La teoria della flessione di Navier: testimonianze delle prime applicazioni nella Francia nel XIX secolo

RIASSUNTOL’oggetto di questo lavoro è la presentazione delle prime applicazioni documentate e riferite a casi reali della teoria dell’elemento inflesso formulata da Claude Navier all’inizio del XIX secolo. Una breve premessa riassume in estrema sintesi i tratti più significativi del percorso che ha condotto alla formalizzazione della teoria dell’elemento inflesso e precede la presentazione di una applicazione della teoria di Navier alla verifica delle travi di un ponte in legno.La scelta del materiale è dovuta al fatto che il legno è adatto, più di altri impiegati in quel periodo, per resistere a sforzi di flessione. L’esempio illustrato nel seguito è tratto da una Nota degli Annales des Ponts et Chaussées nei quali sono riportati altri esempi analoghi. È interessante notare come tutti questi casi facciano riferimento alla medesima tipologia strutturale ideata e brevettata da Ithiel Town nel 1820. Si tratta di ponti pedonali provvisori, costruiti per ripristinare rapidamente la via di comunicazione. Tale schema bene rispondeva alle nuove esigenze di costruire rapidamente e a basso costo molti chilometri di infrastrutture. La diffusione di questo schema strutturale in Francia (e successivamente nel resto d’Europa) è stata possibile grazie ai viaggi-studio e resoconti relativi effettuati da alcuni ingegneri francesi dell’École des Ponts et Chaussées negli Stati Uniti nei primi decenni del XIX secolo.Di seguito viene illustrata l’applicazione della teoria di Navier alla trave del ponte di Vaudreuil di 17 metri di luce. Si tratta soltanto della verifica dello sforzo normale valutato in mezzeria; non viene fatto nessun riferimento alla deformabilità, che in questo caso costituisce un problema da non sottovalutare. ABSTRACTThe subject of this work is the documentation of the first applications to real cases of the bending theory formulated by Claude Navier early in the 19th century.The most significant steps of the path that led to the formalization of the theory are summarized in a brief introduction; this resume precedes the presentation of an elementary application of the theory to the check of a wood bridge beam.The choice of wood is due to the fact that wood is suitable, more than other building materials used in that period, to withstand bending stresses.One of these cases is shown in a Note of the Annales des Ponts et Chaussées; other few examples are repor-ted in later Notes. It is worth noting that all the reported cases refer to the same structural typology designed and patented by Ithiel Town in 1820. Furthermore, all these structures are temporary pedestrian bridges, built to quickly restore the connection. This structural layout fits well to the need for a cheap design of infrastructures extending over several miles. The widespread of this structural scheme in France (and later in Europe as well) was possible thanks to the travels to the United States and to the travel reports by French engineers of the École des Ponts et Chaussées in the first half of the 19th century.In the following, the application of Navier’s theory to the 17 meters span Vaudreuil bridge is shown. In this case only the normal stress at midspan is checked; no reference is made to the deformability, which in this case is a real problem and should not be disregarded

Critères heuristiques de dimensionnement d'éléments fléchis en bois dans les traités français du XVIIIe siècle

Les critères du dimensionnement structurel actuellement utilisés se sont développés et ont connu de nombreux changements au fil du temps. Plus précisément, la période comprise entre la deuxième moitié du XVIIème siècle et la première moitié du XVIIIème siècle revêt un rôle particulièrement important, car elle voit le passage de critères basés sur des rapports de proportion, comme les textes classiques l???ont transmis (Vitruve, Alberti, Palladio, Serlio) à des critères fondés sur des bases scientifiques. Les institutions culturelles françaises, en particulier l'Académie royale des Sciences, constituent le principal contexte dans lequel ce processus se développe d'une manière décisive, en particulier à travers les traités et les manuels d'époque. La lecture de ces textes permet de reconstituer et de documenter les étapes de ce processus. Au début du processus se trouve le texte de Galileo Galilée «Discours et démonstrations mathématiques concernant deux sciences nouvelles», publié en 1638 qui, bien que ne faisant pas partie de ce contexte culturel, marque le début d'une nouvelle phase. Les contributions les plus significatives apportées par Galilée sont l'introduction de la «méthode scientifique» avec, en particulier, la vérification expérimentale de l'hypothèse et l'introduction des caractéristiques mécaniques du matériau d'évaluation de la portée. Les critères précédents se basaient en effet sur des rapports de proportion entre les éléments, indépendamment du matériau avec lequel ils étaient réalisés. Dans le cas particulier de cette étude, le bois a été pris en compte, car ce matériau, contrairement à la maçonnerie, permet d???étudier le comportement en flexion. Le Traité de Mathurin Jousse, Le Théâtre de l'art de charpentier, publié en 1627, ne présente encore aucune référence à des critères de dimensionnement, qui se trouvent en revanche dans L'art de charpenterie, réédition publiée par Philippe de La Hire en 1702. Ce texte propose un tableau où sont reportées les dimensions de base et la hauteur de la section transversale d'un élément en bois, indépendamment de la longueur de l'élément et sans aucune référence explicite aux charges appliquées. Ce tableau avait déjà été publié par Pierre Bullet dans L'architecture pratique. La lecture de ce tableau fait clairement référence aux rapports géométriques de l'époque précédente. La fortune éditoriale et la diffusion de ce texte ont contribué à la transmission du tableau qui sera reproposé pendant de nombreuses années. C???est avec le Traité des ponts, premier traité français sur les ponts, publié en 1716 par Henri Gautier, que commence à émerger la nécessité que les critères de dimensionnement aient des références scientifiquement démontrables. Mais la société d'alors n'est pas encore prête pour que cela advienne, il est en effet nécessaire que les nombreux tests réalisés au cours de ces années soient d'abord exprimés sous forme analytique pour ensuite être confirmés (ou pas) par l'expérience, conformément à la méthode scientifique proposée par Galilée. Ce processus requiert un temps assez long et des compétences longues à acquérir. La Science des ingénieurs, publiée en 1729 par Bernard Forest De Bélidor, joue un rôle fondamental dans la diffusion des critères de dimensionnement, car il bénéficie d???un grand succès éditorial: il est en effet imprimé pendant plus d'un siècle, il est traduit en italien (1832) et en allemand (1857-1858), et l'édition française de 1813 est enrichie de notes critiques de Navier. Les informations contenues dans ce texte constituent le point de départ des études ultérieures jusqu'à la publication du Résumé des Leçons de Navier. Enfin, deux manuscrits conservés dans le Fonds Ancien de l'École des Ponts et Chaussées attestent, malgré quelques imprécisions, de l'application des critères de dimensionnement contenus dans le texte de Belidor. L'étude des textes publiés à cette période souligne le passage de critères heuristiques de dimensionnement à des critères ayant une base scientifique. Le chemin n'est toutefois pas encore entièrement parcouru, et il faudra de nombreux tests effectués par des formules analytiques appropriées avant de pouvoir atteindre la formulation correcte de la portée d'un élément fléchi en bois

Heuristic dimensioning criteria for timber elements in bending in the 18th and 19th centuries

This article investigates the heuristic rules adopted in the 18thcentury in dimensioning wooden elements. Data related to cross section and span are possibly collected for the first time in a table format in the L´Architecture pratique, published in 1691 by Pierre Bullet. The focus is on the design criteria of elements in bending adopted before the formalization of structural mechanics theory by Claude-Louis Navier. In particular, this study aims at investigating the rules that have been guiding carpenters in beam dimensioning. The treatise by Bullet had been reprinted many times and had been widely circulated. In the following decades, many other authors reported the same values in a table format. The wide acceptance of the treatise prompted the author to study the table in depth and to make an attempt in finding a rule that could fit the relationship between data. For this purpose, several attempts have been made based on the supposed knowledge of the 18thand 19thcentury carpenters. The analysis considered both the rule by Galileo Galilei and plainer interpretation attempts between the data sets. Heuristic dimensioning rules reported in the most popular architectural treatises based mainly on geometric proportions were also considered. In addition, both ultimate and serviceability limit state verifications according to Eurocode 5 have been performed to compare traditional and current timber design codes

Evaluating the load bearing capacity of wood elements in early 19th century France

This paper presents a discussion on the long search for the correct solution to the problem of bending with reference to timber beams, spanning over the two centuries long debate from Galileo to Navier. In an overview of the French engineering and architecture treatises written in the 18th and early 19th century, two unpublished French manuscripts are considered; subsequently, attention is focused on the experimental data and bending theory by Jean Baptiste Rondelet and the load bearing tables by Jean Henri Hassenfratz; finally, Navier’s theory and some of its consequences are discussed. One of the first documented applications of this theory to a real design case is also presented; specifically, the verification of a temporary wood bridge built in 1820 in France according to Ithiel Town’s patent is illustrated

SEISMIC PROTECTION OF EXISTING BUILDINGS IN THE ITALIAN EXPERIENCE

The current Italian code for structural design treats extensively the issue of seismic protection of existing buildings. With an approach that may be considered innovative for a building code, the building must be first examined in its different characteristics, including the need for an accurate reconstruction of its history, in order to reach the best possible knowledge of its structural behaviour. In coordination with the code, guidelines specifically devoted to the case of heritage buildings have also been developed. These documents have their roots in older regulations issued at different times during the course of the national history. The development of seismic codes is strictly intertwined with the sequence of significant earthquakes that hit the Country, as new codes were often issued as a consequence of a major seismic event, and with the advancement of earthquake engineering as a discipline. This research follows the path of the main Italian seismic regulations developed from the Country foundation to the present, starting with the Casamicciola earthquake of 1883. The focus is on indications for strengthening the existing building stock and for preserving the cultural heritage that may be found along the entire period considered

TIMBER-TO-TIMBER STRENGTHENING OF A 17TH CENTURY TRADITIONAL TIMBER FLOOR

The subject of this work is the restoration of the timber floors of a 17th century building located in the city center of Milan. According to the Italian Code (Dlgs 42/04), this building is within the Architectural Heritage list. The building was deeply damaged and in order to be used, a restoration intervention was need. The intervention involved the building as a whole: timber roof structures, masonry walls and timber floors. Attention is focused in this paper on the strengthening of the timber floors. The criteria adopted in the design are based on the Guidelines for Cultural Heritage Buildings and on the Chapter 8 of the Technical Italian Code Norme Tecniche sulle Costruzioni (NTC 2008) related to existing buildings. The building has a complex plan, resulting from the aggregation of buildings built in subsequent periods: since their state of preservation is different, different type of interventions is needed. On the basis of the conditions of the timber joists that constitute the floor structure, three types of intervention were identified. Floors in bad state of conservation or with increased loads due to new functions will be substituted adopting the same dimensions of beams and joists, same span and construction technology. The floors that have previously been strengthened with a concrete slab overlaid on the timber floor will be maintained. New floors made with steel beams and bricks placed over the timber floor will be removed and strengthened in order to keep the same level of the timber floor. Finally, original timber floor in good state of conservation but with insufficient cross section dimensions will be strengthened using similar timber beams and joists connected with the original elements through metal fasteners in order to obtain a whole cross section. The leading concept of the whole intervention is to preserve the original structure as much as possible or to consolidate it adopting the less invasive and the more compatible construction technique

G. W. Whistler and the Howe Bridges on the Nikolaev Railway, 1842-1851

The influence of the American engineer George Washington Whistler on the design of the St. Petersburg-Moscow Railway, called the Nikolaev Railway, is discussed. The line, built between 1842 and 1851 and approximately 644 km long, was the first large-scale implementation of railroad transportation in Russia. Whistler recommended a 1,524-mm (5-ft) railroad gauge, which was accepted by the Tsar. He helped design the railway’s first freight and passenger steam locomotives, and he helped organize the manufacturing facility for the production of locomotives and other rolling stock. Because Whistler had successfully built a pioneering Howe truss bridge for the Western Railroad over the Connecticut River in Springfield, Massachusetts in 1841, he was able to persuade Russian engineers to adopt the Howe form for the Nikolaev Railway’s 64 major bridges. The design of the Connecticut River Bridge inspired the renowned Russian engineer Dmitry Jouravsky to perform over 8 years of study on the Howe form. Jouravsky’s contributions to structural engineering and his design adaptations are discussed in the context of the Connecticut River Bridge. Read More: http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29CF.1943-5509.000079

Timber roof structures and seismic response of traditional buildings

The seismic behavior of timber roof structures, present in traditional masorny buildings in many seismic areas, strongly conditions the response of the entire building system. A methodology has been proposed for assessing the seismic vulnerability of timber roof structures