Michael KAWRZA

System identification of cross-laminated timber structures based on dynamic testing  

Since cross-laminated timber (CLT) has been introduced 30 years ago, the application of timber construction has been constantly expanding from single-story buildings to multi-story buildings in residential housing but also in industrial construction. CLT is commonly composed of an uneven number of three, five or seven glued timber layers and used in typical structural engineering applications as floor and wall elements. The individual layers consist of wooden boards, which are placed side by side, and adjacent layers are arranged at an angle, typically perpendicular to each other. Compared to reinforced concrete buildings, timber construction has a high stiffness-to-weight ratio, which allows to build comparatively lightweight structures. Consequently, timber structures are more prone to vibration, and therefore, the design is generally based on serviceability criteria. Advances in timber construction, such as a recently developed star-shaped steel connector that allows to build wide span point-supported CLT slabs without joists, amplify the problem of undesirable vibrations in ways that they may affect the structural integrity of building components. Therefore, one of the aims of this doctoral thesis is to contribute to the understanding of the dynamic behavior of various timber structures, especially timber floors with different boundary conditions made of CLT panels, in-situ and under laboratory conditions, using the methods of system identification and model updating. In order for these methods to be applicable to the investigated timber structures, they need to be adapted, modified and improved, which is another aim of this doctoral thesis.

 First, a pilot study on CLT beams is presented, where it is investigated to which extend structural health monitoring can be applied to CLT structures. To compare the undamaged and damaged states, the modal parameters, i.e. natural frequencies and mode shapes, of the test specimens are used as damage indicators. These parameters are estimated with the developed experimental modal analysis routine that is further extended for application on different CLT structures. Additionally, the modal parameters are the basis for a model updating procedure in which the input parameters of a numerical model are varied until the numerical and experimental results coincide. By performing the experimental modal analysis and model updating in a controlled environment, limitations of the applied procedures are revealed and possible requirements are carried out before testing large-scale test objects.

 The second test object investigated in this doctoral thesis is a large-scale point-supported CLT slab, for which a two-day test campaign in form of an experimental modal analysis was carried out. The dynamic response of the structure was recorded at 651 measurement points distributed over the slab surface. The dense grid was chosen to capture possible local affects in the identified mode shapes due to the point-supports realized with a novel star-shaped steel connector. As a result of this long measurement time, the structure cannot be assumed time invariant since it was exposed to environmental effects, which contradicts with one criterion in modal analysis. Consequently, complex modes are identified during the evaluation of the measured data. However, in this doctoral thesis an approach is presented to minimize the imaginary parts of the mode shape vector components by performing a piecewise central axis rotation. Additionally, to extend the findings of the study on this particular test object, model updating is performed to identify the uncertain elastic parameters and support flexibilities for a finite element model, and subsequently, various parametric studies are performed.

 The point-supported CLT slab could only be investigated in its raw state, i.e. without floor construction. However, in timber engineering, the dynamic performance of a floor needs to be assessed including floor construction. Since information on the evolution of the dynamic properties of timber floors during different construction states is sparse, a CLT floor with floor construction, i.e. elastic bonded fill, footfall sound insulation and screed, and drywall ceiling is examined continuously during the construction phase. Performing system identification in the different construction states, the shaker, which was used to excite the structure in the experimental modal analysis, is identified as disturbance factor. Therefore, in this doctoral thesis, a two-step model updating approach is presented, in which the shaker is considered in the finite element models as a spring-mass system. After calibrating the different numerical models for each investigated state, the shaker model is omitted in the coupled finite element models, and subsequently, the modal properties of the timber floor are computed numerically. Additionally, it is shown that a superficial finite element model of the timber floor, as used in engineering practice, underestimates the natural frequencies of the structure considerably, which underlines the importance of the presented model updating procedure.

 One method to predict the dynamic response of structures is by performing deterministic model updating on a finite element model. The result is a point-estimate of the uncertain input parameters, however, no uncertainty in the experimental data or the input parameters is considered. Therefore, in this doctoral thesis, a stochastic model updating procedure using Bayesian inference is adopted. To perform Bayesian model updating it is necessary to formulate a measure of fit, where commonly the modal parameters of a structure are used, resulting in a modal measure of fit. However, it is shown that using the modal measure of fit for structures with free-free boundary conditions, the outcomes are ambiguous when both the mass and the stiffness properties of the test object are unknown. For this reason, a novel formulation of the measure of fit using cross-signature correlations is proposed. This alternative approach is then verified on a numerical CLT panel and simulated experimental data, and subsequently, the algorithm is used on real test data.



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