Architecture exists where the world of ideas meets the world of materials. From its general scheme all the way to the joinery of the floorboards, the proposed building should serve a guiding idea. Otherwise, architecture is not architecture but simply functional construction. Theater exists within a similar framework, whereby the actor's work is a mundane manifestation of the elements extracted from the world of ideas, making it the perfect conduit to examine the reconciliation of these oppositions: the mundane and the ethereal, the quotidian and the philosophical, the earth and the heavens… By examining the dichotomous relationship between the tectonic and the stereotomic, the project proposed within these pages provides for a spatial experience that will aid its audience in shedding the entrapments of their daily lives as they proceed towards the auditorium to watch a play. As they move through the building, they will walk through six-foot thick brick walls of heavy stereotomy towards a lighter tectonic environment.  As they approach the architectonic auditorium, the horizon, which they could initially only see through small openings within the massive brick walls, becomes more prominent, reminding them of the spherical nature of our world and the existence of an entire universe outside of our frame of reference - a phenomenon which is symbolic of the world of ideas that provides us with theater and architecture. / Master of Architecture

Cette thèse vise à mieux comprendre l'influence de la coupe des pierres sur la résistance des arcs et des voûtes clavés en général, et des couvrements plans en particulier. L'étude historique et typologique des plates-bandes et des voûtes plates, à travers les exemples construits et les traités d'architecture et de coupe des pierres du XVIe au XVIIIe siècle, forme le préalable à l'étude mécanique de ces constructions. Les plates-bandes à joints en~X, les plates-bandes en fausse-coupe, et les voûtes plates d'Abeille sont étudiées en détail en raison de leur stéréotomie savante. Les règles géométriques utilisées pour l'appareillage des plates-bandes, d'une part par les architectes, et d'autre part par les appareilleurs et tailleurs de pierre, émergent de ce travail. Une extension de la méthode des réseaux de forces est proposée, pour tenir compte de l'appareil des voûtes, pour raffiner les réseaux, et pour intégrer rigoureusement les réseaux à la théorie du calcul à la rupture. Des stratégies de calcul pour la recherche des chargements extrêmes, dont la détermination fonde la faisabilité de la technique, sont proposées. Les études mécaniques conduites considèrent les arcs en plein-cintre et dômes hémisphériques, les plates-bandes et voûtes plates, et les voûtes hélicoïdales. Elles illustrent la précision de l'estimatif proposée pour le coefficient de sécurité géométrique, l'influence de la coupe des pierres pour les couvrements plans, et les possibilités et limites de l'application de la méthode des réseaux de forces à l'étude des constructions clavées / This work aims at a better understanding of the influence of stereotomy on the stability of stone-cut archs and vaults in general, and flat archs and flat vaults in particular. A study of the history and typology of flat archs and flat vaults, through the consideration of existing examples and treaties of architecture or stereotomy from 1500 to 1800, is a preambule to the mechanical study of these constructions. Flat archs with X-joints, flat archs en fausse-coupe, and Abeille's flat vaults are studied in detail because of their specific stereotomy. Geometric rules used to determine joint orientation, by architects on the one hand, and by stone masons on the other hand, emerge from this work. An extension of the force network method is presented, in order to take into account the vaults' stonework, to find new equilibrium solutions by refining networks, and to comply rigourously with the theory of yield calculus. Calculus strategies for the search of limit loads, whose determination is essential for the technique, are given. Mechanical studies are conducted on cylindrical archs and hemispherical domes, flat archs and flat vaults, and helicoidal vaults. They show the precision of the geometric safety factor estimate, the influence of stone cutting on flat archs and vaults, and the possibilities and limits of using the force networks method to study stone-cut vaults

Ce travail de thèse s'inscrit dans le contexte du développement de la robotique dans la construction. On s’intéresse ici à la construction robotisée de structures maçonnées complexes en ayant recours à de la vision artificielle. La construction sans cintre étant un enjeu important en ce qui concerne la productivité sur un chantier et la quantité de déchets produits, nous explorons, à cet effet, les possibilités qu'offre la rigidité en flexion inhérente aux maçonneries topologiquement autobloquantes. La génération de ces dernières, classique dans le cas plan, est généralisée ici à la conception de structures courbes, à partir de maillages de quadrangles plans et de manière paramétrique, grâce aux logiciels Rhinoceros 3D / Grasshopper. Pour cela, nous proposons un ensemble d'inégalités à respecter afin que la structure obtenue soit effectivement topologiquement autobloquante. Ces inégalités permettent, par ailleurs, d'introduire un résultat nouveau ; à savoir qu'il est possible d'avoir un assemblage de blocs dans lequel chacun des blocs est topologiquement bloqué en translation, mais un sous-ensemble — constitué de plusieurs de ces blocs — ne l'est pas. Un prototype de maçonnerie à topologie autobloquante est finalement conçu. Sa conception repose sur une découpe des joints d'inclinaison variable qui permet de le construire sans cintre. En parallèle, nous abordons des aspects de vision artificielle robuste pour un environnement chantier, environnement complexe dans lequel les capteurs peuvent subir des chocs, être salis ou déplacés accidentellement. Le problème est d'estimer la position relative d'un bloc de maçonnerie par rapport à un bras robot, à partir de simples caméras 2D ne nécessitant pas d'étape de calibration. Notre approche repose sur l'utilisation de réseaux de neurones convolutifs de classification, entraînés à partir de centaines de milliers d'images synthétiques de l’ensemble bras robot + bloc, présentant des variations aléatoires en terme de dimensions et positions du bloc, textures, éclairage, etc, et ce afin que le robot puisse apprendre à repérer le bloc sans trop de biais d’environnement. La génération de ces images est réalisée grâce à Unreal Engine 4. Cette méthode permet la localisation du bloc par rapport au robot avec une précision millimétrique, sans utiliser une seule image réelle pour la phase d'apprentissage ; ce qui constitue un avantage certain puisque l'acquisition de données représentatives pour l'apprentissage est un processus long et fastidieux. Nous avons également construit une base de données riche, constituée d’environ 12000 images réelles contenant un robot et un bloc précisément localisés, permettant d’évaluer quantitativement notre approche et de la rendre comparable aux approches alternatives. Un démonstrateur réel intégrant un bras ABB IRB 120, des blocs parallélépipédiques et trois webcams a été mis en place pour démontrer la faisabilité de la méthode / The context of this thesis work is the development of robotics in the construction industry. We explore the robotic construction of complex masonry structures with the help of computer vision. Construction without the use of formwork is an important issue in relation to both productivity on a construction site and the amount of waste generated. To this end, we study topological interlocking masonries and the possibilities they present. The design of this kind of masonry is standard for planar structures. We generalize it to the design of curved structures in a parametrical way, using PQ meshes and the softwares Rhinoceros 3D and Grasshopper. To achieve this, we introduce a set of inequalities to respect in order to have a topological interlocked structure. These inequalities allow us to present a new result. Namely, it is possible to have an assembly of blocks in which each block is interlocked in translation, while having a subset — composed of several of these blocks — that is not interlocked. We also present a prototype of topological interlocking masonry. Its design is based on variable inclination joints, allowing construction without formwork. In parallel, we are studying robust computer vision for unstructured environments like construction sites, in which sensors are vulnerable to dust or could be accidentally jostled. The goal is to estimate the relative pose (position + orientation) of a masonry block with respect to a robot, using only cheap cameras without the need for calibration. Our approach relies on a classification Convolutional Neural Network trained using hundreds of thousands of synthetically rendered scenes with a robot and a block, and randomized parameters such as block dimensions and poses, light, textures, etc, so that the robot can learn to locate the block without being influenced by the environment. The generation of these images is performed with Unreal Engine 4. This method allows us to estimate a block pose very accurately, with only millimetric errors, without using a single real image for training. This is a strong advantage since acquiring representative training data is a long and expensive process. We also built a new rich dataset of real robot images (about 12,000 images) with accurately localized blocks so that we can evaluate our approach and compare it to alternative approaches. A real demonstrator, including a ABB IRB 120 robot, cuboid blocks and three webcams was set up to prove the feasibility of the method

The current state of research on the design and construction of late Gothic vaults is principally based on the interpretation of sources, but rarely on surveys of existing vaults. In particular the idea for the criteria upon which the radii of the single ribs and arches were determined (so-called "principal arch"), is found to derive from sources dating from later periods when Gothic vaulting was no longer generally practised. In fact, this interpretation cannot be supported by geometric surveys on existing vaults: the plain contradiction to the actual geometric properties of some of the vaults studied so far have called for a critical revision of this interpretation. For investigating the design criteria and procedures starting from the built object, and also debating the methodological aspects of using the "building as source", a rewarding subject is the vault with curvilinear ribs in the "Hall of Arms" in the Albrechtsburg at Meissen (Germany), which was built by Jacob Heilmann in 1521. This is due to its ambitious design, high quality of execution and good state of preservation. A detailed survey of this structure is presented, discussing different aspects of the design, construction, and detailing, e.g.: Investigations on the geometrical concept of the vault by means of "reverse geometric engineering", on the background of the problem mentioned above. Further, the stone-cutting of the single members of the vault, which offers interesting aspects of standardization and its limits in nerves with double curvature: standardization in medieval constructions has been object of discussion, but not yet studied in the ambit of late Gothic vault construction. The question whether and how the vault surface was determined in the design, being the principle structural feature working as a shell structure; this is of particular interest as the relation between the rib system and the shell is complex and has consequences on the stone-cutting of the arches. The question how the design specifications for the single rib members could be derived from the general concept of the curves (clarified in the survey); the context to the graphic sources and technical prose related to late Gothic vault design and structural design. The aim is to understand the entire design process, the criteria of the decisions taken, their relation to the contemporary theory, and the communication process which took place for the creation of this extremely demanding structure.

The current state of research on the design and construction of late Gothic vaults is principally based on the interpretation of sources, but rarely on surveys of existing vaults. In particular the idea for the criteria upon which the radii of the single ribs and arches were determined (so-called "principal arch"), is found to derive from sources dating from later periods when Gothic vaulting was no longer generally practised. In fact, this interpretation cannot be supported by geometric surveys on existing vaults: the plain contradiction to the actual geometric properties of some of the vaults studied so far have called for a critical revision of this interpretation. For investigating the design criteria and procedures starting from the built object, and also debating the methodological aspects of using the "building as source", a rewarding subject is the vault with curvilinear ribs in the "Hall of Arms" in the Albrechtsburg at Meissen (Germany), which was built by Jacob Heilmann in 1521. This is due to its ambitious design, high quality of execution and good state of preservation. A detailed survey of this structure is presented, discussing different aspects of the design, construction, and detailing, e.g.: Investigations on the geometrical concept of the vault by means of "reverse geometric engineering", on the background of the problem mentioned above. Further, the stone-cutting of the single members of the vault, which offers interesting aspects of standardization and its limits in nerves with double curvature: standardization in medieval constructions has been object of discussion, but not yet studied in the ambit of late Gothic vault construction. The question whether and how the vault surface was determined in the design, being the principle structural feature working as a shell structure; this is of particular interest as the relation between the rib system and the shell is complex and has consequences on the stone-cutting of the arches. The question how the design specifications for the single rib members could be derived from the general concept of the curves (clarified in the survey); the context to the graphic sources and technical prose related to late Gothic vault design and structural design. The aim is to understand the entire design process, the criteria of the decisions taken, their relation to the contemporary theory, and the communication process which took place for the creation of this extremely demanding structure.

The ambitious late Gothic vaults created in the 15th and 16th centuries with their complex shape and complicated meshes of ribs soaring along spatial curves, were extremely demanding in their geometric design. This regards both the design of the whole structure, as also the design specifications for the single stone elements which were prefabricated and fit together on the building site with astonishing precision. In consequence, the particular character of these structures and their geometric features are intrinsically linked to the design routines and the geometric concepts used by the Master Builders. At present, these procedures and methods are not well understood, because they are not documented in original drawings, and because they differ in principle from the modern practice. In consequence, necessary works of repairing and restoring cannot recur to any information related to the original design. Moreover, understanding the characteristics of information transfer from the design to the execution, would cast a light on the information society in which these constructions were created. In several case studies, the geometric concepts of the intricate spatial curve systems of late Gothic vaults have been clarified on the basis of detailed surveys and geometrical analyses carried out on the built objects. On this background, also the existing sources such as historical design treatises could be re-interpreted. In a collaboration between the research group working on the design principles of late Gothic vaults at the Technische Universität Dresden, and expert stone masons specialized on historical working techniques and practical stereotomy at the Cathedral Workshop Œuvre Notre-Dame de Strasbourg, the phases of the design process, such as full-scale drawings on the tracing floor and the production of full-scale models and samples of ribs and keystones, are currently investigated in practical experiments. As result, we propose a complete picture of the design process from the general concept to the setting-out of the single stone elements. Further, we are able to drive general considerations on the Late Medieval and Early Modern design practice for stone structures and trace a new interpretation of the early treatises of stereotomy.

The ambitious late Gothic vaults created in the 15th and 16th centuries with their complex shape and complicated meshes of ribs soaring along spatial curves, were extremely demanding in their geometric design. This regards both the design of the whole structure, as also the design specifications for the single stone elements which were prefabricated and fit together on the building site with astonishing precision. In consequence, the particular character of these structures and their geometric features are intrinsically linked to the design routines and the geometric concepts used by the Master Builders. At present, these procedures and methods are not well understood, because they are not documented in original drawings, and because they differ in principle from the modern practice. In consequence, necessary works of repairing and restoring cannot recur to any information related to the original design. Moreover, understanding the characteristics of information transfer from the design to the execution, would cast a light on the information society in which these constructions were created. In several case studies, the geometric concepts of the intricate spatial curve systems of late Gothic vaults have been clarified on the basis of detailed surveys and geometrical analyses carried out on the built objects. On this background, also the existing sources such as historical design treatises could be re-interpreted. In a collaboration between the research group working on the design principles of late Gothic vaults at the Technische Universität Dresden, and expert stone masons specialized on historical working techniques and practical stereotomy at the Cathedral Workshop Œuvre Notre-Dame de Strasbourg, the phases of the design process, such as full-scale drawings on the tracing floor and the production of full-scale models and samples of ribs and keystones, are currently investigated in practical experiments. As result, we propose a complete picture of the design process from the general concept to the setting-out of the single stone elements. Further, we are able to drive general considerations on the Late Medieval and Early Modern design practice for stone structures and trace a new interpretation of the early treatises of stereotomy.

Η παρούσα διατριβή επανεξετάζει την οριακή ανάλυση ευστάθειας των λίθινων αψίδων. Η οριακή ανάλυση ευστάθειας χρησιμοποιείται σήμερα ως το βασικό εργαλείο αποτίμησης της ευστάθειας τόξων και θολωτών κατασκευών από τοιχοποιία, όπως ακριβώς συνέβαινε και τους τελευταίους τέσσερις αιώνες. Παρά την τόσο μακρόχρονη ιστορία της μεθόδου, δεν έχουν πλήρως διασαφηνιστεί στην επιστημονική κοινότητα θεμελιώδης έννοιες και δεν έχουν σαφώς απαντηθεί ερωτήματα όπως: Ποιες είναι οι φυσικά πραγματοποιήσιμες γραμμές ώθησης και ποιες όχι; Ποια είναι η επίδραση της στερεοτομίας ενός τόξου στην οριακή του ευστάθεια; Ποιος είναι ο ρόλος της αλυσοειδούς καμπύλης και κατά πόσο αυτή είναι μία φυσικά αποδεκτή γραμμή ώθησης; Τι σχέση υπάρχει ανάμεσα στην κλίση της συνισταμένης θλιπτικής δύναμης και στην κλίση της γραμμής ώθησης στο σημείο εφαρμογής της; Η παρούσα διατριβή αναζητά απαντήσεις στα ερωτήματα αυτά, και έχει ως στόχο τη βαθύτερη κατανόηση της οριακής ανάλυσης ευστάθειας των τόξων, με παράλληλη ανάδειξη νέων υπολογιστικών διαδικασιών. Η δομή της παρουσιάζεται συνοπτικά παρακάτω. Στο πρώτο κεφάλαιο γίνεται ιστορική ανάλυση της μεθόδου μέσα από παρουσίαση και σχολιασμό των εργασιών με τη σημαντικότερη συμβολή, από τα μέσα του 17ου αιώνα μέχρι σήμερα. Στο δεύτερο κεφάλαιο επανεξετάζεται ένα από τα πιο κλασικά προβλήματα της μηχανικής: ποιο είναι το ελάχιστο επιτρεπτό πάχος ενός ημικυκλικού τόξου υπό τη δράση του ιδίου βάρους του για να είναι ευσταθές. Παράλληλα απαντώνται τα ερωτήματα που τέθηκαν παραπάνω αναπτύσσοντας νέες κλειστές μαθηματικές εκφράσεις των γραμμών ώθησης μέσω γεωμετρικής προσέγγισης, αλλά και μέσω του λογισμού των μεταβολών. Στο τρίτο κεφάλαιο χρησιμοποιείται παρόμοια διαδικασία για την ανάλυση της γενικής περίπτωσης των ελλειπτικών τόξων, οποιουδήποτε γεωμετρικού λόγου ύψος προς βάση, καθώς δεν είναι διαθέσιμα αναλυτικά αποτελέσματα στη διεθνή βιβλιογραφία, όπως συμβαίνει για τα κυκλικά τόξα. Στο τέταρτο κεφάλαιο εξετάζεται η οριακή ευστάθεια κυκλικών τόξων οποιασδήποτε γωνίας εναγκαλισμού, υπό την ταυτόχρονη δράση του ιδίου βάρους τους και σταθερής οριζόντιας εδαφικής επιτάχυνσης, ενώ υπολογίζεται με ακρίβεια η μορφή που θα έχει ο επικείμενος μηχανισμός κατάρρευσης μαζί με το οριακό πάχος, συναρτήσει της σεισμικής φόρτισης. Τα αποτελέσματα της μαθηματικής ανάλυσης (Κεφ. 2-4) επιβεβαιώνουν την ακρίβεια του λογισμικού που αναπτύχθηκε για τις ανάγκες της διατριβής, καθώς και τα αποτελέσματα που προκύπτουν από εμπορικό λογισμικό της μεθόδου των διακριτών στοιχείων. Στο πέμπτο κεφάλαιο γίνεται εφαρμογή και σύγκριση των πιο αντιπροσωπευτικών υπολογιστικών μεθόδων που απαντώνται σήμερα στη βιβλιογραφία για την αποτίμηση της ευστάθειας και φέρουσας ικανότητας της υπόγειας Θολωτής Διόδου του Σταδίου της Αρχαίας Νεμέας, ενώ η οριακή ανάλυση ευστάθειας αναδεικνύεται ως ένα μοναδικό εργαλείο για την κατανόηση της αλληλεπίδρασης της κατασκευής με το περιβάλλον έδαφος. Επιπλέων των συμπερασμάτων στο τέλος κάθε κεφαλαίου (Κεφ. 2 έως 5), στο έκτο κεφάλαιο παρουσιάζονται τα πιο σημαντικά συμπεράσματα και η συνεισφορά της παρούσας διατριβής. / This doctoral thesis revisits the limit equilibrium analysis of masonry arches. Limit equilibrium analysis is used today as the main analysis method for the assessment of the stability of masonry arches and vaulted structures, and is the outcome of important contributions that happened during the last four centuries. Although this method has a long history and a rich literature, there are still fundamental concepts that have not been thoroughly clarified, such as: What are the physically admissible thrust lines of an arch? How the stereotomy of an arch affects its limit stability? What is the role of the catenary curve (the alysoid)? Is the catenary curve a physically admissible thrust line? What is the relation between the direction of the thrust force and the slope of the thrust line at the point of application of the force? This thesis investigates these questions and aims to a better understanding of the limit equilibrium analysis of masonry arches, and at the same time, to present innovative methodologies and new analysis tools. Chapter 1 presents the work of other authors that have contributed the most to the stability analysis of masonry arches and vaulted structures over the last centuries. Chapter 2 revisits one of the most classical problems of Mechanics—what is the minimum thickness of a semicircular masonry arch subjected to its own weight. At the same time, the analysis presented in this chapter answers to the aforementioned questions through the development of closed-form expressions of the thrust line and the application of calculus of variation. Chapter 3 is focused on the limit equilibrium state of elliptical masonry arches, using the same approaches that were used in Chapter 2. This analysis was motivated from the fact that numerical results have been available in literature only for circular and not for elliptical masonry arches. Chapter 4 computes the location of the imminent hinges and the minimum thickness of circular masonry arches, for every given embrace angle, which can just sustain their own weight, together with a given level of horizontal ground acceleration. The numerical results presented in Chapters 2 to 4 confirm the accuracy of the in-house software that was developed for the needs of this thesis and the results obtained with a representative, commercially available software of the distinct element method. Chapter 5 present a comprehensive structural analysis of the Tunnel-Entrance to the Stadium of Ancient Nemea which ranges from the thrust line limit analysis and the discrete element method, to a 3-dimensional finite-element analysis. Limit equilibrium analysis emerges as a unique analysis method for the assessment of the stability of the structure and its interaction with the surrounding soil. While at the end of every chapter (Chapters 2 to 5) are presented detailed comments and conclusions, Chapter 6 is focused on outlining the most important conclusions and the main contribution of this thesis.