The focus of this dissertation is on the load-bearing capacity of an almost square reinforced-concrete industrial slab, at the Ultimate Limit State and in fire. The variable loads are either heavy vehicles or tanks containing chemical products. The sizable side-length (close to 8 m), the relatively small thickness (35 cm) and the mixed constraints along the four sides (including one free side and one partially-supported side), were all good reasons to stiffen the free side by casting a reinforced-concrete beam, to carry out two tests under life-like loads, and to check the bearing capacity in ordinary conditions and the fire resistance. Following a couple of works on the elastic behavior under the test loads and on a few collapse mechanisms, in this work four mechanisms are recalled and further investigated within Limit Analysis (Method of the Yield Lines). All are characterized by a single free parameter. A fifth mechanism is introduced as well, which is at the same time more realistic and much more complex, as its geometry depends on three free parameters. (Evaluating the the bearing capacity requires the minimization of the collapse load with respect to these three parameters). The analysis at the Ultimate Limit state does not justify retrofitting the slab with the stiffening beam, but the fire checks indicate that the stiffening beam may be required to increase the fire resistence if the fixity level of the fully- or partially-supported sides is small or negligible, as shown by the elastic analysis with finite elements. The analysis at the ultimate limit state confirms that the simplest mechanisms are also the most probable, while the fire checks (under the standard fire) allow to make the following comments: (a) adding the stiffening beam markedly increases (by not less than 50%) the fire duration of the slab; (b) the stiffening beam (which is less heat-sensitive than the slab) forces the collapse mechanisms to shift from those involving the constraints to those occurring inside the slab; (c) the effectiveness of the stiffening beam increases with the fire duration; and (d) the top reinforcement of the slab – little affected by a fire from below – plays a fundamental role, that may be jeopardized by design mistakes in the detailing of the reinforcement (insufficient bonded length of the bars, curtailment of the bars, no or little continuity of the bars along the supports). This work confirms also the necessity to investigate the largest possible number of collapse mechanisms in the case of mixed constraints, all the more in fire conditions, since mere intuition can hardly identify the most probable mechanism and – more often than not – very different mechanisms may yield fairly similar ultimate loads. In fire, the in-time evolution of the bearing capacity of each mechanism and the great relevance of even small increases in the fire resistance (from half a dozen to a few dozens of minutes) contribute to the complexity of the analysis, as a few minutes more in terms of fire resistance may say a lot regarding personal and structural safety, not to mention the fire certification of the structure. Last but not the least, this work contributes to put in the correct perspective the Yield-Line Method, which on the one hand is instrumental in providing information on the structural collapse mode, on the other hand becomes increasingly complex with the increasing number of the free parameters required by the yield-line pattern. To put in competition the Yield-Line Method with nonlinear Finite-Element analysis may be an interesting step forward, with reference to the slab in question, which is at the same time a fairly complex and general structural case.
La tesi riguarda lo studio della capacità portante di una piastra industriale pressochè quadrata in calcestruzzo armato, sia in condizioni ultime (Stato-Limite Ultimo) che in condizioni di incendio, in presenza di carichi variabili dovuti al passaggio di veicoli pesanti oppure allo stoccaggio di prodotti chimici. La luce abbastanza elevata (circa 8 metri), lo spessore relativamente sottile (35 cm) ed i vincoli di tipo misto, con un lato libero ed un’altro parzialmente appoggiato, hanno comportato l’irrigidimento del lato libero con una trave di bordo, l’esecuzione di due prove di carico e la verifica della capacità portante. A valle di un paio di lavori sul comportamento elastico durante le prove e su alcuni possibili cinematismi di collasso, in questa tesi vengono approfonditi 4 cinematismi nell’ambito dell’analisi limite (metodo delle linee di plasticizzazione), caratterizzati da un solo parametro libero, e viene aggiunto un quinto cinematismo, molto realistico ma piuttosto complesso in quanto caratterizzato da tre parametri liberi, rispetto ai quali occorre minimizzare il carico di collasso (= capacità portante). Mentre l’analisi allo stato limite ultimo non giustifica l’aggiunta della trave di bordo, l’analisi al fuoco indica l’opportunità di tale intervento se – come mostrato dall’uso degli elementi finiti in campo elastico-lineare – il grado di incastro lungo i tre lati parzialmente o totalmente appoggiati è modesto (al limite trascurabile). L’analisi allo stato-limite ultimo conferma come i cinematismi più semplici siano anche i più probabili, mentre l’analisi al fuoco (incendio standard) indica come (a) l’aggiunta della trave di bordo possa aumentare sensibilmente (almeno del 50%) la durata di incendio sopportabile dalla struttura, (b) la presenza della trave di bordo (meno sensibile al fuoco della piastra) tenda a spostare i cinematismi di collasso da quelli con partecipazione dei vincoli a quelli totalmente interni alla piastra; (c) l’efficacia della trave di bordo aumenti con la durata dell’incendio; e (d) l’armatura al negativo della piastra – poco sensibile all’incendio lungo l’intradosso – giochi un ruolo essenziale, che può essere compromesso da errori di progettazione relativi ai dettagli (ad esempio, insufficiente lunghezza di ancoraggio delle barre, anticipata piegatura verso il basso, inadeguata continuità in corrispondenza degli appoggi). Più in generale la tesi conferma la necessità di indagare il maggior numero possibile di cinematismi nel caso di vincoli misti, tanto più in presenza di incendio, in quanto l’intuizione non è sufficiente ad individuare il più probabile, e spesso risultano quasi equiprobabili cinematismi molto diversi fra di loro. Ciò acquista ulteriore importanza nel caso di incendio, sia per la diversa evoluzione temporale dei cinematismi, sia perché anche relativamente piccoli incrementi della resistenza all’incendio (qualche decina di minuti) può fare la differenza nel garantire la sicurezza di persone e beni, e nel certificare la struttura. Da ultimo la tesi contribuisce a mettere nella giusta prospettiva il metodo delle linee di plasticizzazione, che se da un lato è unico nel fornire informazioni sulle modalità di collasso, dall’altro diviene rapidamente complesso all’aumentare dei parametri liberi necessari per definire geometricamente i cinematismi. Mettere in competizione il metodo delle linee di plasticizzazione con l’analisi non lineare ad elementi finiti potrebbe essere un proseguimento interessante della tesi, su un caso abbastanza complesso ma anche abbastanza generale come quello esaminato.
Piastre in c.a. con vincoli misti : stato limite ultimo ed incendio
MORAZZINI, SARA
2017/2018
Abstract
The focus of this dissertation is on the load-bearing capacity of an almost square reinforced-concrete industrial slab, at the Ultimate Limit State and in fire. The variable loads are either heavy vehicles or tanks containing chemical products. The sizable side-length (close to 8 m), the relatively small thickness (35 cm) and the mixed constraints along the four sides (including one free side and one partially-supported side), were all good reasons to stiffen the free side by casting a reinforced-concrete beam, to carry out two tests under life-like loads, and to check the bearing capacity in ordinary conditions and the fire resistance. Following a couple of works on the elastic behavior under the test loads and on a few collapse mechanisms, in this work four mechanisms are recalled and further investigated within Limit Analysis (Method of the Yield Lines). All are characterized by a single free parameter. A fifth mechanism is introduced as well, which is at the same time more realistic and much more complex, as its geometry depends on three free parameters. (Evaluating the the bearing capacity requires the minimization of the collapse load with respect to these three parameters). The analysis at the Ultimate Limit state does not justify retrofitting the slab with the stiffening beam, but the fire checks indicate that the stiffening beam may be required to increase the fire resistence if the fixity level of the fully- or partially-supported sides is small or negligible, as shown by the elastic analysis with finite elements. The analysis at the ultimate limit state confirms that the simplest mechanisms are also the most probable, while the fire checks (under the standard fire) allow to make the following comments: (a) adding the stiffening beam markedly increases (by not less than 50%) the fire duration of the slab; (b) the stiffening beam (which is less heat-sensitive than the slab) forces the collapse mechanisms to shift from those involving the constraints to those occurring inside the slab; (c) the effectiveness of the stiffening beam increases with the fire duration; and (d) the top reinforcement of the slab – little affected by a fire from below – plays a fundamental role, that may be jeopardized by design mistakes in the detailing of the reinforcement (insufficient bonded length of the bars, curtailment of the bars, no or little continuity of the bars along the supports). This work confirms also the necessity to investigate the largest possible number of collapse mechanisms in the case of mixed constraints, all the more in fire conditions, since mere intuition can hardly identify the most probable mechanism and – more often than not – very different mechanisms may yield fairly similar ultimate loads. In fire, the in-time evolution of the bearing capacity of each mechanism and the great relevance of even small increases in the fire resistance (from half a dozen to a few dozens of minutes) contribute to the complexity of the analysis, as a few minutes more in terms of fire resistance may say a lot regarding personal and structural safety, not to mention the fire certification of the structure. Last but not the least, this work contributes to put in the correct perspective the Yield-Line Method, which on the one hand is instrumental in providing information on the structural collapse mode, on the other hand becomes increasingly complex with the increasing number of the free parameters required by the yield-line pattern. To put in competition the Yield-Line Method with nonlinear Finite-Element analysis may be an interesting step forward, with reference to the slab in question, which is at the same time a fairly complex and general structural case.| File | Dimensione | Formato | |
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https://hdl.handle.net/10589/141628