Bóvedas y contrarresto del Colegio de Nuestra Señora de la Antigua de Monforte de Lemos : geometría, construcción y mecánica

El Colegio de Nuestra Señora de la Antigua de Monforte de Lemos (1593-1619) constituye el principal ejemplo del clasicismo herreriano de Galicia. Esta tesis analiza los aspectos técnicos de la construcción de sus bóvedas de cantería, en el marco disciplinar de la Historia de la Construcción. El Colegio contiene varios tipos de bóvedas entre las que destacan su cúpula trasdosada y su escalera monumental. Además, se conservan los documentos notariales históricos que describen las obras y una de las monteas más importantes de Galicia. Las bóvedas han sufrido movimientos y algunas presentan importantes deformaciones, que han suscitado preocupación sobre su estabilidad. El estudio se organiza en tres epígrafes: geometría, construcción y mecánica, tres aspectos estrechamente interrelacionados en este tipo de estructuras. La parte de estudio geométrico parte de un levantamiento en el que se emplea una estación total sin reflectante, una técnica que permite una medición muy precisa de la forma real de las bóvedas. Como complemento se ha recurrido a técnicas de escáner fotográfico. Con los datos de las mediciones se han elaborado los dibujos de las bóvedas, y analizado sus medidas e irregularidades. Se ha incluido un análisis metrológico por métodos inductivos, que ha puesto de manifiesto la unidad utilizada en la construcción. El estudio se completa con la recopilación de las reglas de dimensionamiento que figuran en los tratados, que se comparan con las dimensiones de las bóvedas analizadas. En el estudio constructivo se registran los despieces y la configuración constructiva y se contrastan, por un lado, con las soluciones que aparecen en los principales tratados de los siglos XVI, XVII y XVIII, y por otro, con las descripciones que se encuentran en los documentos históricos del Colegio. Se ha prestado especial atención al estudio de estos documentos, que han permitido conocer algunos aspectos originales del proceso de construcción de estas bóvedas. En una de las paredes del claustro se ha identificado una montea inédita cuyo levantamiento y análisis se incorpora en esta parte. En el estudio mecánico se analiza la estabilidad dentro del marco teórico del Moderno Análisis Límite de Estructuras de Fábricas. La comprensión del comportamiento estructural, unida a la precisión de los levantamientos, ha permitido explicar los movimientos de las fábricas e inferir la geometría original de algunas de las bóvedas, no siempre evidente en los casos de fuertes deformaciones. Los estudios realizados hasta ahora en bóvedas de los siglos XVI y XVII permiten vislumbrar un panorama de soluciones constructivas más rico que el que recogen los tratados históricos. Las nuevas técnicas de medición sin contacto abren nuevas posibilidades para analizar estas estructuras. Los casos estudiados todavía son escasos y se necesita un conjunto más amplio para poder realizar un análisis general. Esta tesis aporta el estudio de uno de esos casos con el fin de contribuir al mejor conocimiento de la construcción en España en los siglos XVI y XVII. ABSTRACT The Colegio de Nuestra Señora de la Antigua (1593-1619), in Monforte de Lemos, Spain, is the best example in Galicia of the classicism influenced by the Monastery of El Escorial and his architect, Juan de Herrera. This thesis analyzes the technical aspects of the construction of its masonry vaults within the discipline of Construction History. The Colegio exhibits various types of vaults, among which the extradosed ashlar dome and the grand staircase are particularly worth mentioning. In addition, the legal documents containing thorough specifications of the work, as well as one of the construction drawings at actual size —one of the best examples in Galicia—, have both been preserved to this date. Some of the vaults have undergone important deformations that have raised concerns about their stability. The study is organized in three sections: geometry, construction, and mechanics, the three clearly interrelated in this type of structures. The geometrical study starts out with a metric survey using a reflectorless total station, a technique that allows a very precise measurement of the actual shape of the vault. This technique was complemented with the use of a photo-based 3D scanner. The resulting measurements were used to draw the vaults, and analyze their dimensions and irregularities. An inductive metrological analysis, which was able to reveal the exact metric unit utilized during the construction, is included in this section. The section is completed with the gathering of the dimensional rules appearing in the various historical treatises, which are compared with the dimensions of the actual vaults. The construction study deals with the quartering of the structure, whose results are compared, on the one hand, with the approaches appearing in the main treatises of the 16th- 18th centuries, and on the other, with the descriptions in the historical documents of the Colegio itself. Special attention has been paid to the study of these documents, which have revealed some original aspects in the construction process of the vaults. In one of the cloister’s walls, a hitherto unheard-of construction drawing at actual size was found. Its survey and analysis is included in this section. The mechanical study analyzes the Colegio's vaults stability within the theoretical frame of the Modern Limit Analysis of Masonry Structures. The interpretation of the structural behavior, coupled with the precision of the surveys, has allowed a deep understanding of the masonry’s movements and the original geometry of some of the vaults —not always evident in the case of strong deformations— has been inferred. The studies dealing with XVI and XVII century vaults conducted up to this date show a landscape of constructive solutions far richer than the one suggested in the historical treatises. The new contactless measuring techniques offer exciting possibilities for the analysis of these structures. The cases studied are still few and more would be needed before a general analysis can be attempted. This thesis constitutes one such additional case and its goal is to improve our understanding of Spanish construction in the 16th-17th centuries.

The Islamic Crossed-Arch Domes in Cordoba: Geometry and Structural Analysis of the “Capilla de Villaviciosa”

Crossed-arch domes are a singular type of ribbed vaults. Their characteristic feature is that the ribs that form the vault are intertwined, forming polygons or stars, leaving an empty space in the centre. The earliest known vaults of this type are found in the Great Mosque of Córdoba, built ca. 960 a.C. The type spread through Spain, and the north of Africa in the 10th to the 16th Centuries, and was used by Guarini and Vittone in the 17th and 18th Centuries in Italy. However, it was used only in a few buildings. Though the literature about the structural behaviour of ribbed Gothic vaults is extensive, so far no structural analysis of crossed arch domes has been made. The purpose of this work is, first to show the way to attack such an analysis within the frame of Modern Limit Analysis of Masonry Structures (Heyman 1995), and then to apply the approach to study the stability of the dome of the Capilla de Villaviciosa. The work may give some clues to art and architectural historians to understand better the origin and development of Islamic dome architecture.

Urban Archaeology in Madrid. Experiences and Opportunities to Understand Historical City

In 2015, it will be thirty years since Spanish Historic Heritage Law from 1985 was approved. The results after three decades under this law are necessarily positive and witness how the complex autonomous regional legislation has been promoted, guided and organized in this Heritage field. In addition, the law enforcement has brought into the scene how the numerous public and private initiatives involved in caring, managing, protecting and restoring our cultural heritage have been channeled and regulated, as well as monitoring the impact these initiatives produce on urban archaeology. During this long period of Spanish recent history, cultural heritage -understood as an important development tool, especially when related to cultural tourism- has succeeded in channeling resources for developing the historical research projects, both documental and archaeological, that the Spanish monumental urban ensembles were requiring. In this context, the case of the city of Madrid is a clear example of the significant development that urban Historical Archaeology has experienced in Spain over the last thirty years, especially when dealing with the study of the Middle Ages (8th to 15th centuries) and the Modern Age (16th to 18th centuries). Given the number of interventions and the important results obtained by many of them, Madrid urban archaeology is an extraordinary example of the consequences of implementing new management models, changing criteria and operating procedures, and also, of course, of the conflicts and debates raised regarding heritage, as well as the importance these interventions have implied, which is the main aim of this work.

La deformación del tipo Construcción de bóvedas no-canónicas en España (siglos XVI-XVIII)

Una bóveda no canónica es una bóveda que se adapta a una forma distinta de aquella para la que ha sido inicialmente concebida. Bóvedas raras, anormales, no convencionales, habitualmente consideradas excepciones o casos particulares, resultan ser más frecuentes de lo inicialmente esperado. El interés por este tipo de bóvedas surge a raíz de una investigación inicial sobre las bóvedas empleadas para cubrir espacios de planta anular, como en el caso de las girolas de las iglesias. Sin embargo, el problema de la bóveda anular no puede ser abordado directamente, sino como parte de una investigación más general sobre bóvedas que se deforman para adaptarse a una situación anómala. El análisis de las posibilidades que un determinado tipo de bóveda brinda para resolver el abovedamiento de espacios de planta irregular, trascendiendo el problema de la planta anular, es lo que da origen a esta investigación. La cuestión de las bóvedas deformadas forma parte de un contexto mayor, el de la deformación en arquitectura abovedada. Ante una contradicción, la deformación de la bóveda es sólo una de las posibles opciones que esta arquitectura ofrece para resolver un problema de deformación. La tesis se estructura en dos partes: en la primera parte se analizan los conceptos de forma y deformación en el contexto de la arquitectura abovedada con objeto de sentar las bases para una teoría de las bóvedas no canónicas. El objetivo es establecer un punto de partida para la investigación en un campo que todavía no había sido abordado. En la segunda parte se analizan tres tipos de bóveda desde la perspectiva de las bóvedas no canónicas, a partir de un estudio de casos de bóvedas en España entre los siglos XVI y XVIII. El estudio de la deformación en arquitectura abovedada se centra en el problema de la girola, por tratarse de un caso generalizado de deformación, directamente relacionado con el problema de las bóvedas irregulares y cuyo estudio, llamativamente, no había sido llevado a cabo hasta la fecha. Se propone una primera aproximación al problema de la girola, desde un punto de vista puramente morfológico, al margen de consideraciones históricas. En el caso de las bóvedas deformadas, el análisis se centra en tres tipos de bóveda: la bóveda de crucería, la bóveda de arista y la bóveda baída. Estos tres tipos de bóveda, aunque basadas en criterios formales distintos, están íntimamente relacionados entre sí. Por un lado permiten resolver el mismo problema –planta cuadrada delimitada por arcos–, por otro lado es posible establecer una relación formal entre la bóveda de arista y la bóveda baída a través de la bóveda de crucería. El estudio de casos recogido en la segunda parte de la tesis se fundamenta en dos líneas de investigación, la primera sobre soluciones teóricas de bóvedas no convencionales propuestas en los manuscritos y tratados de cantería, y la segunda sobre bóvedas efectivamente construidas, tratado de establecer una comparación entre teoría y práctica, confrontando el grado de relación entre ambas. Sin embargo este doble análisis sólo se ha podido llevar a cabo en contadas ocasiones. Constatamos que las bóvedas no canónicas reflejadas en los tratados son pocas y apenas se han llevado a la práctica, mientras que las soluciones construidas no responden a modelos teóricos propuestos, manifestando un divorcio entre teoría y práctica. El estudio de estas bóvedas permite poner en cuestión la definición tradicional que relaciona los conceptos de ‘bóveda’ y ‘superficie’. Al iniciar el trabajo nos encontramos con un modelo teórico extremadamente rígido que deja fuera un gran número de bóvedas, obligando a agruparlas bajo el término «no canónicas». El trabajo realizado pone en evidencia lo limitado del modelo. El problema no está en la presencia de bóvedas anómalas, que no se adaptan al modelo tradicionalmente propuesto, sino en la extrema rigidez del modelo. ABSTRACT A non canonical vault is a vault adapted to a different form from that for which was originally conceived. These rare, abnormal, unconventional vaults are usually considered as exceptions or special cases. However they prove to be more frequent than it was initially expected. Interest in this type of vaults arises from an initial research on the vaults used to roof annular spaces, such as ambulatories. Nevertheless, the annular vault question cannot be addressed directly, but as a part of a broader research on distorted vaults; a research on vaults deformed to conform an anomalous layout. The analysis of the possibilities that a particular type of vault provides to solve the vaulting of an irregular layout, beyond the problem of the annular plan is the origin of this research. The argument of deformed vaults is part of a greater context, the context of deformation in vaulted architecture. Facing a contradiction, deforming a vault is just one of the options that vaulted architecture offers to solve a problem of deformation. This dissertation is organised in two parts: in the first part we analyse the concepts of form and deformation in the context of vaulted architecture in order to lay the foundations for a non canonical vaults theory. The objective is to establish a starting point for future research in a field that has not been addressed yet. In the second part, we analyse three types of vault from the perspective of non canonical vaults, based on a case study of Spanish vaults between the 16th and 18th Centuries. The analysis of deformation in vaulted architecture focuses on the question of the ambulatory, because it is a generalized example of deformation, directly related to the problem of irregular vaults. Remarkably, the analysis of these spaces had not been conducted to date. We propose a first approach to the question of the ambulatory, from a purely morphological point of view, setting aside historical considerations. The analysis of deformed vaults focuses on three types of vault: the groin vault, the ribbed vault and the sail vault. These three types of vault, although based on different formal criteria, are closely related between them. On the one hand, they allow to solve the same problem –a square perimeter limited by arcs-; on the other hand, it is possible to establish a formal relationship between the groin vault and the sail vault through the ribbed vault. The case study presented in the second part of this dissertation is based on two research lines: theoretical non conventional vaults solutions proposed on stonecutting treatises; and currently built vaults. The aim of this double analysis was to establish a comparison between theory and practice, comparing the degree of relationship between them. Nevertheless, this double analysis has only been carried out on rare occasions. It is noted that non canonical vaults reflected in treaties are few and hardly been employed, while the built solutions do not meet proposed theoretical models, expressing a divorce between theory and practice. The analysis of these vaults allows us to question the traditional definition that connects the concepts of 'vault' and 'surface'. When we began this research, we found an extremely rigid theoretical model that leaved out many vaults, forcing to group them under the term of «non canonical vaults». This research evidences the limitations of the model. The problem is not the presence of abnormal vaults, which cannot adapt to the traditional model, but in the very high stiffness of the model.

Preliminary Study and Proposal for Restoring a Jesuit College at Saragossa, Spain

A historical study and a construction pathology survey were conducted prior to proposing a solution for restoring the upper windows on the south side of Old San Carlos College at Saragossa (16th-17th centuries), wich had been forteited to add a third storey to the cloister. Althought initially designed to a simple large hall format, the church is a harmonius blend of Aragonese Gothic architecture and typical Jesuit scheme, consisting in a central nave flanket by chapel-confessional and raised galleries for the community. A subsequent enlargement of the roof, wich rests on the original framing over the central nave, reduced the mechanical strength of the principal rafters on the opposite side, prompting a concomitant imbalance of forces that has affected the entire structure. In view of the foregoing, in addition to restituting the upper window, the proposal solution envisages restoring the roof over the central nave to its original design, and with the interior lighting in the church.

Aerodynamic Optimization of a High-speed Train using Genetic Algorithms

Genetic algorithms (GA) have been used for the minimization of the aerodynamic drag of a train subject to front wind. The significant importance of the external aerodynamic drag on the total resistance a train experiments as the cruise speed is increased highlights the interest of this study. A complete description of the methodology required for this optimization method is introduced here, where the parameterization of the geometry to be optimized and the metamodel used to speed up the optimization process are detailed. A reduction of about a 25% of the initial aerodynamic drag is obtained in this study, what confirms GA as a proper method for this optimization problem. The evolution of the nose shape is consistent with the literature. The advantage of using metamodels is stressed thanks to the information of the whole design space extracted from it. The influence of each design variable on the objective function is analyzed by means of an ANOVA test.

Spanish ribbed vaults in the 15th and 16th centuries

Proceedings of the First International Congress on Construction History : Madrid, 20th-24th January 2003

Ethics and materials: Some Spanish Cases

The problem is general: modern architects and engineers are trying to understand historic structures using the wrong theoretical frame, the classic (elastic) thery of structures developed in the 19th Century for iron and stell, and in the 20th century for reinforced concrete, disguised with "modern" computer packages, mainly FEM, but also others. Masonry is an essentially different material, and the structural equations must be adapted accordingly. It is not a matter of "taste" or "opinion", and the consequences are before us. Since, say 1920s, historic monuments have suffered the aggression of generations of archietcts and engineers, trying to transform masonry in reinfored concrete or steel. The damage to the monuments and the expense has been, and is, enormous. However, as we have an adequate theory (modern limit analysis of masonry structures, Heyman 1966) which encompasses the "old theory" used successfully by the 18th and 19th Century practical engineers (from Perronet to Sejourné), it is a matter of "Ethics" not to use the wrong approach. It is also "contra natura" to modify the material masonry with indiscriminate injections, stitchings, etc. It is insane to consider, suddenly, that buildings which are Centuries or milennia old, are suddenly in danger of collapse. Maintenance is necessary but not the actual destruction of the constructive essence of the monument. A cocktail of "ignorance, fear and greed" is acting under the best of intentions.

Process of Expropriation of Buildings for the Construction of the New Dock of the Port of Cartagena (Spain) in the 18th Century

The need of the Bourbon monarchy to build a Naval Base in the Bay of Cartagena (Spain) during the eighteenth century, implied performing various actions on the environment which allowed the construction of the new dock. One of the priority actions was the transformation of the watershed of the streams that flowed into Mandaraches´s sea. For this reason, a dike was designed and constructed in the northern part of the city. The design of this great work, which was designed as a fortification of the city, was subject to considerable uncertainties. Its proximity to the city involved the demolition of several buildings in the San Roque´s neighborhood. The greater or lesser number of affected buildings and the value of the just indemnification for the expropriation of them, become decisive factors to determine if the work was viable for the Royal Estate or not.

Late Gothic German Vault Design Methods and Its Relationship with Spanish Ribbed Vaults

The arrival of European master masons to Burgos and Toledo during the mid-fifteenth century was essential for the promotion of the late Gothic ribbed vault design techniques in Spain. The Antigua Chapel in Seville Cathedral, designed by the Spanish master mason Simón de Colonia on 1497, provides an outstanding case study on this subject. This vault is characterized by the interlacing of the ribs near the springing, reflecting the influence of German ribbed vault designs. This paper analyses the relationship between German ribbed vaults and their design methods with those of Spanish ribbed vaults; with particular attention to the presence of ribs that cut through one another above the springing, materialized in the work of Simón de Colonia. This characteristic is reflected in some manuscripts in the German area, like the Wiener Sammlungen (15th-16th centuries) and the Codex Miniatus 3 (ca. 1560-1570), but no Spanish documents of the same period make reference to it.

Tres iglesias sajonas fortificadas en Transilvania, Rumanía: Hosman, Pelişor y Moşna

Saxon colonization in Transylvania occurred from 12th Century with the establishment of the populations with certain degree of freedom and autonomy. External threats over this territory obliged to the fortification of their churches, mainly between 15th and 16th Centuries with the advance of Turkish Empire. The fortification of the churches consists on the building of walls with gates and flanking towers, and also with the incorporation of several defensive elements over the apses. Most outstanding characteristics of this fortified system are the homogeneity in typology, construction and polyorcetic, without detracting of the singularity of each one of the more of 150 conserved churches. The article presents an actual state of the art. Also, it develops the main historical elements and it explains the architectonic typology and the constructive characteristics. At last, defensive elements are analyzed from the comparative and deep study through three proper examples: the churches of Hosman, Pelisor and Mosna. La colonización sajona de Transilvania se produjo a partir del siglo XII con el asentamiento de poblaciones con cierto grado de libertad y autonomía. Las amenazas externas sobre este territorio obligaron a la fortificación de sus iglesias, principalmente entre los siglos XV y XVI ante el avance del imperio turco. La fortificación de las iglesias consta de la construcción de murallas con puertas y torres de flanqueo, además de la incorporación de diversos elementos poliorcéticos sobre las cabeceras de las iglesias. Las características más relevantes de este sistema fortificado es la homogeneidad tipológica, constructiva y poliorcética sin menoscabo de la singularidad de cada una de las más de 150 iglesias conservadas. El artículo presenta un estado de la cuestión actualizado, además de desarrollar los elementos históricos más relevantes, explicar la tipología arquitectónica y las característica constructivas y analizar los elementos poliorcéticos desde el estudio comparado y profundo de tres ejemplos característicos: las iglesias de Hosman, Pelisor y Mosna.

Technological development in Spanish gothic vaults design

The principle of complexity as the evolution vector of the gothic style was an idea largely developed by Paul Frankl. The high complexity reached in the 15th and 16th centuries was possible thanks to the geometrical resources developed in the workshops of the medieval stonemasons. The search for more sophisticated designs was possible also with the higher standardization, so that the most complex ribbed vault could be built with ribs that had all the same curvature and with voussoirs that were therefore identical. Spanish Gothic architecture has been deeply studied from a historical and artistic point of view. The present paper, as a complement to these analyses, aims to point out some of the geometrical methods and technological improvements that late medieval masons were able to develop. In that way, some selected vaults have been measured, in order to study their geometry and design process. Also scale models of some vaults have been built at the Escuela de Arquitectura (Madrid) to validate these geometrical principles. More than just a research method, the scale models allow to understand the medieval construction techniques, and they are a powerful pedagogical tool with which pupils can reach a rewarding experience based on the “medieval-way” praxis.

Crossed-arch vaults in late-gothic and early Renaissance vaulting: a problem in building technology transfer

Crossed-arch vaults are a particular type of ribbed vaults. Their main feature is that the ribs that form the vault are intertwined, forming polygons or stars and leaving an empty space in the middle. The firsts appear in Córdoba in the second half of the 10th Century. Afterwards, the type diffused through Spain and North Africa, 11th_13th Centuries. These vaults reappear in Armenia in the 13th Century. In the 14th and 15th Century a few examples are found both in England (Durham, Raby) and Central Europe (Prague, Landshut, Vienna). At about the same time, Leonardo da Vinci produced designs for the Tiburio (Ciborium) of Milan cathedral with a cross-arched structure and proposed tests to assess the strength; he also, made use of the same pattern of vault for Renaissance centralized churches. Eventually, the type can be tracked through the 17th (Guarini) and 18th (Vittone) Centuries, until Spanish post war architecture in the 1940-60s (Moya). Some questions arose, which so far, have not been answered. How was it possible that a particular type of vault had such enormous geographical spread? How was it transmitted from Córdoba to the Caucasus? The matter is one of transfer of knowledge, ideas, and technology; it relates both aesthetics and construction.

La escalera de caracol con ojo a finales del S.XV y comienzos del S.XVI: el caso de la ciudad y tierra de Segovia

Este trabajo de investigación se ha centrado en la escalera de caracol con ojo también denominado caracol de mallorca, en sus primeras apariciones a finales del s.XV y comienzos del s.XVI durante el llamado periodo tardogótico. Este elemento aparentemente sencillo presenta, sin embargo, una gran diversidad de esquemas geométricos. Todavía a día de hoy, no hay explicación del por qué de la mayor difusión de unos con respecto a otros. El objetivo de este trabajo ha sido valorar el papel que el confort/seguridad de uso así como la economía en el trabajo –sencillez de ejecución y coste económico– tuvieron en el contexto de la difusión de este elemento arquitectónico. Este estudio ha analizado en base a estos criterios objetivos, la geometría de cada uno de los esquemas tipo que resuelven la formación del hueco central característico este tipo de escaleras, con la intención de determinar las causas objetivas que pudieron motivar la desigual expansión de los mismos. Una vez determinado el marco teórico, se han establecido dos líneas para abordar el problema. Por un lado se ha planteado el análisis de los modelos teóricos recogidos en los distintos textos de cantería escritos por autores españoles desde finales del s.XVI. Si bien en la época en que se escribieron, la arquitectura gótica como sistema había desaparecido, alguno de sus elementos más característicos, como la escalera de caracol, continuaban empleándose. Las trazas del caracol con ojo recogidas en estos textos, describen habitualmente las soluciones geométricas más frecuentes e incluso los ejemplos construidos más conocidos, los cuales fueron levantados en su mayoría en el período en el cual se desarrolla esta investigación. Por otro lado, este estudio se plantea el análisis de modelos construidos existentes en la Ciudad y Tierra de Segovia. La razón que justifica dichos límites geográficos, la encontramos en que la mayor parte del patrimonio gótico existente en este área fue construido entre finales del s.XV y comienzos del s. XVI. Ambos grupos, modelos teóricos y modelos construidos, recogen la herencia gótica heredada en la construcción de este elemento arquitectónico. Cada una de estas dos líneas establecidas han seguido una metodología específica adaptada al objeto de análisis, si bien ambas se basan en un primer análisis individual y posterior análisis comparativo de los modelos seleccionados. Estos análisis han permitido identificar los distintos esquemas empleados para resolver el hueco central, lo que ha posibilitado establecer una clasificación general de los mismos en tres grupos: caracol con ojo de solución radial, el caracol con ojo de solución no radial y el caracol con ojo de solución tangencial. A partir de los datos y resultados obtenidos del análisis comparativo de los parámetros geométricos que afectan al confort/seguridad de uso y economía en el trabajo de dichos esquemas, podemos concluir que a pesar que los tres esquemas identificados resuelven el caracol con ojo de forma muy similar, el predominio de la solución radial y la caída en el olvido de las soluciones tangencial y no radial estuvieron justificados. ABSTRACT This work focused on the helical staircase, also known as mallorca staircase, in the late 15th and the early 16th centuries. This seemingly simple element, presents however a wide variety of geometrical designs. Still to date, there is no explanation of why some of them were limited use, while others had a wide impact. The aim of this study was to assess the influence which comfort, safety and work economy –ease of construction and financial cost– had on their widespread. This study analysed, following these objective criteria, the geometry of the different designs, which solve the characteristic inner aperture of this type of staircase. And thus, find the reasons, which motivated their uneven spread. Once the theoretical framework was developed, two research lines were set up to address the problem. On one hand, this study analysed the theoretical helical staircases described in the early Spanish texts, which were written since the end of the 16th century. Although these texts were written after the Gothic Architecture system had already disappeared, some of its more representative elements like the helical staircase were still in use. The traces of the helical stair, which are included in these texts, describe the most frequently-used designs and even the most famous real examples which were usually constructed in the Late Gothic period. On the other hand, this study analysed some real helical staircases, which were constructed in the Ciudad y Tierra de Segovia. The reason for choosing these geographical limits is that most of the Gothic buildings of this area were constructed between the end of the 15th and the early 16th centuries, during the Late Gothic period. Both groups, theoretical and constructed samples, collect the Gothic construction tradition of the helical stair. Each of these research lines followed a specific methodology, which was adapted to the research object. Nevertheless, both are based on a first individual analysis of each selected example and a later on comparative one. These analysis allowed the identification of the different layouts which solve the inner aperture of the helical staircase, what made possible to set up a broad classification in three groups, according to the geometrical design strategy that solves the central aperture: the helical staircase by radial solution, the helical staircase by non-radial solution and the helical staircase by tangent solution. The research findings of the comparative analysis of their geometrical parameters, which have an impact in the comfort, safety and work economy, have shown that although all of them solve the helical staircase in a really similar way, the fade into oblivion of the non-radial and tangent approaches was objectively motivated.