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1_Descrizione dell'involucro
L’ edificio preso in esame con destinazione d'uso di civile abitazione è composto da 4 piani fuori terra con la presenza di mensole a sbalzo sui due lati corti e di una scala centrale con trave a ginocchio. L’esercitazione è volta a dimensionare i singoli elementi in calcestruzzo armato (mensole, travi e pilastri).
Maglia strutturale
La pianta è costituita da 6 campate sul lato lungo di 5m x 4m ognuna e lungo il lato corto da 4 campate da 4 m ognuna con la presenza di mensole di 2 m di sbalzo fuori dal lato corto dell'edificio.
L’altezza di ciascun interpiano è di 3,5 e la scala composta da due rampe lunghe 2,70 m, un pianerottolo posizionato ad una altezza di 1,75 m di dimensioni 1,30m x 2,50m.
![](/strutture/sites/default/files/users/Giorgio.Tabelli/Assonometria.png)
![](/strutture/sites/default/files/users/Giorgio.Tabelli/Pianta.png)
Le travi principali della costruzione si sviluppano parallelamente al lato lungo dell'edificio, prolungandosi fino alle mensole. L'orditura dei travetti è perpendicolare all'asse delle travi principali e rimane costante in tutti i solai.
2_Analisi dei carichi
Per i carichi permanenti presenti nel solaio, questo e le sue componenti verranno analizzati per trovare il peso superficiale, mentre per il carico accidentale, verrà preso il valore dalla normativa.
![](/strutture/sites/default/files/users/Giorgio.Tabelli/Solaio.png)
Analisi del solaio:
![](/strutture/sites/default/files/users/Giorgio.Tabelli/TABELLA%20CARICHI.jpg)
Una volta individuati i valori dei carichi abbiamo determinato la combinazione allo Stato Limite Ultimo (Qu):
Qu = (1,3 x Qs) + (1,5 x Qp) + (1,5 x Qa) = 11,25 KN/m2
3_Predimensionamento
Abbiamo iniziato individuando l’orditura dei solai per capire quali travi fossero le principali e quali le secondarie.
Successivamente abbiamo potuto individuare le diverse aree di influenza per stabilire i diversi carichi uniformemente distribuiti da assegnare a ciascuna delle travi.
![](/strutture/sites/default/files/users/Giorgio.Tabelli/Screenshot%20%28411%29.png)
Ipotizzando che il sistema di trave utilizzata sia doppiamente appoggiata (qL2)/8, abbiamo calcolato il momento massimo con la formula (QuL2)/8.
Per progettare la sezione imponiamo che queste tensioni, nei loro valori masssimi, siano pari ai valori di progetto (fcd).
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ove:
xc = distanza dell'asse neutro dalla sommità [mm]
hu = altezza utile della sezione [mm]
n = coefficiente di omogeneizzazione
fcd = resistenza di progetto del calcestruzzo [MPa]
fyd = resistenza di progetto dell'acciaio per armatura [MPa]
Poiché questo parametro comparirà spesso lo semplificheremo con il parametro beta.
![](data:image/png;base64,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)
Sappiamo che il momento flettente esterno è dato da una coppia interna che vede la compressione sul calcestruzzo e la trazione sull’acciaio (figura sotto).
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![](data:image/jpeg;base64,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)
Dopo una serie di calcoli possiamo arrivare a scrivere l’equazione da cui esplicitare il valore minimo dell’altezza utile (hu) che si può semplificare introducendo il parametro r.
![](data:image/png;base64,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)
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)
Da cui definisco hu
![](data:image/png;base64,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)
4_Dimensionamento travi principali e travi secondarie
Tramite i fogli Excel, sono state dimensionate le strutture orizzontali di un solaio tipo. In particolare, sono state dimensionate le sezioni delle travi principali al centro del piano (PR_C), travi secondarie al centro del piano (SEC_C), travi principali perimetrali (PRI_Per) e le travi perimetrali sulla facciata con i balconi (Sec_Per). Dopo il progetto sono state verificate per osservarne le adeguatezze.![](/strutture/sites/default/files/users/Giorgio.Tabelli/TRAVI%20SEZIONI.png)
5_Dimensionamento pilastri
![](/strutture/sites/default/files/users/Giorgio.Tabelli/Aree%20di%20influenza.png)
![](/strutture/sites/default/files/users/Giorgio.Tabelli/pianta%20pilastri.png)
In ogni piano ci sono 4 tipi di pilastri che sono stati presi in esame e dimensionati. ogni pilastro ha una sua area di influenza, a seconda della sua posizione nell'involucro. Questo passaggio è stato eseguito con la tabella Excel.
![](/strutture/sites/default/files/users/Giorgio.Tabelli/pilastri%20p.png)
Facendo riferimento alla pianta della descrizione dell'edificio, si può capire di quali pilastgri si tratta. Il pilastro C4 è un pilastro posto al centro dell'edificio, quindi quello più sollecitato dello sforzo di compressione, mentre gli altri sono posti in facciata, in particolare B1 si trova nel lato lungo, A3 nel lato corto, sotto la mensola ed il pilastro A1 è il pilastro angolare, il meno caricato.
Più piani sono presenti sopra e più grande sarà la sezione di un pilastro, per via dell'aumento del carico agente su di esso.
6_Dimensionamento mensole
Con un altro file Excel, sono state dimensionate le mensole.
Sono state progettate 2 sezioni, la mensola principale, che prosegue sull'asse delle travi principali e si sviluppa nello sbalzo, e la trave secondaria, che collega le 2 travi principali, sul bordo del balcone.
![](/strutture/sites/default/files/users/Giorgio.Tabelli/MENSOLE%20SEZIONI.png)
7_Analisi del modello
Una volta assegnate le sezioni trovate ai frames del modello si SAP2000, sono stati assegnati pure i carichi uniformi sulle travi e sulle mensole.
Prima di aver avviato l'analisi abbiamo assegnato ad ogni impalcato il diapham. In seguito è stata effettuata l'analisi alla combinazione allo SLU dei carichi dei solai, delle travi e dei pilastri.
![](/strutture/sites/default/files/users/Giorgio.Tabelli/3d%20ex.png)
![](/strutture/sites/default/files/users/Giorgio.Tabelli/Immagine%202020-11-23%20152556.png)
![](/strutture/sites/default/files/users/Giorgio.Tabelli/Immagine%202020-11-22%20111825.png)
![](/strutture/sites/default/files/users/Giorgio.Tabelli/normale.png)
Qui il diagramma degli Sforzi Normali N.
![](/strutture/sites/default/files/users/Giorgio.Tabelli/momenti%20slu.png)
Qui il diagramma dei momenti M.
![](/strutture/sites/default/files/users/Giorgio.Tabelli/deformata.png)
Qui la configurazione deformata dell'edificio.
8_Ridimensionamento delle sezioni
In seguito ai dati trovati nelle analisi dell'edificio, sono state riviste le caratteristiche delle sezioni delle componenti strutturali, laddove non bastassero o ci fosse un spreco eccessivo di materiale. Per la maggior parte delle correzioni, sono state rimpicciolite le sezioni.
![](/strutture/sites/default/files/users/Giorgio.Tabelli/TRAVI%20SEZIONI.png)
Sopra: sezioni delle travi riviste.
![](/strutture/sites/default/files/users/Giorgio.Tabelli/MENSOL%20TABELLE.png)
Sopra: sezioni delle mensole modificate.
![](/strutture/sites/default/files/users/Giorgio.Tabelli/TABELLA%20PILASTRI.png)
![](/strutture/sites/default/files/users/Giorgio.Tabelli/formula%20pilastri.png)
Sopra: verifica della resistenza dei pilastri e delle eccentricità.
Quindi, dopo aver analizzato l'edificio con le sezioni delle componenti strutturali ridimensionate, esso risulta verificato.
![](/strutture/sites/default/files/users/Giorgio.Tabelli/3d%20deformata.png)
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