to solve a certain problem, which in this case is to understand the static situation of the Milan Cathedral's apse, applying a number of elementary steps, following a precise order. The instructions are the algebraic formulas needed to find the weights and forces within the structure. Thus, the algorithm implemented within a programmed code with a computer is implemented: Matlab. By implementing the algorithm, or rather, the algorithms explained in the chapter can get the static response given by the program, it is also easy to modify some variables to get the static response of the structure in case of alteration of certain situations. In the final chapter, direct visual observation will confirm the static analysis performed. The historical disadvantages and disadvantages observed, together with the data provided in the archives of the Venerable Factory, are examined about the ongoing measurements of pylon movements. In the course of the master degree "Project and protection of the built heritage", for the thesis it was chosen to study with some degree of deepening, an architectural good of great value, such as the Milan Cathedral. In particular, it was chosen to understand the static structure of the Duomo's Bishop, the oldest part of the building and not particularly thorough in recent studies relating to this building, of such remarkable artistic and symbolic significance in the city in which it resides. The paper presented here intends to link different aspects: historical, architectural, geometric, structural, past damage, and predicting future damage. Here, in order to achieve the stated purpose, in particular, we strive in the static discipline to understand the observable degradations and disadvantages. Starting from the historical analysis, the construction of the building began in 1386 following the style of the Gothic bloom, but the events that characterized its construction are not limited to the chronology of events but also include formal debates on the most appropriate geometries A canvas cathedral important. Afterwards, a new three-dimensional digital geometric model, functional for static calculations, was rebuilt. Having only two-dimensional plants and sections generously provided by the Venerable Factory, it had to be derived from the geometries of the essential logical relationships. During this phase, problems of representation, such as those of the Gothic cruising times, were solved through a digital modeling program, without the aid of a laser pad. The method set out in the second chapter allows you to solve the problem more quickly and economically, with an approximation error that can be neglected. The method of limit analysis followed in the third chapter captures essential aspects of the structural typology and has the value of the synthesis view from the results. The developments of the limit analysis in the study of collapse states and collapse mechanisms also take into account the tendency to rigid particle kinematics and system mechanisms, which are related to observable cracks. The limits of the method are in the reduced attention given to two aspects: strength and deformability. Resistance can be studied with more modern methods of construction science and technique, displacements and deformations of the deformable continuous important for slim structures are also subject to more in-depth studies. Finally, the method does not address problems of degradation of materials and viscous sliding phenomena (creeps), the elaborate is therefore the basis for a wider future intervention. The whole process of analysis is an algorithm, a procedure that tries to solve a certain problem, which in this case is to understand the static situation of the Milan Cathedral's apse, applying a number of elementary steps, following a precise order. The instructions are the algebraic formulas needed to find the weights and forces within the structure. Thus, the algorithm implemented within a programmed code with a computer is implemented: Matlab. By implementing the algorithm, or rather, the algorithms explained in the chapter can get the static response given by the program, it is also easy to modify some variables to get the static response of the structure in case of alteration of certain situations. In the final chapter, direct visual observation will confirm the static analysis performed. The historical disadvantages and disadvantages observed, together with the data provided in the archives of the Venerable Factory, are examined about the ongoing measurements of pylon movements. In the course of the master degree "Project and protection of the built heritage", for the thesis it was chosen to study with some degree of deepening, an architectural good of great value, such as the Milan Cathedral. In particular, it was chosen to understand the static structure of the Duomo's Bishop, the oldest part of the building and not particularly thorough in recent studies relating to this building, of such remarkable artistic and symbolic significance in the city in which it resides. The paper presented here intends to link different aspects: historical, architectural, geometric, structural, past damage, and predicting future damage. Here, in order to achieve the stated purpose, in particular, we strive in the static discipline to understand the observable degradations and disadvantages. Starting from the historical analysis, the construction of the building began in 1386 following the style of the Gothic bloom, but the events that characterized its construction are not limited to the chronology of events but also include formal debates on the most appropriate geometries A canvas cathedral important. Afterwards, a new three-dimensional digital geometric model, functional for static calculations, was rebuilt. Having only two-dimensional plants and sections generously provided by the Venerable Factory, it had to be derived from the geometries of the essential logical relationships. During this phase, problems of representation, such as those of the Gothic cruising times, were solved through a digital modeling program, without the aid of a laser pad. The method set out in the second chapter allows you to solve the problem more quickly and economically, with an approximation error that can be neglected. The method of limit analysis followed in the third chapter captures essential aspects of the structural typology and has the value of the synthesis view from the results. The developments of the limit analysis in the study of collapse states and collapse mechanisms also take into account the tendency to rigid particle kinematics and system mechanisms, which are related to observable cracks. The limits of the method are in the reduced attention given to two aspects: strength and deformability. Resistance can be studied with more modern methods of construction science and technique, displacements and deformations of the deformable continuous important for slim structures are also subject to more in-depth studies. Finally, the method does not address problems of degradation of materials and viscous sliding phenomena (creeps), the elaborate is therefore the basis for a wider future intervention. The whole process of analysis is an algorithm, a procedure that tries to solve a certain problem, which in this case is to understand the static situation of the Milan Cathedral's apse, applying a number of elementary steps, following a precise order. The instructions are the algebraic formulas needed to find the weights and forces within the structure. Thus, the algorithm implemented within a programmed code with a computer is implemented: Matlab. By implementing the algorithm, or rather, the algorithms explained in the chapter can get the static response given by the program, it is also easy to modify some variables to get the static response of the structure in case of alteration of certain situations. In the final chapter, direct visual observation will confirm the static analysis performed. The historical disadvantages and disadvantages observed, together with the data provided in the archives of the Venerable Factory, are examined about the ongoing measurements of pylon movements. In the course of the master degree "Project and protection of the built heritage", for the thesis it was chosen to study with some degree of deepening, an architectural good of great value, such as the Milan Cathedral. In particular, it was chosen to understand the static structure of the Duomo's Bishop, the oldest part of the building and not particularly thorough in recent studies relating to this building, of such remarkable artistic and symbolic significance in the city in which it resides. The paper presented here intends to link different aspects: historical, architectural, geometric, structural, past damage, and predicting future damage. Here, in order to achieve the stated purpose, in particular, we strive in the static discipline to understand the observable degradations and disadvantages. Starting from the historical analysis, the construction of the building began in 1386 following the style of the Gothic bloom, but the events that characterized its construction are not limited to the chronology of events but also include formal debates on the most appropriate geometries A canvas cathedral important. Afterwards, a new three-dimensional digital geometric model, functional for static calculations, was rebuilt. Having only two-dimensional plants and sections generously provided by the Venerable Factory, it had to be derived from the geometries of the essential logical relationships. During this phase, problems of representation, such as those of the Gothic cruising times, were solved through a digital modeling program, without the aid of a laser pad. The method set out in the second chapter allows you to solve the problem more quickly and economically, with an approximation error that can be neglected. The method of limit analysis followed in the third chapter captures essential aspects of the structural typology and has the value of the synthesis view from the results. The developments of the limit analysis in the study of collapse states and collapse mechanisms also take into account the tendency to rigid particle kinematics and system mechanisms, which are related to observable cracks. The limits of the method are in the reduced attention given to two aspects: strength and deformability. Resistance can be studied with more modern methods of construction science and technique, displacements and deformations of the deformable continuous important for slim structures are also subject to more in-depth studies. Finally, the method does not address problems of degradation of materials and viscous sliding phenomena (creeps), the elaborate is therefore the basis for a wider future intervention. The whole process of analysis is an algorithm, a procedure that tries to solve a certain problem, which in this case is to understand the static situation of the Milan Cathedral's apse, applying a number of elementary steps, following a precise order. The instructions are the algebraic formulas needed to find the weights and forces within the structure. Thus, the algorithm implemented within a programmed code with a computer is implemented: Matlab. By implementing the algorithm, or rather, the algorithms explained in the chapter can get the static response given by the program, it is also easy to modify some variables to get the static response of the structure in case of alteration of certain situations. In the final chapter, direct visual observation will confirm the static analysis performed. The historical disadvantages and disadvantages observed, together with the data provided in the archives of the Venerable Factory, are examined about the ongoing measurements of pylon movements. /

Nell’ambito del corso di laurea magistrale “Progetto e tutela del patrimonio costruito”, per la tesi si è scelto di studiare con un certo grado di approfondimento, un bene architettonico di grande valore, quale il Duomo di Milano. In particolare si è scelto di comprendere la statica della struttura dell’Abside del Duomo, la parte più antica della costruzione e non particolarmente approfondita negli studi recenti relativi a tale edificio, di così notevole rilevanza storico artistica e simbolo della città in cui risiede. L’elaborato qui presentato intende collegare diversi aspetti: storico, architettonico, geometrico, strutturale, di danneggiamento passato e di previsione del danno futuro. Qui, per raggiungere lo scopo enunciato, in particolare ci si cimenta nella disciplina della statica per comprendere i degradi ed i dissesti osservabili. Si parte dall’analisi storica, la costruzione dell’edificio è iniziata nel 1386 seguendo lo stile del gotico fiorito, ma gli eventi che ne hanno caratterizzato l’edificazione non si limitano alla cronologia degli avvenimenti ma comprendono anche dibattiti formali sulle geometrie più adeguate per una cattedrale di tela importanza. In seguito è stata ricostruito un nuovo modello geometrico digitale tridimensionale, funzionale ai calcoli statici. Avendo solo piante e sezioni bidimensionali, generosamente fornite dalla Veneranda Fabbrica, si è dovuto ricavare dalle geometrie dei rapporti logici essenziali. Durante questa fase sono stati risolti problemi di rappresentazione, come quello delle volte a crociera gotiche, grazie ad un programma di modellazione digitale, senza l’ausilio di un rilievo laser. Il metodo esposto nel secondo capitolo permette di risolvere il problema in maniera più rapida ed economica, con un errore di approssimazione che può essere trascurato. Il metodo dell’analisi limite seguito nel terzo capitolo coglie aspetti essenziali della tipologia strutturale, ed ha il pregio della visione di sintesi data dai risultati. Gli sviluppi dell'analisi limite nello studio degli stati di cedimento e dei meccanismi di collasso prendono in considerazione anche la tendenza a cinematismi di parti rigide e meccanismi del sistema, che sono in relazione con le fessurazioni osservabili. I limiti del metodo sono nella ridotta attenzione data a due aspetti: la resistenza e la deformabilità. La resistenza può essere studiata con metodi più moderni della scienza e tecnica delle costruzioni, gli spostamenti e le deformazioni del continuo deformabile importanti per strutture snelle sono anch'essi oggetto di studi più approfonditi. Infine il metodo non affronta problemi di degrado dei materiali e di fenomeni di scorrimento viscoso (creep), l’elaborato si pone quindi come base per un più ampio intervento futuro. L’intero procedimento di analisi è un algoritmo, una procedura che tenta di risolvere un determinato problema, che in questo caso è comprendere la situazione statica dell’abside del Duomo di Milano, applicando un certo numero di passi elementari, seguendo un preciso ordine. Le istruzioni sono le formule algebriche necessarie a trovare i pesi e le forze all’interno della struttura. È stato implementato quindi l’algoritmo svolto all’interno di un codice programmato con un calcolatore: Matlab. Implementando l’algoritmo, o meglio, gli algoritmi spiegati nel capitolo è possibile ottenere la risposta statica data dal programma, è semplice inoltre modificare alcune variabili per ottenere la risposta statica della struttura in caso di alterazione di determinate situazioni. Nel capitolo conclusivo, l’osservazione visiva diretta confermerà l’analisi statica effettuata. Vengono esaminati i dissesti storici e i dissesti osservati, unitamente ai dati forniti dalle relazioni in Archivio della Veneranda Fabbrica circa le misurazioni in corso dei movimenti dei piloni.