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hyperstatic: Antoni Gaudí i Cornet TRUSSES

  TRAVATURE IPERSTATICHE

Le travi continue rientrano nella categoria delle travi inflesse e sono caratterizzate dall'essere sostenute da più di due appoggi e dall'essere prive di sconnessioni interne. Si noti che gli appoggi sono tutti costituiti da carrelli, idonei quindi a consentire il libero esplicarsi delle dilatazioni assiali, tranne uno, in genere intermedio, che è fisso, per impedire gli spostamenti rigidi paralleli all'asse. Un esempio di trave continua è riportato nella figura 8.8.

Fig. 8.8. Trave continua

The continuous beam has a lot of uncertainty as there are intermediate supports. The degree of hyperstaticity is then given by n - 2 with n number of supports. It may be associated with any main system obtained eg. removing intermediate supports and replacing them with the reactions, as shown in Figure 8.9 where both n = 7 .

Figure 8.9. Mainline obtained by removing the supports abundant

This choice, however, may be adopted when the degree of hyperstaticity is low, while it is generally more convenient to introduce the kind of internal incoherence M = 0, ie the hinges.

Eg. In the case of continuous beam on four supports (see Fig. 8.10) can take the main structures shown in Figure 8.11. These patterns are linked to the name of the engineer. Bavarian GH Gerber so that he named.

Figure 8.10. Continuous beam on four supports

Figure 8.11. Examples of isostatic continuous beams, beams Gerber

8.6.2. L'equazione dei tre momenti

La scelta di struttura principale più conveniente risulta in genere quella ottenuta introducendo delle cerniere in corrispondenza degli appoggi. A questa scelta restano associati, come incognite iperstatiche, i momenti flettenti sugli appoggi, come indicato nella figura 8.12. Questa scelta risponde alla regola generale che consiglia di adottare delle strutture principali alle quali corrispondano delle configurazioni deformate le più vicine possibili a quella della struttura iperstatica alla quale sono associate.

Fig. 8.12. Esempio the main structure of the continuous beam on four supports.

It may be noted that in a system as the main transmission has chosen not to share a field to another so that, in the case of a continuous beam on n supports, (see fig. 8.8), to write the general equation of Mueller-Breslau, we can examine a field consists of two adjacent fields, as shown in Figure 8.13.

Figure 8.13. This main structure

, referring to the support m-th, where he made the disconnection M m = 0 , esprimerà la condizione di continuità della trave ossia la condizione che la linea elastica abbia una tangente unica e quindi una rotazione relativa nulla fra le due sezioni facenti capo alla sconnessione, cioè:

(8.14)

dove rappresenta la rotazione della sezione C m considerata appartenente alla campata di sinistra e la rotazione della medesima sezione pensata appartenente alla campata di destra. Naturalmente si tratta di rotazioni indotte dai carichi, dai cedimenti vincolari, dalle variazioni termiche e dalle incognite iperstatiche sulla struttura principale.
Trattandosi di travi inflesse, ed possono più agevolmente calcolarsi mediante il teorema di Mohr illustrato al paragrafo 7.2.5.
Supponendo che la trave continua abbia rigidezza costante per ogni campata, è facile vedere che ed possono calcolarsi come qui di seguito indicato.
Rotazioni indotte dai carichi:

(8.15)

Le reazioni e rappresentano le reazioni vincolari della trave ausiliaria sottoposta al carico fittizio p* costituito dal diagramma dei momenti flettenti. Le rotazioni ed sono perciò ottenute dividendo e rispettivamente per ed .

Le reazioni e , note come termini di carico , si possono calcolare, una volte per tutte, per le condizioni di carico più frequenti. Nella tabella seguente sono riportati i valori di e per alcune condizioni di carico.

Rotazioni indotte dalle incognite iperstatiche:

(8.16)

(8.17)

Rotazioni indotte dai cedimenti vincolari:


Se indichiamo con , ed i cedimenti, supposti anelastici, degli appoggi , e rispettivamente, posto





is:

(8.18)

Taking into account all the contributions, the matching equation (8.14) gives rise to the following expression:

(8.19)

The (8.15) assumes a particularly simple form when the beam is a stiffness constant that is when we can ask:

In this case, the fact (8.19) is simplified in the following:

(8.20)

The general equation (8.18), as well as (8.19 ) contains the unknown moments on three consecutive supports. It is therefore known as the equation of three moments. In the form (8.20) it is also known as equation Bertot - Clapeyron. From these equations we can write as many as the number of intermediate supports or in the degree of hyperstaticity. The first and the last equation contains only two unknown moments as is

They therefore take the form:

first equation:

(8.21)

last equation:

(8.22)

But if the details A and B are stuck, and the moments are statically indeterminate. In this case requires two additional equations that can be easily write by observing that if the joints A and B settlements are home to a corner and b respectively, for the two bays of the shore , you can write

(8.23)

would lead to the two additional equations are searching

(8.24)

is interesting to note that the equations (8.24) can also be obtained instead of thinking that each of the joints A and B there is a pair of supports are very close to each other, comprising a light field that is infinitesimal. It is thus possible to write an equation analogous to (8.20) namely:

putting in (8.20) can be arrived at:

while putting , we arrive at: both equations obtained coincide with (8.24).

We are thus able, in any case, writing a number of congruence equations equal to the number of unknowns. Solving this system of algebraic equations is reached values \u200b\u200bof bending moments at the supports. We are then able to calculate the support reactions and draw the diagrams of the stress characteristics M and T .

8.6.3. Joint reactions

The study of the continuous beam is completed with the calculation of reactions, easily obtained once we know the bending moments at the supports. In fact, with reference to Figure 8.14, where the load applied on the m-th span is, for simplicity, limited to a single concentrated force , the bending moment at the end of the span, that is:

Figure 8.14. Calculation of reaction forces

(8.25)

which implies the cut on the left of that span

(8.26 )

is clear that if the first is the support of the continuous beam then constrain the reaction coincides with . Otherwise it is easy to see that in a generic section S of abscissa z , cutting and bending moment are valid:

• If the section S is right load

(8.27)

• If the section S is to the left of the load


The binding reaction is easily obtained by noting that it follows from the first of the cut to the right of the span is given by:

(8.28)

While it can be deduced from Figure 8.14:

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Antoni Gaudí i Cornet was born in 1852 in Reus, near Tarragona. He studied in Barcelona and Reus since 1869 and became interested in restoration, working with different English architects and studying the work of Viollet-le-Duc.
of 1878 and its first building, Vincens home in Barcelona, \u200b\u200bwhich already noticed his love for the Gothic and Moorish architecture and his taste for exuberant decor, even more evident in the subsequent construction, the building Guëll (1885-1889), also 'it in Barcelona, \u200b\u200ba huge complex, now somewhat changed. In 1883 began work on the Sagrada Familia church, again in Barcelona, \u200b\u200bwhich is his masterpiece, left unfinished. The building is a brilliant expression of Neo-Gothic style and floral, of the twelve towers planned, only four were completed.
project so the villa in El Capricho Comillas (1883-1885), built the already mentioned Palau Guell and the College of Teresina in Barcelona, \u200b\u200bthe archbishop of Astorga, the Casa de los Botines (1892-1894) and the chapel Güell in Santa Coloma, notable for the use of stained glass and colored tiles and the original structural solutions. Majolica was then widely used in the Park Guell in Barcelona, \u200b\u200ba work famous for its attractive originality here the 'architects lived until his death, which occurred in 1926. died hit by a tram, leaving many unfinished works. Latest
his work was the restoration work for the Cathedral of Majorca, the construction of the villa Bellesguard (1900-1902) and houses Batlló and Mila in Barcelona, \u200b\u200bwhere undulating rhythms prevail.

Antoni Gaudí was , together with the Belgian architects Victor Horta and Henry van de Velde and the Scot Charles Rennie Mackintosh, one of the leaders of the movement called Art Nouveau. Art Nouveau The years of transition from the nineteenth to the twentieth century are marked by a profound crisis. On the one hand continuing its optimistic faith in scientific progress, which seems unstoppable and likely to bring solution to every human problem. On the other hand we realize that this "happiness" universal is only apparent. If the middle class is rich in power, he is exploiting the work of the lower classes, forced to fight for a better quality of life. And the technical progress is not necessarily linked to the process of humanity, he risks to mechanize man kills spirituality, so it will be necessary instead to consider the technique as an end in itself, look for a "supplement of soul". This is one of the aspirations of the current culture, which manifests itself first and especially in France, called " decadence." It is in this decadent atmosphere that was born and spread throughout Europe that the Art Nouveau movement in French-speaking countries, Modern style in England, Modernism in Spain, Jugendstil in Germany, or Liberty Flowers in Italy . From the sociological point of view Art Nouveau is a new phenomenon , impressive complex that would meet what is believed to be the "need of art" of the entire community. All categories of social behaviors of the urban neighborhoods, building in all its types, furniture, urban and domestic, art and decorative arts, the furniture, clothing, personal adornment, the show. Because of the way in which it spreads is a true fashion, in the sense and the importance that fashion takes in an industrial society also economically. It is the taste of the modern bourgeoisie, unconventional, enthusiastic industrial progress, he considers his intellectual privilege, which also correspond to social responsibilities.

Park Guëll One of the most debated issues in the twentieth century is that of unity and the distinction of the arts: whether the arts are different techniques with which it operates a unique and supreme, art, or if each of them realize distinct values. The problem is related to the relationship of artistic techniques with the technology of the time and that the function of art in today's world. In Art Nouveau prevails generally idealistic view of addiction of all the arts, including Gaudi, but with the difference that the unit is rather merge. The opportunity to experience the possibilities of this (and synthesis) and Parc Güell, which in 'idea of \u200b\u200bthe customer would return in the urban plan of a garden city on the outskirts of Barcelona. The theme is proposed that Gaudí is the mutual integration of art forms and natural forms. The performance reflects the assumption of religion, which is essential for Gaudi, regardless of the purpose of the building. The forms of creation are infinitely various, because any restraint imposed on the imagination is a limit to the variety of forms, only freeing the imagination you reach that infinite variety of forms which makes the agreement with the infinite variety of natural forms. Because the technique is at the service of fantasy and imagination has no limits, the technical problems that Gaudi has to face are more difficult than those related to technology in the service of reason: not only is aware of Gaudi all the technical innovations of his time, but to overcome them, just to show that the technique has a 'relative importance. Parc Guell has a clear amusements. The technique must allow freedom complete the game. The buildings are crumbling and intentionally crooked, or seem about to collapse, since they seem made of soft material, to melt like snow in the sun. They're on a miracle, and of course, is the technique of the artist who does the miracle. Gaudi's work not only meets the manufacturer, that defines the structures, the sculptor, who fashions the masses, and the painter, qualifying areas by the color, but the work brings together many specialty crafts: patchwork , pottery, wrought iron, etc.. Rebuild it the kind of medieval construction site, where the artist was the leader of the workers and was not acting as a designer, but as a direttore d’ orchestra. 

 

La Sagrada Familia Il monumentale edificio del Temple Espiatori de la Sagrada Familia è l’opera più famosa di Gaudí, e più rappresentativa del suo genio, tanto da convertirsi negli anni in uno dei simboli più famosi di Barcellona. Il cantiere della chiesa aprì nel 1883, sul sito di un progetto neogotico precedente, e Gaudí vi installò il suo studio and almost moved there. The Catalan artist devoted to the construction of the Sagrada Familia, which was to embody the synthesis of his architectural thinking, the whole last part of life, deep her strong religious sentiment. After Gaudí's death in 1926, the work continued, but had to stop the years of the English Civil War. In 1936, the notes and the notes were lost original of Gaudí during a bombardment. The construction work resumed in 1952, and opened a world of fierce debate on the validity of drawings and maquettes used for further work. The original plan provided for three sides respectively dedicate alla nascita, crocifissione e risurrezione di Gesù, e 18 torri destinate a rappresentare, oltre alla figura del Cristo, i dodici Apostoli, i quattro Evangelisti, e la Vergine Maria. L’unica facciata ultimata personalmente da Gaudí è quella della Natività, sul lato est mentre quella della Passione ad ovest, con le sue quattro torri, venne portata a termine tra il 1954 e il 1976. Nel 1987 lo scultore Josep M. Subirachs si unì al progetto. Oggi, il cantiere della Sagrada Familia è un sito di grande attrazione turistica, completato da un piccolo Museo, dove vengono illustrate ai visitatori le varie fasi, presente e future, della costruzione della cattedrale. Senza contare che dalle torri già ultimate si gode una bellissima view of Barcelona.