De Serio, Fabiana (2017) Masonry structures modelled as assemblies of rigid blocks. [Tesi di dottorato]


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Item Type: Tesi di dottorato
Lingua: English
Title: Masonry structures modelled as assemblies of rigid blocks
De Serio,
Date: 10 April 2017
Number of Pages: 145
Institution: Università degli Studi di Napoli Federico II
Department: Strutture per l'Ingegneria e l'Architettura
Dottorato: Ingegneria strutturale, geotecnica e sismica
Ciclo di dottorato: 29
Coordinatore del Corso di dottorato:
Pasquino, MarioUNSPECIFIED
Angelillo, MaurizioUNSPECIFIED
Date: 10 April 2017
Number of Pages: 145
Uncontrolled Keywords: Masonry, unilateral materials, helical stairs, rigid blocks, settlements.
Settori scientifico-disciplinari del MIUR: Area 08 - Ingegneria civile e Architettura > ICAR/08 - Scienza delle costruzioni
Date Deposited: 25 Apr 2017 22:08
Last Modified: 13 Mar 2018 07:51
DOI: 10.6093/UNINA/FEDOA/11698


The broad topic of the present work is Statics and Kinematics of masonry structures made of monolithic blocks, that is rigid bodies submitted to unilateral constraints, loaded by external forces, and undergoing small displacements. Specifically, in this work, we study the effect, in term of internal forces, of specified loads, by using given settlements/eigenstrains to trigger special regimes of the internal forces. Although our main scope here is the analysis of masonry structures made of monolithic pieces, and whose blocks are not likely to break at their inside, the theory we use applies also to general masonry structures, such as those made of bricks or small stones. Such structures may actually fracture everywhere at their inside, forming rigid blocks in relative displacement among each other. If the partition of the structure is fixed in advance, we may search the displacement field u, which is a possible solution of a displacement type boundary value problem, by minimizing the potential energy of the loads, over the finite dimensional set of the rigid displacements of the blocks. Actually, the functional is linear in u, then, if the supports of the strain singularities, i.e. the potential fractures, are fixed in advance, the minimization of reduces to the minimization of a linear functional under linear unilateral and bilateral constraints. This simple theory, based essentially on Heyman’s model for masonry, is applied to cantilevered stairs, or, more precisely, to spiral stairs composed of monolithic steps with an open well. In the present work, a case study, the triple helical stair of the convent of San Domingos de Bonaval is analysed, by employing a discrete model. The convent of San Domingos de Bonaval, founded by St. Dominic de Guzman in 1219, is located in the countryside of San Domingos, in the Bonaval district of Santiago de Compostela. The majority of the buildings of the convent which are still standing, were built between the end of XVII and the beginning of XVIII centuries in Baroque style by Domingo de Andrade. A triple helical stair of outstanding beauty and structural boldness was also built by Andrade to connect the cloister with the stairs of the main building. This extraordinary triple helical staircase consists of three separate inter-woven coils, composed of 126 steps each. The three separate ramps lead to different stories and only one of them comes to the upper viewpoint. The steps are made of a whole stone piece of granite; they are built in into the outer cylindrical wall for a length of 0.3 m, and set in an inner stone rib. The steps do not apparently join (or even touch) each other but at their very end. A likely set of given settlements of the constraints is imposed on the structure, and the corresponding piecewise rigid displacement is found by minimizing the potential energy. Then the dual static problem is dealt with, by identifying the equilibrium of the individual steps and of the entire structure. The whole calculation procedure is carried out with the programming language Matlab. After a comparative analysis of the results, in particular with reference to the internal forces and internal moments diagrams (torsional and flexural moments, axial and shear forces) for all the steps, a possible explanation of the reason why such bold structure is standing safely, is given.


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