Modelling cross-laminated timber floors in dynamic analysis - Eigenfrequency prediction
Abstract: In the late 1990s cross-laminated timber (CLT) was developed. The development of CLT was a project aimed to produce a structural product that could compete with the concrete industry and contribute to a reduced effect on the environment, due to the low environmental impact of timber in relation to other building materials. CLT elements are usually constructed as panels which contain multiple layers of laminations, where every second layer is oriented in a 90-degree angle to adjacent layers. The layup and the youth of CLT implies that design approaches for timber structures available today are not fully applicable to CLT. The final design of wooden floor slabs is most often governed by serviceability limit state requirements, often relating to deflection and vibration in the vertical direction. An employed method to analyse the vibration susceptibility of wooden floor slabs is through a numerical analysis, which is executed with software that uses the nite element method. To produce models that have the same characteristic behaviour as a real floor design is of great importance. Research concerning how to create appropriate models of CLT floor slabs has been performed, although, more research is necessary to be able to determine modelling features regarding support conditions, material properties and other modelling options. In this Master's dissertation, an evaluation of how different modelling options affect the modal response up to 80 Hz of a CLT floor slab is presented. The necessary level of detail of the structure of a CLT floor and the possibility to simplify the description of the material properties and still obtaining relevant results in terms of modal behaviour was evaluated. Four finite element models were assembled with different levels of detail, based on a selected CLT floor element. An analytical evaluation was performed, based on a derivation of the fundamental frequency for a simply supported beam considered as a continuous media, which also is given in the recommended design codes (Eurocode 5). The most advanced model that was created is three-dimensional and includes five layers, all individual laminations and a gap of 0.2 millimetres between the laminations. The second model is three-dimensional and each of the five layers of laminations are modelled as one unit; the gap is excluded. The third model, is two-dimensional and includes all the five layers. The fourth model, is a two-dimensional plate where no individual layers or laminations are modelled. In addition, an analytic model was created where the fundamental frequency was evaluated. The result of the finite element analyses shows that there are great similarities of the modal response between the three most advanced models that include the orthotropic characteristics, while the fourth model and the models with modied material parameters diverge. This indicates that the individual layers of laminations and the orthotopic characteristics are necessary to include in the modelling to produce an accurate model of a CLT floor when analysing modal response up to 80 Hz. The individual laminations are, however, not necessary to model. The use of isotropic characteristics did not give satisfactory results. If only the fundamental frequency is of interest, a simple one-dimensional model is sufficient to predict accurate modal behaviour. The finite element models were able to produce an accurate prediction of the fundamental frequency, the fourth model (the two-dimensional plate model) required some tuning of the material properties to give an accurate response.
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