A beam finite element for the analysis of structures in fire

Walls, Richard Shaun (2016-12)

Thesis (DPhil)--Stellenbosch University, 2016.

Thesis

ENGLISH ABSTRACT: All building structures require a specified fire resistance rating and numerous procedures have been produced for ensuring this. In engineering practice designers can generally not perform detailed structural fire designs on buildings due to the high computational modelling requirements of most modern structures, and so they typically resort to conservative prescriptive methods instead. Hence, design engineer orientated methods are required to improve fire safety while providing more economical buildings. The goal of this dissertation is to provide a simple, but technically accurate, model for the analysis of structures in fire, including composite structures, which considers buildings as skeletal frames. To achieve this end a beam finite element has been developed that has a moving, eccentric neutral axis that accounts for material properties that change as structures heat up. A composite bending stiffness, axial stiffness and resultant thermal forces are calculated for a generic cross-section. Material and geometric nonlinearity is considered. The properties of any number of materials (e.g. a steel beam, concrete slab and reinforcing steel) are represented by single beam properties. These calculated beam properties can be included in either commercially available, but simple, finite element software or advanced finite element modelling tools. The only assumption required is that Euler-Bernoulli behaviour, where plane sections remain plane, must hold. A methodology for including rebar tension stiffening at elevated temperatures has been included based on modifying an ambient temperature model. A series of numerical case studies are presented, comparing the results of the proposed beam formulation against finite element models using shell elements. Results between these models (which includes deflections, stresses, strains and neutral axis positions) typically differ by 0-5% when Euler-Bernoulli assumptions hold. Furthermore, case studies and experimental results from real fire tests in the literature were also analysed by the proposed formulation coupled with relatively simple finite element software. The deflections of structures in fire predicted by the proposed model are well within acceptable tolerances for fire engineering systems, and typically comparable to more complex models in the literature. The model developed has been used to investigate eleven different beams consisting of steel beams, concrete slabs and composite steel-concrete beams, along with conducting a series of parametric studies. With further research and the inclusion of three-dimensional behaviour the method could become a valuable tool for the analysis of structures in fire.

AFRIKAANSE OPSOMMING: Alle geboustrukture vereis 'n bepaalde brandbestandheid gradering en talle prosedures bestaan om dit te verseker. Ontwerpers in ingenieurspraktyk is in die algemeen nie in staat om gedetailleerde rasionale brand ontwerpe vir strukture uit te voer nie, as gevolg van die hoë numeriese modellering vereistes vir meeste moderne strukture. Daarom gebruik ingenieurs tipies konserwatiewe voorskriftelike metodes. Dus is eenvoudiger, ontwerp-georiënteerde modellering metodes nodig om brandveiligheid te verbeter terwyl meer ekonomiese geboue verskaf word. Die doel van hierdie verhandeling is om 'n eenvoudiger, maar tegnies akkuraat, model vir die analiese van strukture, insluitend saamgestelde strukture, in brande te voorsien waarin geboue as skeletale rame beskou word. Om hierdie doel to bereik is ‘n balk eindige element ontwikkel wat ‘n bewegende, eksentriese neutrale as (NA) gebruik om die veranderinge in die eienskappe van materiale in ag te neem. ‘n Saamgestelde buigingstyfheid, aksialestyfheid en resulterende temperatuurkragte word vir ‘n generiese dwarssnit bereken. Materiaal en geometriese nielineariteit is beskou. Die eienskappe van ‘n aantal materiale (bv. ‘n staalbalk, betonblad en bewapeningstaal) word deur enkele balk eienskappe verteenwoordig. Hierdie berekende balk eienskappe kan ingesluit word in kommersiël beskikbare, maar eenvoudige, eindige element sagteware, of gevorderde eindige element modellering gereedskap. Die enigste benodigde aanname is dat Euler-Bernoulli gedrag, waar ‘n gegewe dwarsnit in ‘n enkele vlak bly, moet gebruik word in die analiese. 'n Metode vir die insluiting van bewapeningstaal trekspanning verstywing by hoë temperature is ingesluit, wat ontwikkel is deur 'n wysiging van 'n kamertemperatuur model. ‘n Aantal numeriese gevallestudies word aangebied. Resultate van die metode en ‘n Abaqus model met gebruik van dop elemente is vergelyk. Die resultate van die modelle (wat defleksies, spanning, vervorming en NA posisies insluit) is tipies binne 0-5% van mekaar wanneer Euler-Bernoulli aannames gebruik word. Verder is gevallestudies en eksperimentele resultate uit die literatuur ook geanalieseer met gebruik van die metode gekoppel met relatief eenvoudige eindige element sagteware. Die defleksies vir brand situasies soos bereken met gebruik van die voorgestelde model is binne aanvaarbare toleransies vir brand ingenieurswese stelsels, en is tipies vergelykbaar met meer komplekse modelle uit die literatuur. Die voorgestelde model is gebruik om elf verskillende balke, wat bestaan uit staal balke, betonblaaie en saamgestelde balke, te ondersoek. 'n Reeks van parametriese studies is ook uitgevoer. Met verdere navorsing en die insluiting van driedimensionele gedrag kan die metode 'n waardevolle hulpmiddel word vir die analiese van strukture in 'n brande.

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