Stochastic analysis of clear timber as a structural material

Wood/timber has been widely used for house and bridge construction. It is a widely available natural material that necessitates low energy for the production, following simple processes. The environmentally friendliness, together with the low cost of raw material makes it an efficient building material. Moreover, timber possesses attractive mechanical properties such as high specific strength and stiffness. In contrast, timber constructions have, to a large extent, been based on experience and craftsmanship, which prevents taking full advantage of this material. There are several reasons for this. Timber has a complex mechanical behavior being a natural highly anisotropic fiber composite, with properties that are also affected by moisture content. For specific species, geographical location, local growth conditions and moisture content, the material properties depend, among others, on the age, the structural imperfections, the location of timber within the tree, and load history. Consequently, the mechanical properties of timber are, inherently, highly variable. Variability of timber properties includes statistical and spatial variabilities, referred to as random spatial variability (RSV). This entails adopting a probabilistic/stochastic approach to analysis of timer structures. The aim of this research is to understand and model the effect of the RSV on the clear timber mechanical properties, as well as the experimental characterization of RSV for clear timber, and also to develop a stochastic finite element framework for random response assessment of clear timber components. A size effect model was developed which takes into account the RSV in the strength field. The theory of random fields was used for this purpose. Using the spectral representation scheme, realizations of strength field in each specimen were generated. The stochastic response was obtained via the Monte Carlo method. The model results was compared to the existing experimental data in the literature. Also, an analytical expression was provided to facilitate the application of the model. Clear timber specimens of different lengths were fabricated for longitudinal tensile tests. Local deformations along the lengths of the specimens were recorded during the tests in order to characterize the RSV in longitudinal properties. A connection between the mesostructure of the clear wood and its local elastic modulus was observed. Statistics concerning the elastic modulus, strength and strain to failure and the effect of length change on these properties were extracted. The correlations between the strength, the elasticity and the density were obtained. Transverse properties were also investigated which are of particular importance in some applications such as mechanical and adhesively-bonded timber joints. Regularly positioned and randomly positioned specimens were cut from different timber boards. Statistics and size effects concerning the elastic modulus, strength and strain to failure as well as the correlation between the properties were studied. The spatial variability in the transverse elastic modulus, the tensile strength and the failure strain was also experimentally studied. Mesostructural patterns of clear timber were shown to have a direct effect on the local elastic modulus. Finally, a stochastic finite element framework was established by combining the spectral representation scheme for RSV modelling and the finite element software ABAQUS in a non-intrusive manner. This framework can be used for the stochastic structural response assessment of timber structural components made of clear timber. To show the applicability of the model in real applications, the failure of adhesively bonded double-lap timber joints were simulated under tensile loading. The effect of size on the strength was also taken into account. The results were in a fairly well agreement with the available experimental data in the literature.