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Lumber is wood that has been processed into uniform and useful sizes (dimensional lumber), including beams and planks or boards. Lumber is mainly used for construction framing, as well as finishing (floors, wall panels, window frames). Lumber has many uses beyond home building. Lumber is sometimes referred to as timber in England, Australia and New Zealand, while in most parts of the world (including the United States and Canada) the term timber refers specifically to unprocessed wood fiber, such as cut logs or standing trees that have yet to be cut. Lumber may be supplied either rough-sawn, or surfaced on one or more of its faces. Rough lumber is the raw material for furniture-making, and manufacture of other items requiring cutting and shaping. It is available in many species, including hardwoods and softwoods, such as white pine and red pine, because of their low cost. Finished lumber is supplied in standard sizes, mostly for the construction industry – primarily softwood, from

Stochastic analysis of clear timber as a structural material

Alireza Farajzadeh Moshtaghin

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.

EPFL2016

Tragverhalten und Bemessung von Holz-Glas-Verbundträgern unter Berücksichtigung der Eigenspannungen im Glas

Klaus Kreher

The construction principles of "Timber-Glass-Composite-Girders" demand practical and theoretical research to ensure reliable designs. Toward this objective the mathematical description of load-bearing and the non-rigid bond is the subject of this work, i.e. to define the contributing parameters for the design of these girders. The non-rigid-bond of the adhesive joint is of great importance because of its influence on the load-bearing of the system as a whole. The loading of girders is dominated by permanent forces thus leading to the obligation of knowing the long-term behaviour of the system and its components. The definition of the characteristic values, taking into account the long-term load-bearing, is an intrinsic part of this investigation. It can be shown that the load-bearing of the girders depends on the fracture of the glass panes. The properties of glass-fractures are a function of the residual internal prestresses due to the heat-strengthening of the panes. The load-bearing, particularly the post-cracked behaviour, changes with respect to the intensity of these internal prestresses. The timber is able to reinforce the cracked glass, leading to a ductile load-bearing behaviour as in the girders, with a dependency upon the size of the remaining fractures. A model based on the differential equations of the non-rigid bond is defined in order to calculate the loading-peaks of the adhesive joint and the material loading itself. The characteristic values of the non-rigid bond, such as the number and distances between cracks and the load introducing length, were evaluated in tests on composite slabs and small scale girders. The existing calculation models which take into account non-rigid bonding were modified to adapt the influence of the width and thickness of the adhesive joint. In order to calculate the stressing of the material the existing calculation models were adapted to calculate the post-cracked situation. The load-bearing behaviour of glass-panes bent with respect to its strong neutral axis needs other safety-considerations than panes, bent off their plane. It is shown that the existing safety considerations subject to the use of glass can not easily be adapted onto the composite girders. The bending with respect to the strong neutral axis and the reinforcement of the glass of the timber demands a different hypothesis to adapt the fractural mechanical analysis and to establish a safe limit conception. This is part of the performed research of this document. The following descriptions present briefly the obtained results: Depending on the quality of the glass (residual stresses due to heat-strengthening, e.g. annealed glass, heat-strengthened glass, fully tempered glass), the ductility and the mode of failure of the girders does change. As a result of its failure mode, annealed glass without internal prestresses offers the highest remaining load-carrying potential after the first crack has appeared. This ductility and thus the structural safety, diminishes with an increasing degree of internal prestressing due to thermal treatment. Heat-strengthened glass (with various degrees of prestressing, various residual stresses) shows a decrease in remaining load-carrying capacity with an increasing degree of prestressing until it fails in a brittle mode as fully toughened glass does. This has to be well considered in respect to safety considerations. Girders with panes made of glass having internal residual stresses due to heat strengthening below 50N/mm2 are considered to collapse ductily, residual stresses bigger than 50N/mm2 cause brittle failure. The effective stiffness of the girders decreases under permanent loads in function of the bondage. Both, timber and adhesive take part in this decrease; the influence of both of the involved materials has been defined. Since the design of conventional glass constructions which uses the concept of principle stresses cannot be adapted, unidirectional shear stresses had to be determined for the shear strength of glass, which is defined as 25N/mm2 for annealed glass. The characteristic values of the adhesive to define the non-rigid bonds have been determined, likewise the influence of the width and thickness of the adhesive joint. The load introducing length, the distances between cracks and the number of cracks are defined with tests on composite slabs. A model to describe the theoretical bond with the defined parameters based on the differential equations was developed. This model allows the calculation of the material stressing at the load introduction and on both sides of a crack. To calculate the stressing of glass and timber existing calculation models which take into account non-rigid bonding were modified to adapt the influence of the width and thickness of the adhesive joint. In order to calculate the stressing of the material the existing calculation models were adapted to calculate the post-cracked situation. The safety factors for the influences of the glass surface, environmental conditions, load duration and the parameters of fracture mechanical analysis as developed as they are known for semi-probabilistic safety concepts for glass constructions cannot easily be adopted. The bending with respect to the strong neutral axis demands a different hypothesis in order to adapt the fractural mechanical analysis and to develop the safety parameters. For the reliable design of timber-glass-composite-girders a contribution to the appropriate use of probabilistic, semi-probabilistic and deterministic safety concepts are given. A realised construction (Hotel "Palafitte" in Monruz (NE)) shows an example and the experience made in designing girders.

EPFL2004

Spatial variability in longitudinal elastic modulus of clear timber

Alireza Farajzadeh Moshtaghin, Steffen Franke, Thomas Keller

Different factors such as age, location of timber within the tree, structural imperfections, load history such as wind and snow etc. can affect the material properties of timber taken from the same species, and grown in the same geographical location and local growth conditions. Consequently, there is a high variability in the mechanical properties [1-2]. This variability is both spatial and random, and is sometimes referred to as ‘random spatial variability’ [3]. Four groups of specimens of different lengths were prepared and their quasi-static behavior was experimentally investigated under tensile loading. In addition to the global displacement monitoring, the local deformations along the length of each specimen were measured. The effect of the mesostructure of the clear timber on the local elastic modulus was examined. The spatial variability of the elastic modulus was experimentally characterized. Also, Statistics concerning the elastic modulus for different lengths were derived and compared.

2015