Buone pratiche e Tecnologie Appropriate per la gestione delle risorse idriche ed il risparmio energetico in ambito urbano e rurale

Questa tesi di dottorato tratta il tema delle Tecnologie Appropriate e delle Buone Pratiche per la gestione delle risorse idriche ed il risparmio energetico nell’ambito dell’abitato urbano e rurale. Viene fatta una breve panoramica sulle principali teorie e metodologie che fino ad oggi hanno fatto da linee guida per la progettazione sostenibile e il corretto utilizzo delle risorse. Questa visione d'insieme servirà per esprimere delle valutazioni e trovare dei comuni dominatori per proporre una nuova metodologia d'approccio alla gestione delle risorse con particolare attenzione rivolta alla condizione presente e alla zona d’intervento. Site specific sustainability Approach (S3A). I casi studio: • Un progetto di approvvigionamento idrico e di desalinizzazione delle acque per un’oasi del Sahara marocchino. • Un progetto di ricerca della Columbia University e della NASA legato alla sostenibilità urbana di New York che analizza i benefici apportati dall'installazione di coperture verdi nell'area di Manhattan da un punto di vista della gestione delle risorse idriche, energetiche e delle componenti ambientali. • Un progetto di verde verticale e giardino pensile a Milano. • Un progetto di approvvigionamento idrico sostenibile e gestione del verde per la città di Porto Plata in Repubblica Domenicana. Approfondimenti e sperimentazioni. • E’ stato approfondito il tema della distillazione solare per la dissalazione e potabilizzazione delle acque in zone rurali desertiche ed isolate. • E’ stato progettato e realizzato un prototipo innovativo di distillatore tubolare con collettore solare parabolico. Il prototipo è stato testato nei laboratori della Columbia University di New York. • Sono state approfondite le Khettaras o Qanat, tunnel sotterranei per l’approvvigionamento idrico nelle zone aride. • Infine sono stati approfonditi i benefici apportati dalle coperture a verde (tetti verdi) e dal verde verticale nelle zone urbane dal punto di vista della gestione delle risorse idriche ed il risparmio energetico.

Tetti verdi: Analisi sperimentale e Modellazione numerica

I tetti verdi rappresentano, sempre più frequentemente, una tecnologia idonea alla mitigazione alle problematiche connesse all’ urbanizzazione, tuttavia la conoscenza delle prestazioni dei GR estensivi in clima sub-Mediterraneo è ancora limitata. La presente ricerca è supportata da 15 mesi di analisi sperimentali su due GR situati presso la Scuola di Ingegneria di Bologna. Inizialmente vengono comparate, tra loro e rispetto a una superficie di riferimento (RR), le prestazioni idrologiche ed energetiche dei due GR, caratterizzati da vegetazione a Sedum (SR) e a erbe native perenni (NR). Entrambi riducono i volumi defluiti e le temperature superficiali. Il NR si dimostra migliore del SR sia in campo idrologico che termico, la fisiologia della vegetazione del NR determina l'apertura diurna degli stomi e conseguentemente una maggiore evapotraspirazione (ET). Successivamente si sono studiate la variazioni giornaliere di umidità nel substrato del SR riscontrando che la loro ampiezza è influenzata dalla temperatura, dall’umidità iniziale e dalla fase vegetativa. Queste sono state simulate mediante un modello idrologico basato sull'equazione di bilancio idrico e su due modelli convenzionali per la stima della ET potenziale combinati con una funzione di estrazione dell’ umidità dal suolo. Sono stati proposti dei coefficienti di correzione, ottenuti per calibrazione, per considerare le differenze tra la coltura di riferimento e le colture nei GR durante le fasi di crescita. Infine, con l’ausilio di un modello implementato in SWMM 5.1. 007 utilizzando il modulo Low Impact Development (LID) durante simulazioni in continuo (12 mesi) si sono valutate le prestazioni in termini di ritenzione dei plot SR e RR. Il modello, calibrato e validato, mostra di essere in grado di riprodurre in modo soddisfacente i volumi defluiti dai due plot. Il modello, a seguito di una dettagliata calibrazione, potrebbe supportare Ingegneri e Amministrazioni nella valutazioni dei vantaggi derivanti dall'utilizzo dei GR.

Mitigazione dell'isola di calore attraverso i tetti verdi: il caso di studio di Via Terracini a Bologna

Con il termine “tetti verdi” si intendono vere e proprie coperture vegetate, che fungono da valida alterativa alle tipologie convenzionali a coppi oppure in guaina impermeabilizzante. Per quanto questi possano essere considerati una soluzione moderna relativa alle diverse Best Management Practices (BMP), in realtà sono stati realizzati e sfruttati fin dall'antichità. Dagli anni Settanta ad oggi hanno preso sempre più piede in Europa e negli altri continenti a causa dei molteplici benefici che li accompagnano a livello ambientale. All'interno di questo studio ci si pone l‟obiettivo di valutarne i vantaggi, principalmente a livello energetico ed idraulico, riscontrati in letteratura, direttamente sul campo, grazie al sito di studio presso la sede di Ingegneria di via Terracini, Bologna. Sulle coperture del LAGIRN (Laboratorio di Geoingegneria e Risorse Naturali), infatti, nell‟estate 2013 sono stati realizzati due tetti verdi (uno a Sedum, che sarà indicato con la sigla GR, e uno con piante autoctone, identificato con la sigla NA). Tramite il confronto tra le temperature registrate grazie a diversi tipi di strumentazione, è stato possibile quantificare i comportamenti delle coperture su scala annuale, non solo l‟una rispetto l‟altra, ma anche in rapporto a una porzione di tetto lasciata a guaina bituminosa (indicato con la sigla RR). Considerando il ruolo della vegetazione come strumento per la mitigazione del fenomeno d‟isola di calore urbana, infine, con l‟ausilio del software CFD denominato ENVI-met si è modellata l‟intera area del Lazzaretto e si sono simulati tre diversi scenari: 1) Lo stato attuale 2) Una situazione ipotetica con tutte coperture a Sedum 3) Una situazione ipotetica con tutte coperture con specie autoctone per la giornata estiva più calda e per un comune giorno di Ottobre, a seguito di una minuziosa calibrazione. Il confronto tra la situazione reale e quelle supposte dimostra la validità dei green roofs nella lotta al riscaldamento delle grandi città.

A model for radiofrequency electromagnetic field predictions at outdoor and indoor locations in the context of epidemiological research

We present a geospatial model to predict the radiofrequency electromagnetic field from fixed site transmitters for use in epidemiological exposure assessment. The proposed model extends an existing model toward the prediction of indoor exposure, that is, at the homes of potential study participants. The model is based on accurate operation parameters of all stationary transmitters of mobile communication base stations, and radio broadcast and television transmitters for an extended urban and suburban region in the Basel area (Switzerland). The model was evaluated by calculating Spearman rank correlations and weighted Cohen's kappa (kappa) statistics between the model predictions and measurements obtained at street level, in the homes of volunteers, and in front of the windows of these homes. The correlation coefficients of the numerical predictions with street level measurements were 0.64, with indoor measurements 0.66, and with window measurements 0.67. The kappa coefficients were 0.48 (95%-confidence interval: 0.35-0.61) for street level measurements, 0.44 (95%-CI: 0.32-0.57) for indoor measurements, and 0.53 (95%-CI: 0.42-0.65) for window measurements. Although the modeling of shielding effects by walls and roofs requires considerable simplifications of a complex environment, we found a comparable accuracy of the model for indoor and outdoor points.

Eficiencia de la retención hídrica de las cubiertas vegetadas

La inundación repentina en áreas urbanas por sobrecarga de las redes de drenaje es un problema recurrente con impactos negativos de importancia creciente. Las cubiertas vegetadas ("naturadas") retienen parte de la lámina de agua precipitada, reduciendo el escurrimiento superficial y generando hidrogramas de escorrentía directa con caudales pico menores y más retardados. Dichas propiedades hacen que esta tecnología pueda contribuir a reducir la sobrecarga de cauces urbanos. En esta comunicación se presentan los primeros resultados (parciales) de la determinación de la eficiencia de retención hídrica (en forma indirecta a partir de la cantidad de agua percolada), en parcelas de ensayo que simulen "cubiertas naturadas", con dos profundidades de sustrato y con dos situaciones respecto a la cobertura (con y sin vegetación). Los mismos muestran una tendencia positiva de las "cubiertas naturadas" en la contribución a la reducción del escurrimiento, siendo mayor la retención en las parcelas vegetadas y sustrato de mayor espesor.

Eficiencia en la retención del agua de lluvia de cubiertas vegetadas de tipo "extensivo" e "intensivo"

La inundación en áreas urbanas por sobrecarga de las redes de drenaje es un problema recurrente de importancia creciente. Las cubiertas vegetadas (naturadas) retienen parte de la lámina de agua precipitada, reduciendo el escurrimiento superficial y generando hidrogramas de escorrentía directa con caudales pico menores y más retardados. Estas propiedades hacen que esta tecnología pueda contribuir a reducir la sobrecarga de cauces urbanos. Los resultados obtenidos a lo largo de casi dos años de estudio permitieron estimar una capacidad de retención de las cubiertas ensayadas (en la Ciudad de Buenos Aires), que ha sido variable en función de la precipitación, del grado de cobertura y profundidad del sustrato. Es así que el porcentaje retenido ha sido alto (73% a 100%) con precipitaciones menores o iguales a los 20 mm, alrededor del 60% con lluvias de 35 a 40 mm, y con precipitaciones cercanas a 100 mm los porcentajes de retención se redujeron notablemente, alcanzando valores cercanos al 30%. Estos resultados posicionan las cubiertas vegetadas, para las condiciones y sitio del ensayo, como una alternativa dentro del manejo hídrico integrado en cuencas urbanas.

Traditional Building Adaptation to New Requirements: Historic Center of Arequipa, Perú

The traditional buildings in the historic center of the city of Arequipa, Perú, recently declared of human heritage, are of volcanic tuff both in walls and in vaulted roofs on the ground floor. Having been built in the 18th century and up to the beginning of the 20th century, they have suffered many damages from the seismic movements registered in this region. Due to this, many of them have had to be rebuilt. In this presentation, the different changes to adapt the city of Spanish colonial origin to the present tertiary use are analyzed.

Similarities and Differences in Barrel Vaults of Traditional and Stately Houses in the Historic Centre of Arequipa, Perú

The traditional architecture of the centre of the city of Arequipa has been analyzed by comparing floor-plans of houses from the eighteenth and nineteenth centuries in order to explain the reasons behind the arrangement of their constructional elements and the evolution of said elements and floor-plans. The historic centre of Arequipa, a city located in the South of Perú, South America (Latitude 16°23' South, Longitude 71 °31' West), is based on a ground plan from 1540 that was set during the city's Spanish foundation. It was declared Patrimony of the Humanity by UNESCO. The manorial architecture is widely known for its decorated fronts and one-of-a-kind designs, but its differences with respect to the popular architecture are not based exclusively on decorative aspects. Peru's colonial period finished around 1825, but the barrel-vault, construction style continued in Arequipa through 1868, when an earthquake destroyed the city. Thereafter, the vaults were replaced by roofs made of rails, with cinders made out of the lava stone. The stately houses belonged to the founding families who settled around the main square on forty nine blocks that formed a square-grid, street layout. Also belonging to this category are the houses of landlords and traders from post-colonial times.

La barrera del análisis estructural y la representación gráfica en el desarrollo de los proyectos arquitectónicos: el caso de la Ópera de Sidney

En numerosas ocasiones a lo largo de la historia la imaginación de los creadores ha ido por delante de las posibilidades técnicas de cada momento. Así, muchas de estas nuevas ideas han requerido largos periodos de tiempo para materializarse como realidad construida, hasta que el desarrollo tecnológico e industrial hubo alcanzado un grado de madurez suficiente. En el campo de la arquitectura, estas limitaciones técnicas se han ido acotando paulatinamente hasta desembocar en la situación actual en la que cualquier planteamiento formal puede ser representado gráficamente y analizado desde un punto de vista estructural, superádose de este modo la barrera existente históricamente en el tratamiento de las formas. A lo largo del presente tesis doctoral se analiza cómo la formulación del Método de los Elementos Finitos en la década de los cincuenta y las curvas de Bézier en la década de los sesenta del siglo pasado y la posterior generalización de los ordenadores personales y de los programas informáticos asociados (C.A.D. y F.E.M. principalmente) en los estudios de arquitectura e ingeniería a partir de la década de los noventa, posibilitó el desarrollo de cualquier propuesta arquitectónica, por compleja que ésta fuese, provocando una verdadera revolución a nivel formal en el mundo de la arquitectura, especialmente en el campo de la edificación singular o icónica. Se estudia este proceso a través de ocho edificios; cuatro anteriores y otros tantos posteriores a la desaparición de la barrera anteriormente referida, establecida de forma simbólica en la década de los años ochenta del siglo XX: Frontón de Recoletos en Madrid, Edificio Seagram en Nueva York, Habitat ’67 en Montreal, Ópera de Sídney, museo Guggenheim de Bilbao, ampliación del Victoria & Albert Museum en Londres, tanatorio “Meiso no Mori” en Gifu y nueva sede de la CCTV en Pekín. De entre ellos, la Ópera de Sídney, obra del arquitecto danés Jørn Utzon, condensa gran parte de los aspectos relevantes investigados en relación a la influencia que los métodos de representación y análisis estructural ejercen en la concepción y construcción de las obras de arquitectura. Por este motivo y por considerarse un hito de la arquitectura a nivel global se toma como caso de estudio. La idea general del edificio, que data de 1956, se enmarca en una época inmediatamente anterior a la del desarrollo científico y tecnológico anteriormente referido. Esta ausencia de herramientas de diseño disponibles acordes a la complejidad formal de la propuesta planteada condicionó enormente la marcha del proyecto, dilatándose dramáticamente en el tiempo y disparándose su coste hasta el punto de que el propio arquitecto danés fue separado de las obras antes de su conclusión. Además, la solución estructural finalmente construida de las cubiertas dista mucho de la prevista por Utzon inicialmente. Donde él había imaginado unas finas láminas de hormigón flotando sobre el paisaje se materializó una estructura más pesada, formada por costillas pretensadas de hormigón con unas secciones notablemente mayores. La forma también debió ser modificada de modo ostensible respecto a la propuesta inicial. Si este edificio se pretendiese construir en la actualidad, con toda seguridad el curso de los acontecimientos se desarrollaría por senderos muy diferentes. Ante este supuesto, se plantean las siguientes cuestiones: ¿sería posible realizar un análisis estructural de la cubierta laminar planteada por Utzon inicialmente en el concurso con las herramientas disponibles en la actualidad?; ¿sería dicha propuesta viable estructuralmente?. A lo largo de las siguientes páginas se pretende dar respuesta a estas cuestiones, poniendo de relieve el impacto que los ordenadores personales y los programas informáticos asociados han tenido en la manera de concebir y construir edificios. También se han analizado variantes a la solución laminar planteada en la fase de concurso, a través de las cuales, tratando en la medida de lo posible de ajustarse a las sugerencias que Ove Arup y su equipo realizaron a Jørn Utzon a lo largo del dilatado proceso de proyecto, mejorar el comportamiento general de la estructura del edificio. Por último, se ha pretendido partir de cero y plantear, desde una perspectiva contemporánea, posibles enfoques metodológicos aplicables a la búsqueda de soluciones estructurales compatibles con la forma propuesta originalmente por Utzon para las cubiertas de la Ópera de Sídney y que nunca llegó a ser construida (ni analizada), considerando para ello los medios tecnológicos, científicos e industriales disponibles en la actualidad. Abstract On numerous occasions throughout history the imagination of creators has gone well beyond of the technical possibilities of their time. Many new ideas have required a long period to materialize, until the technological and industrial development had time to catch up. In the architecture field, these technical limitations have gradually tightened leading to the current situation in which any formal approach can be represented and analyzed from a structural point of view, thus concluding that the structural analysis and the graphical representation’s barrier in the development of architectural projects has dissappeared. Throughout the following pages it is examined how the development of the Finite Element Method in the fifties and the Bezier curves in the sixties of the last century and the subsequent spread of personal computers and specialized software in the architectural and engineering offices from the nineties, enabled the development of any architectural proposal independently of its complexity. This has caused a revolution at a formal level in architecture, especially in the field of iconic building. This process is analyzed through eight buildings, four of them before and another four after the disappearance of the above mentioned barrier, roughly established in the eighties of the last century: Fronton Recoletos in Madrid, Seagram Building in New York Habitat '67 in Montreal, Sydney Opera House, Guggenheim Museum Bilbao, Victoria & Albert Museum extension in London, Crematorium “Meiso no Mori” in Gifu and the new CCTV headquarters in Beijing. Among them, the Sydney Opera House, designed by Danish architect Jørn Utzon, condenses many of the main aspects previously investigated regarding the impact of representation methods and structural analysis on the design and construction of architectural projects. For this reason and also because it is considered a global architecture milestone, it is selected as a case study. The building’s general idea, which dates from 1956, is framed at a time immediately preceding the above mentioned scientific and technological development. This lack of available design tools in accordance with the proposal’s formal complexity conditioned enormously the project’s progress, leading to a dramatic delay and multiplying the final budget disproportionately to the point that the Danish architect himself was separated from the works before completion. Furthermore, the built structure differs dramatically from the architect’s initial vision. Where Utzon saw a thin concrete shell floating over the landscape a heavier structure was built, consisting of prestressed concrete ribs with a significantly greater size. The geometry also had to be modified. If this building were to built today, the course of events surely would walk very different paths. Given this assumption, a number of questions could then be formulated: Would it be possible to perform a structural analysis of Utzon’s initially proposed competition-free-ways roof’s geometry with the tools available nowadays?; Would this proposal be structurally feasable?. Throughout the following pages it is intended to clarify this issues, highlighting personal computers and associated software’s impact in building design and construction procedures, especially in the field of iconic building. Variants have also been analyzed for the laminar solution proposed in the competition phase, through which, trying as far as possible to comply with the suggestions that Ove Arup and his team did to Jørn Utzon along the lengthy process project, improving the overall performance of the building structure. Finally, we have started from scratch and analyzed, from a contemporary perspective, possible structural solutions compatible with Utzon’s Opera House’s original geometry and vision –proposal that was never built (nor even analyzed)-, taking into consideration the technological, scientific and industrial means currently available.

Evaluación del potencial fotovoltaico del Campus Sur de la Universidad Politécnica de Madrid

El presente proyecto engloba el estudio del potencial fotovoltaico del Campus Sur de la Universidad Politécnica de Madrid. Este estudio se divide en tres partes. En primer lugar, se calcula la productividad del campus. En segundo lugar, se diseña la disposición de los generadores fotovoltaicos en los terrenos disponibles. Como paso final, se realiza un estudio económico de distintos supuestos. Para realizar los cálculos de productividad, se utiliza IESPRO, un programa desarrollado en Matlab©, junto con una aplicación complementaria desarrollada en el mismo lenguaje. Gracias a estos dos software es posible obtener una estimación muy realista de la energía anual generada. El aprovechamiento del terreno se estudia con la ayuda del software libre Sketchup©. Gracias a esta aplicación, es posible la reconstrucción del Campus Sur en 3D. Dicha reconstrucción incluye edificaciones y vegetación, facilitando la distribución de los generadores fotovoltaicos en todas las zonas, pudiendo evitar zonas con sombreado o no aptas para la instalación, y maximizando la utilización del terreno. El conjunto de los análisis anteriores permiten determinar el rendimiento energético del Campus Sur en sus distintas configuraciones, es decir, únicamente instalando generadores fotovoltaicos en las azoteas de los edificios, o la instalación en todo el terreno disponible, el cual incluye las azoteas y los descampados. Este rendimiento energético, comparado con el consumo anual de todo el campus, permite estimar el coste financiero de llevar a cabo la instalación y su rentabilidad, todo ello detallado en el estudio económico. El estudio económico se basa en dos supuestos, el primero de ellos, únicamente tiene en cuenta la instalación en las azoteas de los edificios. El segundo estudio, incluye los descampados y las azoteas. Con estos dos estudios se puede verificar la viabilidad del proyecto, facilitando datos concretos sobre las ventajas de cada uno de ellos. ABSTRACT. The aim of this work is to study the photovoltaic potential in the South Campus of the Polytechnic University of Madrid. The work has been divided into three parts. The first one is focused on the calculus of the solar harvesting productivity of the South Campus. The second part is centered in the development of the complete photovoltaic system layout design, taking into account the available placement. In the third part, an economic study considering several different scenarios is carried out. In order to calculate the solar productivity, the MATLAB based software tool IESPRO together with a complementary application developed in MATLAB as well, have been used. These programs allow to obtain an accurate estimation of the generated annual energy. The land use is studied with the help of free software SketchUp. With this application, it is possible to rebuild the South Campus in 3D. This reconstruction includes: buildings and vegetation, facilitating the distribution of photovoltaic generators in all areas, to avoid shaded or unsuitable areas for the installation, and maximizing land use. All the above analysis allow determining the energy efficiency of the South Campus for two different configurations, i.e., installing solar photovoltaic arrays only on the roofs of the buildings, or installing solar photovoltaic arrays throughout the land available, including vacant lots and rooftops. The facilities final cost and the cost effectiveness are estimated by comparing the energy efficiency with the South Campus total consumption. This study is based on two different scenarios: the first one considers the solar arrays installation in the buildings roofs, and the second one includes in the layout the vacant lots and rooftops. These studies allow verifying the feasibility of the project, and provide specific information related to the advantages and drawbacks of each scenario.

Resonancias de los paradigmas científicos en las arquitecturas de la Escuela de Madrid

Los años cincuenta y sesenta son los años de la incorporación definitiva de la arquitectura española al panorama internacional. Entre los arquitectos que protagonizan ese salto sin retorno, se encuentra el grupo de aquellos que unos años más tarde serán denominados por Juan Daniel Fullaondo como Escuela de Madrid. Carlos Flores, en su libro Arquitectura Española Contemporánea 1880-1950, se refiere a esos arquitectos como aquellos que se aplicaban a la difícil tarea de restablecer en España un tipo de arquitectura que conectaba con las teorías, soluciones y lenguajes establecidos por Europa durante las primeras décadas del siglo XX. Sigfried Giedion plantea en Espacio, Tiempo y Arquitectura el origen de una nueva tradición, surgida a partir de la revolución óptica de principios de siglo. Con tradición se refiere a una nueva cultura, que abarca la interrelación de las diferentes actividades del hombre: la similitud de los métodos que se usan en la arquitectura, la construcción, la pintura, el urbanismo o la ciencia. Esa novedad, fundamentada en su independencia y desvinculación con el periodo anterior, se inscribe dentro del esquema evolutivo que Thomas Kuhn plantea en su texto La Estructura de la Revoluciones Científicas, conforme a periodos no acumulativos. Kuhn habla del surgimiento de anomalías en cada periodo, origen de las crisis de pensamiento cuya explicación precisará un necesario cambio paradigmático. En la ciencia, en el campo de la óptica Thomas Young demuestra a principios del siglo XIX la naturaleza ondulatoria de la luz con su experimento de doble rendija; en el electromagnetismo se produce el salto conceptual que supone la postulación de la existencia del campo eléctrico por parte de Michael Faraday, y en termodinámica la consideración apuntada por Planck de que la radiación de la energía de produce de forma discreta, a través de cuantos. En las artes plásticas, paralelamente, Gleizes y Metzinger, en su recopilación de logros cubistas recogida en Sobre el Cubismo, hablan de la evolución sufrida durante el siglo XIX por la pintura: desde el idealismo de principios de siglo, para pasando por el realismo y la representación impresionista de la realidad, concluir prescindiendo de la perspectiva clásica. También la matemática, una vez desarrolladas por Gauss o Lobachevsky y Bolyai geometrías coherentes que incumplen el quinto postulado de Euclides, terminará dando validez a través de Riemann a los espacios ambiente en los que habitan dichas geometrías, desvinculando la relación directa entre espacio geométrico –el espacio ambiente al que da lugar un tipo de geometría- y el espacio físico. Capi Corrales refleja en su libro Contando el Espacio, cómo hasta la teoría de la relatividad y el cubismo, las geometrías no euclídeas no se hicieron notorias también fuera del campo de las matemáticas. El origen de la nueva tradición con la que Giedion se refiere a la nueva cultura de la modernidad coincide con los saltos paradigmáticos que suponen la teoría de la relatividad en las ciencias y el cubismo en las artes plásticas. Ambas se prolongan durante las primeras décadas hasta la teoría cuántica y la abstracción absoluta, barreras que los dos principales precursores de la relatividad y el cubismo, Einstein y Picasso, nunca llegan a franquear. En ese sentido Giedion habla también, además del origen, de su desarrollo, e incorpora las aportaciones periféricas en la arquitectura de Brasil, Japón o Finlandia, incluyendo por tanto la revisión orgánica propugnada por Zevi como parte de esa nueva tradición, quedando abierta a la incorporación tardía de nuevas aportaciones al desarrollo de esa cultura de la modernidad. Eliminado el concepto de la estética trascendental de Kant del tiempo como una referencia absoluta, y asumido el valor constante de la velocidad de la luz, para la teoría de la relatividad no existe una simultaneidad auténtica. Queda así fijada la velocidad de la luz como uno de los límites del universo, y la equivalencia entre masa y energía. En el cubismo la simultaneidad espacial viene motivada por la eliminación del punto de vista preferente, cuyo resultado es la multiplicidad descriptiva de la realidad, que se visualiza en la descomposición en planos, tanto del objeto como del espacio, y la consecuente continuidad entre fondo y figura que en arquitectura se refleja en la continuidad entre edificio y territorio. Sin la consideración de un punto de vista absoluto, no existe una forma auténtica. El cubismo, y su posterior desarrollo por las vanguardias plásticas, hacen uso de la geometría como mecanismo de recomposición de la figura y el espacio, adoptando mecanismos de penetración, superposición y transparencia. Gyorgy Kepes indica en El Lenguaje de la Visión que la descomposición cubista del objeto implica la sucesiva autonomía de los planos, hasta convertirse en elementos constituyentes. Algo que refleja las axonometrías arquitectónicas de Van Doesburg y que culmina con los espacios propuestos por Mies van der Rohe en sus primeros proyectos europeos. Estos mecanismos, encuentran eco en los primeros planteamientos de Javier Carvajal: en la ampliación del Panteón de españoles del cementerio de Campo Verano, un recinto virtual reconstruido mentalmente a partir del uso de tres únicos planos; o en el Pabellón de Nueva York, que organiza su planta baja desde el recorrido, introduciendo el parámetro temporal como una dimensión más. Al uso diferenciado del plano como elemento constituyente, Carvajal incorpora su plegado y su disposición conformando envolventes como mecanismo de cualificación espacial y formal, potenciando la prolongación entre arquitectura y territorio. Una continuidad que quedará culminada en las dos viviendas unifamiliares construidas en Somosaguas. La descomposición volumétrica conduce a unos niveles de abstracción que hace precisa la incorporación de elementos de la memoria -fuentes, patios, celosías…- a modo de red de señales, como las que Picasso y Braque introducen en sus cuadros para permitir su interpretación. Braque insiste en el interés por el espacio que rodea a los objetos. Una búsqueda de la tactilidad del espacio contraria a la perspectiva que aleja el objeto del observador, y que en los jardines de las viviendas de Somosaguas parece emanar de su propia materialidad. Un espacio táctil alejado del espacio geométrico y que Braque identifica con el espacio representativo en el que Poincaré, en La Ciencia y la Hipótesis, ubica nuestras sensaciones. Desdibujar los límites del objeto prolonga el espacio indefinidamente. Con el paso en el arte griego del mito al logos, se abre paso a la matemática como herramienta de comprensión de la naturaleza hasta el siglo XIX. Leon Lederman, en Simetría y la Belleza del Universo, apunta a que una de las mayores contribuciones de la teoría de Einstein es hacer cambiar el modo de pensar la naturaleza, orientándolo hacia la búsqueda de los principios de simetría que subyacen bajo las leyes físicas. Considerando que la simetría es la invariancia de un objeto o un sistema frente a una transformación y que las leyes físicas son las mismas en cualquier punto del espacio, el espacio de nuestro universo posee una simetría traslacional continua. En la ocupación del espacio de las primeras propuestas de Corrales y Molezún aparecen estructuras subyacentes que responden a enlosetados: paralelogramos sometidos a transformaciones continuas, que la naturaleza identifica tridimensionalmente con los grupos cristalográficos. Las plantas del museo de Arte Contemporáneo de la Castellana, la residencia de Miraflores, el pabellón de Bruselas o la torre Peugeot pertenecen a este grupo. La arquitectura como proceso de ocupación continua del territorio y de su trasposición al plano de cubierta, se materializa en líneas estructurales coincidentes con la estructura matemática de sus simetrías de traslación cuya posibilidad de prolongación infinita queda potenciada por el uso de la envolvente transparente. Junto a esta transparencia literal, inherente al material, Colin Rowe y Robert Slutzky nos alertan sobre otra transparencia inherente a la estructura: la transparencia fenomenal, ilustrada por los cuadros de Juan Gris, y cuya intuición aparece reflejada en la casa Huarte en Puerta de Hierro de Madrid. Corrales y Molezún insisten en una lectura de su volumetría alejada de la frontalidad, en la que los contornos de sus cubiertas inclinadas y las visuales tangenciales sugeridas por la organización de sus recorridos introducen una estructura diagonal que se superpone al entendimiento ortogonal de su planta, dibujando una intrincada red de líneas quebradas que permiten al espacio fluctuar entre las secuencia volumétrica propuesta. Los datos relativos al contenido energético de la luz y el concepto de átomo parten de la consideración de la emisión de energía en cuantos realizada por Planck, y concluyen con una circunstancia paradójica: la doble naturaleza de la luz -demostrada por la explicación de Einstein del efecto fotoeléctrico- y la doble naturaleza de la materia -asumida por Bohr y demostrada por el efecto Compton-. Schrödinger y Heisenberg formularán finalmente la ecuación universal del movimiento que rige en las ondas de materia, y cuya representación matemática es lo que se conoce como función de onda. El objeto es así identificado con su función de onda. Su ondulatoriedad expresará la probabilidad de encontrarse en un lugar determinado. Gyorgy Kepes subraya la necesidad de simplificar el lenguaje para pasar de la objetividad que aún permanece en la pintura cubista a la abstracción total del espacio. Y es así como los artistas plásticos reducen los objetos a simples formas geométricas, haciendo aflorar a la vez, las fuerzas plásticas que los tensionan o equilibran, en un proceso que acaba por eliminar cualquier atisbo de materia. Robert Rosenblum en La Pintura Moderna y la Tradición del Romanticismo Nórdico habla de cómo ese rechazo de la materia en favor de un vacío casi impalpable, campos luminosos de color denso que difunden un sereno resplandor y parecen engendrar las energías elementales de la luz natural, está directamente vinculado a la relación con la naturaleza que establece el romanticismo nórdico. La expresión de la energía de la naturaleza concentrada en un vacío que ya había sido motivo de reflexión para Michael Faraday en su postulación del concepto de campo eléctrico. Sáenz de Oíza incide en la expresión de la condición material de la energía en su propuesta junto a José Luis Romany para la capilla en el Camino de Santiago. La evocación de diferentes fuerzas electromagnéticas, las únicas junto a las gravitatorias susceptibles de ser experimentadas por el hombre, aparecerán visualizadas también en el carácter emergente de algunas de sus obras: el Santuario de Aránzazu o Torres Blancas; pero también en la naturaleza fluyente de sus contornos, la dispersión perimetral de los espacios -el umbral como centro del universoo la configuración del límite como respuesta a las tensiones germinales de la naturaleza. Miguel Fisac, a la vuelta de su viaje a los países nórdicos, aborda una simplificación lingüística orientada hacia la adecuación funcional de los espacios. En el Instituto de Daimiel, el Instituto de formación del profesorado o los complejos para los Padres Dominicos en Valladolid o Alcobendas, organiza progresivamente la arquitectura en diferentes volúmenes funcionales, incidiendo de un modo paralelo en la manifestación de los vínculos que se establecen entre dichos volúmenes como una visualización de las fuerzas que los tensionan y equilibran. En ellos la prolongación de la realidad física más allá de los límites de la envolvente ya es algo más que una simple intuición. Un proceso en el que el tratamiento de la luz como un material de construcción más, tendrá un especial protagonismo. En la iglesia de la Coronación, la iluminación del muro curvo escenifica la condición ondulatoria de la luz, manifestándose como si de un patrón de interferencia se tratara. Frente a la disolución de lo material, el espacio se manifiesta aquí como un medio denso, alejado de la tradicional noción de vacío. Una doble naturaleza, onda y partícula, que será intuido también por Fisac en la materia a través de su uso comprometido del hormigón como único material de construcción. Richard Feynmann nos alerta de la ocupación del espacio por multitud de fuerzas electromagnéticas que, al igual que la luz, precisan de receptores específicos para captar su presencia. Sus célebres diagramas suponen además la visualización definitiva de los procesos subatómicos. Al igual que la abstracción absoluta en las artes plásticas, esas representaciones diagramáticas no son asimilables a imágenes obtenidas de nuestra experiencia. Una intuición plasmada en el uso del diagrama, que irán adquiriendo progresivamente los dibujos de Alejandro de la Sota. La sección del gimnasio Maravillas recoge los trazos de sus principales elementos constructivos: estructura, cerramientos, compartimentaciones…, pero también, y con la misma intensidad, los de las fuerzas que generan su espacio, considerando así su condición de elementos constituyentes. El vacío, nos deja claro Sota, es el lugar donde habitan dichas tensiones. La posterior simplificación de las formas acompañadas de la obsesión por su aligeramiento, la casi desaparición de la envolvente, incide en aquella idea con la que Paul Klee define la actividad del artista en su Teoría del Arte Moderno, y en la que se transmite el distanciamiento hacia lo aparente: No se trata de reproducir lo visible, se trata de volver visible. Así, en Bankunión y Aviaco, como en tantos otros proyectos, frente al objetivo de la forma, Sota plantea el límite como la acotación de un ámbito de actuación. Su propia representación aséptica y diagramática transmite la renuncia a una especificidad espacial. Gilles Deleuze expresa ese posicionamiento en Pintura, el Concepto de Diagrama: el diagrama como la posibilidad de cuadros infinitos, o la posibilidad infinita de cuadros. Aparece así una concepción probabilística del espacio en la que frente a la renuncia por la forma, la tendencia al aligeramiento, y lo difuso de su definición – ideas claras, definición borrosa, en palabras de Llinás referidas al modo de operar de Sota-, la insistente atención a algunos elementos como escaleras, protecciones o miradores parece trasmitir la idea de que la arquitectura queda condensada en aquellos acontecimientos que delatan su condición dinámica, transitoria. Primando la relación frente al objeto, el vínculo frente a lo tangible. English summary. The fifties and sixties were the years of the final incorporation of Spanish architecture to the international scene. Among the architects who star that no return leap, is the group of those who a few years later will be named by Juan Daniel Fullaondo as Escuela de Madrid. Carlos Flores, in his book Arquitectura Española Contemporánea 1880-1950, refers to those architects as those that applied to the difficult task of restoring in Spain an architecture that connected with theories, solutions and established languages in Europe during the first decades of the twentieth century. Sigfried Giedion proposes in Space, Time and Architecture, the origin of a new tradition, arising from the optical revolution at the beginning of the century. With tradition he refers to a new culture, covering the interplay of different human activities: the similarity of the methods used in architecture, building, painting, urban planning or science. This new feature, based on its independence and detachment from the previous period, is part of the evolutionary scheme that Thomas Kuhn proposes in his text The Structure of Scientific Revolutions, according to non-accumulative periods. Kuhn talks about the emergence of anomalies in each period, origin of thought crisis whose explanation will require a paradigm shift needed. In science, in the field of optical Thomas Young demonstrates at the early nineteenth century the wave nature of light with its double-slit experiment , in electromagnetism the postulation of the existence of the electric field by Michael Faraday involves a conceptual leap, and in thermodynamic, the consideration pointed by Planck about quantum energy radiation. In the arts, in a parallel process, Gleizes and Metzinger , in his collection of cubism achievements on their book Du Cubisme, speak of evolution occurring during the nineteenth century by the painting: from the idealism of beginning of the century, going for realism and impressionist representation of reality, and finishing regardless of the classical perspective . Mathematics also, once developed by Gauss and Lobachevsky and Bolyai consistent geometries that violate Euclid's fifth postulate , will end validating Riemann’s ambient spaces in which these geometries inhabit, decoupling the direct relationship between geometric space -the space environment that results in a type of geometry- , and physical space. Capi Corrales reflectes in his book Contando el Espacio, that non-Euclidean geometries were not noticeable outside the field of mathematics until the theory of relativity and cubism. The origin of the new tradition that Giedion relates to the new culture of modernity coincides with paradigmatic leaps pointed by the theory of relativity in science and Cubism in the visual arts. Both are extended during the first decades until quantum theory and absolute abstraction, barriers that the two main precursors of relativity and cubism, Einstein and Picasso never overcome. In that sense Giedion speaks about the origin, but also the development, and incorporates peripheral inputs from Brazil, Japan and Finland architecture, thus including organic revision advocated by Zevi as part of this new tradition, being open to the late addition of new contributions to the development of that culture of modernity. Removed the concept of Kant's transcendental aesthetics, of time as an absolute reference, and assumed the constant value of the speed of light, theory of relativity says there is no authentic concurrency. It is thus fixed the speed of light as one of the limits of the universe, and the equivalence of mass and energy. In cubism, spatial simultaneity results from the elimination of preferential points of view, resulting in the multiplicity descriptive of reality, which is displayed in decomposition levels, both the object and the space, and the resulting continuity between figure and background that architecture is reflected in the continuity between building and land. Without the consideration of an absolute point of view, there isn’t an authentic shape. Cubism, and its subsequent development by the vanguard arts, make use of geometry as a means of rebuilding the figure and space, taking penetration mechanisms, overlapping and transparency. Gyorgy Kepes suggest in Languaje of Vision, that cubist decomposition of the object involves successive planes autonomy, to become constituent elements. Something that reflects the Van Doesburg’s architectural axonometrics and culminates with the spaces proposed by Mies van der Rohe in his first European projects. These mechanisms are reflected in the first approaches by Javier Carvajal: the extension of Spanish Pantheon in Campo Verano Cemetery, virtual enclosure mentally reconstructed from 24 the use of only three planes, or in the Spanish Pavilion of New York, which organizes its ground floor from the tour, introducing the time parameter as an additional dimension. Carvajal adds to the differential use of the plane as a constituent, Carvajal incorporates its folding and forming enclosures available as a mechanism for spatial and formal qualification, promoting the extension between architecture and territory. A continuity that will be completed in the two houses built in Somosaguas. Volumetric decomposition, as the fragmentation achieved in the last cubist experiences, needs the incorporation of elements of memory - fountains, patios, shutters...- as a network of signals, such as those introduced by Picasso and Braque in their paintings to allow their interpretation. Braque insists in his interest in the space surrounding the objects. A search of the tactility of space contrary to the perspective, which moves the observer away from the object, and that in the gardens of Somosaguas seems to emanate from its own materiality. A tactile space away from the geometric space and Braque identified with the representative space in which Poincaré in La Science et l´hypothèse, located our feelings. To blur those boundaries of the object extends the space indefinitely. With the passage in Greek art from myth to logos, it opens up to mathematics as a tool for understanding the nature until the nineteenth century. Leon Lederman, in Symmetry and beautiful Universe, suggests that one of the greatest contributions of Einstein's theory is to change the mindset of nature, namely the search for symmetry principles that underlie physical laws. Considering that symmetry is the invariance of an object or system from a transformation and that physical laws are the same at any point in space, the space of our universe has a continuous translational symmetry. In the space occupation of the first proposals by Corrales and Molezún underlying structures appear that match enlosetados: parallelograms under continuous transformations, which nature identifies tridimensionally with the crystallographic groups. Plants in the Contemporary Art Museum in La Castellana, the residence in Miraflores, the Brussels pavilion or the Peugeot tower belong to this group. The architecture as a process of continuous occupation of the territory and of its transposition to the deck, embodied in structural lines coincide with the mathematical structure of the translational symmetry and infinite extension whose possibility is enhanced by the use of the transparent cover. Alongside this literal transparency inherent to the material, Colin Rowe and Robert Slutzky alert us another transparency inherent in the structure: phenomenal transparency, illustrated by the Juan Gris’ works, and whose intuition is reflected in the Huarte’s house in Puerta de Hierro in Madrid. Corrales and Molezún insist on a reading of its volume away from the frontal, in which the outline of their inclined roofs and tangential visual suggested by the organization of his circulations introduce a diagonal structure which overlaps the orthogonal understanding of its plant, drawing an intricate web of broken lines that allow the space fluctuate between the volumetric sequence proposal. Information concerning to the energy mean of light and the concept of atom start from the consideration by Plank about the energy emission, and conclude with a paradoxical situation: the dual nature of light - demonstrated by the explanation of Einstein's photoelectric effect-, and the dual nature of matter -assumed by Bohr and demonstrated by the Compton effect-. Finally, Schrödinger and Heisenberg will formulate the universal movement equation governing in undulatory matter, whose mathematical representation is what is known as a wave function. The object is thus identified with its wave function. Its undulatory expression speaks about the probability of being found in a certain place. Gyorgy Kepes emphasizess the need to simplify the language to move from the objectivity that still remains in the cubist painting to the total abstraction of the space. And this is how artists reduced the objects to simple geometric shapes, making emerge at a time, the plastic forces that tense or balance them, in a process that eventually eliminate any trace of matter. Robert Rosenblum in Modern Painting and the Northern Romantic Tradition. Friedrich to Rothko talks about how this rejection of matter in an almost impalpable vacuum: dense color light fields that broadcast a serene glow and seem to generate the elemental energies of natural light is directly linked to the relationship with nature that sets the northern romanticism. An expression of the power of nature concentrated in a vacuum which had been reason for thought by Michael Faraday in his application of the concept of electric field. Saenz de Oíza touches upon the material expression of the energy in its proposal with Jose Luis Romany to the chapel on the Camino de Santiago. The presence of electromagnetic forces, the only ones with the gravitational one capable of being experienced by the man will also visualize in the emerging nature of some of his works: the sanctuary of Aránzazu or Torres Blancas, but also in the flowing nature of its contours, and the inclusion of interest in the realization of space fluctuating boundary: the threshold as the center of the universe. Miguel Fisac, back from his trip to the Northern Countries, starts on a linguistic simplification oriented to the functional adequacy of spaces. In the Daimiel Institute, in the Institute to Teacher Formation or in the complex to the Dominican Fathers in Valladolid or Alcobendas, progressively organized into different functional volumes architecture, focusing in a parallel way in the manifestation of the links established between these volumes as a visualization of the forces that tense and balance them. The prolongation of the physical reality beyond the limits of the envelope is already something more than a simple intuition. A process in which the treatment of light as a construction material, have a special role. In the Coronation church, curved wall lighting dramatizes the undulatory condition of the light, manifesting as if an interference pattern is involved. Versus the dissolution of the material, the space is expressed here as a dense atmosphere, away from the traditional notion of the vacuum. A dual nature, wave and particle, which is also sensed by Fisac in his committed use of concrete as a unique construction material. Richard Feynman alerts us to the occupation of space by many electromagnetic forces, which like the light, require specific receptors to capture their presence. His famous diagrams also involve the final visualization of atomic processes. As absolute abstraction in the visual arts, these representations are not assimilated to images obtained from our experience. A diagrammatic nature, abstracted from figuration, which will obtein the pictures of Alejandro de la Sota. The section of Maravillas gym collects traces of its main building blocks: structure, enclosures... but also, and with the same intensity, of the forces that generate their space as constituent elements. Sota makes it clear: the vacuum is where inhabit these tensions. The subsequent simplification of forms, accompanied by the obsession with his lightening, the near disappearance of the envelope, touches upon that idea which Paul Klee defines the activity of the artist in his Modern Art Theory, the spacing out to the apparent: it is not to reproduce the visible, it is to turn visible. Thus, in Bankunión and Aviaco, as in many other projects, against the shape, raises the limit as the dimension of a scope. His own aseptic and diagrammatic representation transmits waiver to a spatial specificity that Gilles Deleuze clearly expressed in Painting. The Concept Diagram: The diagram as the possibility of infinite pictures, or infinite possibility of the picture. Thus appears the probabilistic concept of space in which, opposite to the diffuse of its definition -clear ideas, diffuse definition, as Llinas said- the insistent attention to some elements like stairs, guards or lookouts seems to concentrate the architecture in its dynamic condition, transitional. The relationship opposite the object, the link opposite the tangible.

Great roof marquee in the new railway station for high speed trains of Málaga

The new railway station of María Zambrano for AVE (Spanish high-speed trains) located in Malaga, has been inaugurated in November 2006, just on the site of the former railway station. The new railway station with an investment of 134.7 million Euros occupies a surface of 51.377 m2, five times the surface of the former station. The enclosure is the biggest intermodal transport and commercial center of Spain which comprises a parking of 21,000 m2 for 1,300 parking places, one commercial area and a hotel of 35 m height, with a total extension constructed of approximately 100,000 m2.

Wind tunnel study on the influence of different parapets on the roof pressure distribution of low-rise buildings

High suction loads appear on roofs of low-height buildings. The use of parapets with appropriate height at the roof edges alleviates these loads. The performance of six parapet configurations to decrease the suction loads induced on roofs by oblique winds has been studied in a low speed wind tunnel. The studied parapet configurations include vertical wall parapets, either solid or porous, and cantilevered parapets formed by a small horizontal roof close to the building roof. Low-height parapets with a medium porosity and cantilevered parapets are more efficient than solid parapets to reduce the wind suctions generated on the roofs by conical vortices.

Urban agriculture in the new framework of green cities.

Urban Agriculture was a common practice in the old times. However after a period of low interest by urban population there is a movement of renaissance of urban agriculture especially in the new megalopolis. It is important to understand the role of UA in the new framework, and the interface of urban and rural agricultures, with their comparative advantages. Thus, we describe the impact of UA in several scenarios: political, socioeconomic and environmental. As a consequence several actions should be developed for improving the situation, with the stimulus to UA: urban planning, food value chain, appropriate technology, education and extension services, entertainment and leisure, selection of botanic varieties and agrochemical inputs, design and landscape and good farming practices. As a complement, there is an analysis of the Urban Greening Value Organization in our society. In the paper there is a description of the situation of urban agriculture in Spain (located mainly in roofs, walls, indoor and ground places) the existence of local regulations, barriers and opportunities in the new situation. Due to the social dimension of urban agriculture there are some comments about the role of the more significant stakeholders, and the goals and the structure of the neighbor communities.

Air Mines. Urban Space Station

Air Mines The sky over the city's port was the color of a faulty screen, only partly lit up. As the silhouette of nearby buildings became darker, but more clearly visible against the fading blur-filter of a background, the realization came about how persistent a change had been taking place. Slowly, old wooden water reservoirs and rattling HVAC systems stopped being the only inhabitants of roofs. Slightly trembling, milkish jellyfish-translucent air volumes had joined the show in multiples. A few years ago artists and architects seized upon the death of buildings as their life-saving media. Equipped with constructive atlases and instruments they started disemboweling their subjects, poking about their systems, dumping out on the street the battered ugliness of their embarrassing bits and pieces, so rightly hidden by facades and height from everyday view. But, would you believe it? Even ?old ladies?, investment bankers or small children failed to get upset. Of course, old ladies are not what they used to be. It was old ladies themselves that made it happen after years of fights with the town hall, imaginative proposals and factual arguments. An industry with little financial gains but lots of welcome externalities was not, in fact, the ground for investment bankers. But they too had to admit that having otherwise stately buildings make fine particulate pencils with their facades was not the worse that could happen. Yes, making soot pencils had been found an interesting and visible end product of the endeavor, a sort of mining the air for vintage writing tools one can actually touch. The new view from the street did not seem as solid or dignified as that of old, and they hated that the market for Fine Particulates Extraction (FPE, read efpee) had to be applied on a matrix of blocks and streets that prevented undue concentration of the best or worse solutions. It had to be an evenly distributed city policy in order for the city to apply for cleaning casino money. Once the first prototypes had been deployed in buildings siding Garden Avenue or Bulwark Street even fast movers appreciated the sidekick of flower and plant smell dripping down the Urban Space Stations (USS, read use; USSs, read uses) as air and walls cooled off for a few hours after sunset. Enough. It was all nice to remember, but it was now time to go up and start the lightweight afternoon maintenance of their USS. Coop discussions had taken place all through the planning and continued through the construction phase as to how maintenance was going to be organized. Fasters had voted for a pro, pay a small amount and let them use it for rent and produce. In the end some neighbors decided they were slow enough to take care and it was now the turn. Regret came periodically, sometimes a week before, and lasted until work actually started. But lately it had been replaced by anxiety when it needed to be passed over to the next caretaker. It did not look their shift was good enough and couldn?t wait to fix it. Today small preparations needed to be made for a class visit next day from a nearby cook school. They were frequenters. It had not been easy, but it shouldn?t have been that hard. In the end, even the easiest things are hard if they involve a city, buildings and neighbors. On the face of the data, the technicalities and the way final designs had been worked out for adaptation to the different settings, the decision of where to go was self evident, but organization issues and the ever-growing politics of taste in a city of already-gentrified-rodents almost put the project in the frozen orbit of timeless beautiful future possibilities. This is how it was. A series of designs by XClinic and OSS had made it possible to adapt to different building structures, leave in most cases the roof untouched and adapted a new technology of flexing fiberglass tubes that dissipated wind pressure in smooth bending.......