In terms of developing knowledge to enable more effective use of performance based engineering (PBE), one of the key limitations is the lack of an easy to use integrated computational tool that is also robust and comprehensive enough to enable automated modelling of more realistic fire scenarios, i.e., the structural response to localised or travelling fires. The main objective of this thesis is to establish such an integrated computational tool, which shall be based on the OpenSees software framework and facilitated by specially developed approaches to achieve higher efficiency of the integrated analysis. This includes the analysis of heat transfer from the fire to structural members, as well as the analysis of structural response to elevated temperatures during the fire. In this thesis, the research begins with the investigation of the feasibility of dimensional reduction for heat transfer analyses of structural members subjected to localised fire action (SFPE and Eurocode 1 fire models), which can be numerically represented by a linear or exponential correlation between incident heat flux and radial distance. Accurate estimates of the error induced by dimensional reduction are presented under strongly varying localised heat fluxes that represent the most non-uniform fire conditions in a building compartment. It is shown that beams and slabs can be adequately modelled with a lower dimensional heat transfer analysis for ordinary building fires. Using this approach, the complexity of heat transfer modelling and the required computing resource and user effort can both be significantly reduced, especially in cases where structural members are subjected to localised fire action. Thermo-mechanical simulations are presented to address the behaviour of structural members subjected to localised fire action, for which a ThermalAction- Wrapper is developed to approximate the temperature distribution from a mixed-order interpolation between sections (beam) or locations (slab). For concrete slabs subjected to localised fire, MITC4 based shell elements are used to account for material and geometric nonlinearities. An integrated simulation environment is developed, which is designed to be a computational tool that requires limited input but provides a comprehensive solution to the problem of simulating large structural frame and sub-frame response under realistic fire scenarios. A considerable amount of code has been written to create and operate the building model, and to process the heat fluxes from the design fires to the structure and the consequential structural response to the evolution of temperatures within it. Parametric studies have been performed to investigate the computational performance of the newly developed elements in modelling beams and slabs subjected to different cases of localised fire action. The results suggest that 3 to 6 force-based beam elements can adequately describe the localised response however more elements are required for quadratic distribution of incident heat flux and higher temperatures, which is due to the degradation of material strength that governs the accuracy especially when the members are heavily loaded. For slabs exposed to localised fires, centre fires are found to produce greater deflections than corner fires, while lateral restraints applied to the slabs may also lead to higher deflections. A small-scale three dimensional structural frame is modelled as a demonstration of the tool, tested against a number of localised fire scenarios. The global behaviour of the structure with the local effects induced by the fire action and partially damaged fire protection are investigated. Severe damage can be found in the members exposed to a single whole compartment fire, in contrast with the relatively small deflections that are observed when a fully protected column is engulfed by a localised fire. However if the passive fire protection is partially damaged, collapse may occur in the column as a result of load magnification because of the redistribution. To the author's knowledge this is the first piece of research that has been able to develop a practically feasible approach to enable efficient coupled computation of the response of structural frames to realistic fire scenarios on a freely available open source software platform. Currently this kind of analysis can only be carried out by just two or three large consulting firms because of the prohibitive commitment of analyst time and effort and to a lesser extent the need for significant computing resources. The work of this thesis will contribute enormously towards making high-end performance based engineering of structural fire resistance a much more practical proposition for small and medium size structural consultancies. Furthermore, the choice of OpenSees, which is a very well respected software framework for simulating structural response to earthquakes naturally enables this work to be extended to the simulating the multi-hazard structural resistance, such as in the event of a fire following an earthquake which may have locally damaged passive fire protection.

Dans ce travail, la méthode homogénéisation de multi-échelle, ainsi que diverses méthodes non homogénéisation, seront présentés pour étudier le comportement dynamique des structures périodiques. La méthode de multi-échelle commence par la séparation d'échelles. Dans ce cas, une échelle microscopique pour décrire le comportement local et une échelle macroscopique pour décrire le comportement global sont introduites. D'après la théorie de l'homogénéisation, la longueur d'onde est supposée grande, et la longueur de la cellule doit être beaucoup plus petite que la longueur caractéristique de la structure. Ainsi, le domaine d'homogénéisation est limité à la première zone de propagation. Le modèle d'homogénéisation traditionnel utilise des valeurs moyennes des éléments, mais le domaine de validité pratique est beaucoup plus petit que la première bande interdite. Alors, le développement de nouveaux modèles homogénéisés est beaucoup motivé par cet inconvénient. Par rapport au modèle d'homogénéisation traditionnel, équations d'ordre supérieur sont proposées pour fournir des modèles homogénéisation plus précises. Deux méthodes multi-échelles sont introduites: la méthode de développement asymptotique, et la méthode de l'homogénéisation des milieux périodiques discrètes (HMPD). Ces méthodes seront appliquées de façon séquentielle dans le cas d'onde longitudinale et le cas d'onde transversale. Les mêmes modèles d'ordre supérieur sont obtenus par les deux méthodes dans les deux cas. Ensuite, les modèles proposés sont validés en examinant la relation de dispersion et de la fonction de réponse fréquentielle. Des solutions analytiques et la méthode des ondes éléments finis(WFEM) sont utilisés pour donner les références. Des études paramétriques sont effectuées dans le cas infini, et deux différentes conditions aux limites sont prises en compte dans le cas fini. Ensuite, le HMPD et CWFEM sont utilisés pour étudier les vibrations longitudinales et transversales des structures réticulées dans le cas 1D et 2D. Le domaine de validité du HPDM est réévalué à l'aide de la fonction de propagation identifiée par le CWFEM. L'erreur relative au nombre d'onde obtenue par HPDM est illustré sur la fonction de la fréquence et le rapport d'échelle. Des études paramétriques sur l'épaisseur de la structure sont réalisées par la relation de dispersion. La dynamique des structures finies sont également étudiés en utilisant la HPDM et CWFEM. / In this work, the multi-scale homogenization method, as well as various non homogenization methods, will be presented to study the dynamic behaviour of periodic structures. The multi-scale method starts with the scale-separation, which indicates a micro-scale to describe the local behaviour and a macro-scale to describe the global behaviour. According to the homogenization theory, the long-wave assumption is used, and the unit cell length should be much smaller than the characteristic length of the structure. Thus, the valid frequency range of homogenization is limited to the first propagating zone. The traditional homogenization model makes use of material properties mean values, but the practical validity range is far less than the first Bragg band gap. This deficiency motivated the development of new enriched homogenized models. Compared to traditional homogenization model, higher order homogenized wave equations are proposed to provide more accuracy homogenized models. Two multi-scale methods are introduced: the asymptotic expansion method, and the homogenization of periodic discrete media method (HPDM). These methods will be applied sequentially in longitudinal wave cases in bi-periodic rods and flexural wave cases in bi-periodic beams. Same higher order models are obtained by the two methods in both cases. Then, the proposed models are validated by investigating the dispersion relation and the frequency response function. Analytical solutions and wave finite element method (WFEM) are used as references. Parametric studies are carried out in the infinite case while two different boundary conditions are considered in the finite case. Afterwards, the HPDM and the CWFEM are employed to study the longitudinal and transverse vibrations of framed structures in 1D case and 2D case. The valid frequency range of the HPDM is re-evaluated using the wave propagation feature identified by the CWFEM. The relative error of the wavenumber by HPDM compared to CWFEM is illustrated in the function of frequency and scale ratio. Parametric studies on the thickness of the structure is carried out through the dispersion relation. The dynamics of finite structures are also investigated using the HPDM and CWFEM.

This doctoral thesis concerns flanking transmission in light weight, wooden multi-storey buildings within the low frequency, primarily 20-120 Hz. The overall aim is to investigate how the finite element method can contribute in the design phase to evaluate different junctions regarding flanking transmission. Two field measurements of accelerations in light weight wooden buildings have been evaluated. In these, two sources; a stepping machine, and an electrodynamic shaker, were used. The shaker was shown to give more detailed information. However, since a light weight structure in field exhibit energy losses to surrounding building parts, reliable damping estimates were difficult to obtain. In addition, two laboratory measurements were made. These were evaluated using experimental modal analysis, giving the eigenmodes and the damping of the structures. The damping for these particular structures varies significantly with frequency, especially when an elastomer is used in the floor-wall junction. The overall damping is also higher when elastomers are used in the floor-wall junction in comparison to a screwed junction. By analysing the eigenmodes, using the modal assurance criterion, of the same structure with two types of junctions it was concluded that the modes become significantly different. Thereby the overall behavior differs. Several finite element models representing both the field and laboratory test setups have been made. The junctions between the building blocks in the models have been modeled using tie or springs and dashpots. Visual observation and the modal assurance criterion show that there is more rotational stiffness in the test structures than in the models. The findings in this doctoral thesis add understanding to how modern joints in wooden constructions can be represented by FE modelling. They will contribute in developing FE models that can be used to see the acoustic effects prior to building an entire house. However, further research is still needed. / Denna doktorsavhandling behandlar flanktransmission i flervåningshus med trästomme, inom det lågfrekventa området, främst 20-120 Hz. Det övergripande målet är att undersöka hur finita elementmetoden kan bidra i konstruktionsfasen för att utvärdera olika knutpunkters inverkan på flanktransmissionen. Två fältmätningar av accelerationer i trähus har utvärderats. I dessa har två olika lastkällor använts, i den första en stegljudsapparat och i den andra en elektrodynamisk vibrator (shaker). Det visades att shakern kan ge mer detaljerad information, men eftersom vibrationerna även sprider sig till omgivande byggnadsdelar vid fältmätningarna var det svårt att estimera tillförlitliga dämpningsdata även då shaker användes. Fältmätningarna följdes av två mätningar i laborationsmiljö. Dessa två experiment utvärderades med experimentell modalanalys, vilket ger egenmoder och dämpning hos strukturerna. Dämpningen för dessa trähuskonstruktioner varierar kraftigt med frekvens. Extra stora variationer registreras då en elastomer användes i knutpunkten mellan golv och vägg. Den totala dämpningen är generellt högre när elastomerer används i knutpunkten mellan golv och vägg i jämförelse med då knutpunkten är skruvad. Genom att analysera egenmoder och deras korrelationer (MAC), för samma trästruktur men med olika typer av knutpunkter, drogs slutsatsen att knutpunkten drastiskt förändrar strukturens dynamiska beteende. Flera finita elementmodeller av både fält- och laboratorieuppställningar har gjorts. I dessa har knutpunkterna mellan byggnadsdelar modellerats helt styvt eller med hjälp av fjädrar och dämpare. Visuella observationer av egenmoder och korrelationen dem emellan visar att det finns mer rotationsstyvhet i försöken än i finita elementmodellerna. Resultaten i denna doktorsavhandling har gett förståelse för hur knutpunkter i träkonstruktioner beter sig och kan simuleras med finit elementmodellering. Vidare kan resultaten bidra till utvecklingen av FE-modeller som kan användas för att kunna se de akustiska effekterna redan under konstruktionsstadiet. Dock behövs ytterligare forskning inom området.