Wedges and plate-bandes: mechanical theories after De la Hire

Plate-bandes are straight masonry arches (they are called, also, flat arches or lintel arches). Ideally they have the surfaces of extrados and intrados plane and horizontal. The stones or bricks have radial joints converging usually in one centre. The voussoirs have the form of wedges and in French they are called "claveaux". A plate-bande is, in fact, a lintel made of several stones and the proportions of lintels and plate-bandes are similar. Proportions of plate-bandes, that is the relationship between the thickness t and the span s (t/s)varies, typically between 1/4–1/3 in thick plate-bandes, and is less than 1/20 in the most slender ones. A ratio of circa 1/8 was usual in the 18th Century and follows a simple geometrical rule: the centre form with the intrados an equilateral triangle and the plate-bande should contain an arc of circle. The joints are usually plane, but in some cases present a «rebated» or «stepped» form. Plate-bandes exert an inclined thrust as any masonry arch. This thrust is usually very high and it requires either massive buttresses, or to be built in the middle of thick walls. Master builders and architects have tried since antiquity to calculate the abutment necessary for any arch. A modern architect or engineer will measure the arch thrust in units of force, kN or tons. Traditionally, the thrust has been measured as the size of the buttresses to resist it safely. Old structural rules, then, addressed the design problem establishing a relationship between the span and the depth of the buttress. These were empirical rules, particular for every type of arch or structure in every epoch. Thus, the typical gothic buttress is 1/4 of the vault span, but a Renaissance or baroque barrel vault will need more than 1/3 of the span. A plate-bande would require more than one half of the span; this is precisely the rule cited by the French engineer Gautier, who tried unsuccessfully to justify it by static reasons. They were used, typically, to form the lintels of windows or doors (1-2 m, typically); in Antiquity they were used, also, though rarely, at the gates of city walls or in niches (ca. 2 m, reaching 5.2 m). Plate-bandes may show particular problems: it is not unusual that some sliding of the voussoirs can be observed, particularly in thick plate-bandes. The stepped joints on Fig. 1, left, were used to avoid this problem. There are other «hidden» methods, like iron cramps or the use of stone wedges, etc. In seismic zones these devices were usual. Another problem relates to the deformation; a slight yielding of the abutments, or even the compression of the mortar joints, may lead to some cracking and the descent of the central keystone. Even a tiny descent will convert the original straight line of the intrados in a broken line with a visible «kink» or angle in the middle. Of course, both problems should be avoided. Finally, the wedge form of the voussoirs lead to acute angles in the stones and this can produce partial fractures; this occurs usually at the inferior border of the springers at the abutments. It follows, that to build a successful plate-bande is not an easy matter. Also, the structural study of plate-bandes is far from simple, and mechanics and geometry are related in a particular way. In the present paper we will concentrate on the structural aspects and their constructive consequences, with a historical approach. We will outline the development of structural analysis of plate-bandes from ca. 1700 until today. This brief history has a more than purely academic interest. Different approaches and theories pointed to particular problem, and though the solution given may have been incorrect, the question posed was often pertinent. The paper ends with the application of modern Limit Analysis of Masonry Structures, developed mainly by professor Heyman in the last fifty years. The work aims, also, to give some clues for the actual architect and engineer involved in the analysis or restoration of masonry buildings.

Efectos sociales y urbanísticos generados por la implantación del sistema de transporte masivo “Transbarca” en la ciudad de Barquisimeto, Estado Lara, Venezuela

El propósito principal de éste trabajo tiene que ver con los procesos de modelado del espacio social, utilizando como campo de estudio los efectos sobre la morfología urbana generados por la implantación del sistema de transporte Masivo Transbarca en la ciudad venezolana de Barquisimeto. La investigación se apoya en buena medida en las teorías de la morfología social elaboradas por el sociólogo E. Durkheim y desarrolladas sobre todo en el campo del urbanismo por M. Halbwachs. En ellas se vincula la morfología social con su sustrato material, la forma urbana, desde una perspectiva sociológica. De igual manera se consideran categorías conceptuales como fragmentación y segregación, según otros enfoques (M. Castells y Reales). El trabajo se desarrolla según una metodología empírica, realizando análisis cuantitativos de los fenómenos que se consideran indicativos (el mercado de vivienda, por ejemplo) y comprobando su relación con la cualificación del espacio urbano donde destacan los procesos de remodelación de la centralidad que resultan de la implantación del Transporte Masivo. Desde esta perspectiva, la solución al transporte colectivo adquiere una dimensión que trasciende su papel como pieza fundamental para el buen funcionamiento de la ciudad moderna en crecimiento, con independencia de que sea capaz de ofrecer una solución a ese desafío, para convertirse en un instrumento de ordenación de la ciudad que afecta a la morfología social y urbana, que supone profundas alteraciones del centro urbano propiamente dicho, que implica una redistribución de los grupos sociales en el espacio reformado de la ciudad: un proceso de remodelación y transformación del espacio funcional y social, presentado como una solución a los problemas de movilidad. También en Venezuela, como en otras partes, la evolución de la morfología social está relacionada con profundos cambios ocurridos en los sustratos físico-estructurales de las ciudades, que a su vez se vinculan con la dinámica de los procesos de globalización que nutren la dinámica interna de construcción y reconstrucción de esos espacios. SUMMARY The main purpose of this work deals with modeling processes of social space, using as a field of study the effects on urban morphology generated by the implementation of the transport system Transbarca Mass in the Venezuelan city of Barquisimeto. The research was based largely on theories of social morphology developed by sociologist E. Durkheim and developed primarily in the field of urban M. Halbwachs. They linked the social morphology with its substrate material, urban form, from a sociological perspective. Similarly conceptual categories are considered as fragmentation and segregation, as other approaches (M. Castells and Royals). The work is developed as an empirical methodology, performing quantitative analysis of the phenomena that are considered indicative (the housing market, for example) and checking its relation to the qualification of urban space which include remodeling processes resulting from the centrality the implementation of mass transportation. From this perspective, collective transport solution acquires a dimension that transcends its role as a cornerstone for the functioning of the modern city growing, regardless of who is able to offer a solution to this challenge, to become an instrument of City management affecting the social and urban morphology, reflecting profound alterations in the city center itself, which implies a redistribution of social groups in the city renovated space: a process of renovation and transformation of social and functional space presented as a solution to mobility problems. Also in Venezuela, as elsewhere, the development of social morphology is associated with profound changes in the physical and structural substrates of cities, which in turn are linked to the dynamics of globalization processes that nourish the internal dynamics construction and reconstruction of these areas.

Ergociudad: concepción modélica de la calidad de vida urbana desde la perspectiva de la ergonomía y el diseño urbano

Este documento corresponde a la Tesis para optar al grado de Doctor en Arquitectura y Urbanismo en el marco del Programa de Doctorado conjunto de la Universidad Politécnica de Madrid y la Universidad de Chile. La investigación realizada es de carácter exploratorio-descriptivo con el propósito de establecer y relacionar conceptualmente las teorías y principios de la ergonomía y del diseño urbano, para proponer desde un enfoque sistémico criterios de confort en el diseño de la ciudad, que contribuyan a la calidad de vida y la vida urbana, dando a luz lineamientos para la “Ergociudad”; concepto que surge de la unión de las palabras Ergonomía y Ciudad. Al estudiar a diversos autores se concluye en la carencia de referentes de confort y de políticas basados en la relación empírica del ser humano en la ciudad que posibiliten la configuración del medio ambiente urbano a partir de ella. La ciudad se piensa y se construye desde su estructura y no desde una mirada sistémica e integrada de los factores dimensionales, ambientales y psicosociales condicionantes del confort en sus distintas escalas. La mirada respecto del desarrollo de la ciudad es físico constructiva y, por tanto, deja de lado el problema de los estresores o de la percepción de los factores de riesgo en el entorno construido. El tema central de esta tesis es proponer una estructura modélica de calidad de vida urbana denominada Ergociudad en base a los fundamentos teóricos de la Ergonomía y el Diseño Urbano y establecer el “Índice Ergourbano”, como representación de los factores ergonómicos presentes en la ciudad. En este marco, el enfoque de la ergonomía y sus prestaciones han sido trabajados en orden a facilitar mecanismos para disponer de sus procedimientos y de su modelo de análisis relacional a otras escalas. El concepto de “Ergociudad” y su propuesta de exploración desde las personas, postula una mirada sobre los problemas que enfrenta el ser humano en la ciudad considerando la dimensión de lo humano, desde perspectivas psicológicas y sociológicas para establecer y configurar la percepción de estrés y bienestar; la dimensión de lo urbano, representada por los objetos que componen el entorno (en sus distintas escalas); y, la dimensión de lo perceptual, que definiría el concepto de confort en la forma de comprender el mundo sensorial. Los resultados de la investigación confirman la hipótesis de trabajo en términos de demostrar que la percepción de disconfort en la ciudad reflejado en un índice de evaluación perceptual espacial denominado índice Ergourbano obtenido de las mediciones en situ de los factores ergonómicos del entorno. Los resultados finales de la tesis han permitido identificar variables afines en los aspectos espaciales y perceptuales. Ello mediante la exploración de las situaciones urbanas y sus conexiones para establecer el grado de adecuación del espacio urbano a las prácticas, usos y modos de las personas en la ciudad. Una vez aplicado y validado el método desarrollado se ha llegado a obtener información suficiente para aumentar el nivel de conocimiento sobre el espacio urbano con un enfoque relacional que permite entenderlo desde la experiencia de las personas que lo habitan, insistiendo en su aporte metodológico y proyectual considerando la inexistente aplicación de información que vincule la ergonomía a esta escala urbana. ABSTRACT This document corresponds to the thesis to obtain the degree of Doctor of Architecture and Urbanism in the framework of the combined doctorate program of the Technical University of Madrid and the University of Chile. The research carried out is of a descriptive–explanatory nature with the objective of establishing and conceptually relating the theories and principals of ergonomics (or human factors) and urban design. This is done in order to propose, from a systematic focus, comfort criteria in the design of cities that contribute to quality of life and urban life, giving birth to chacteristics for “Ergocity”; concepts that arise from the union of the words ergonomic and city. After studying diverse authors, one concludes the lack of references toward comfort and policies based on the empirical relation of humans in the city that allow for the configuration of the urban environment based on comfort. The city is thought out and built from its structure and not from a systematic and integrated viewpoint of the dimensional, environmental and psychosocial factors, determining factors of comfort in its distinct scales. The view regarding the development of the city is physical constructive and, therefore, leaves aside the problem of the stress factors or the perception of risk factors in the constructed environment. The central theme of this thesis is to propose a quality model of urban life entitled Ergo-city, based on the fundamental theories of the ergonomics and urban design, and to establish an “Ergourban index” as representation of the ergonomic factors present in the city. In this framework, the focus of ergonomics and its services have been used in order to facilitate mechanisms to arrange their procedures and their model of relational analysis on other scales. The concept of “Ergocity”and its offer of exploration from a people perspective, proposes a look at the problems that humans face in the city considering the nonhuman dimension, from psychological and sociological perspectives to establish and configure la perception of stress and well-being: the urban dimension, represented by the objects that the surroundings are made up of (on their distinct scales), and the perceptual dimension, which will define the concept of comfort by means of understanding the sensorial world. The results of the research confirm the working hypothesis in terms of demonstrating the perception of discomfort in the city reflected in an index of perceptual/spatial evaluation named ergo-urban obtained from in situ measurements of the ergonomic factors of the surroundings. The final results of the thesis have permitted the identification the identification of variables related to the spatial and perceptual aspects. All of this through the exploration of the urban situations and their connections in order to establish the level of adaptation of the urban space to the practices, uses and modes of the people in the city. Once applied and validated, the method of development has led to the collection of sufficient information to increase the level of knowledge of the urban space with a relational focus that allows us to understand it from the experience of the people who inhabit said space, persisting with its methodological and projective contribution considering the inexistent application of information that links the ergonomics on an urban scale.