Keywords: glulam beams, water-vapour diffusion, non-linear analysis, creep, shrinkage, mechano-sorptive effect, finite element method.

It is well known that wood deforms more extensively if relative humidity in surrounding air changes. The water content in wood changes with a slight delay with respect to changes of relative humidity in surrounding air. Structures made of wood deform due to mechanical load, thermal load and changes of water content which result in shrinkage and swelling. Two important phenomena can be observed in wood as well: normal or viscous creep, which can be defined as the change of deformation in constant loading conditions, and mechano-sorptive effect which is a coupled effect of mechanical load and changing water content. The second phenomenon was first observed and reported in 1964 by Hearmon and Paton [1]. Several authors dealt with mechano-sorptive effect (see e.g.: Hunt and Shelton [2], Ranta-Maunus [3], Toratti [4]). In their papers experimental results as well as numerical models are presented.

The numerical analysis consists of two phases: the determination of water content and the mechanical analysis. Generally, the water transport in wood and mechanical behaviour are coupled. However, we assume that the deformation of the structure does not have a major effect on water transport in wood. In this way the numerical procedure simplifies considerably. First, the distribution of water content is evaluated by solving differential equation of diffusion. The results of the first computational stage are used as the input data for the second part of the numerical analysis, in which the mechanical response of the beam is assessed. The stress-strain state and the deflections of the beam are determined by the computer program NonWood, based on highly accurate non-linear beam finite element. In the paper we present a material model which links elastic, viscous, mechano-sorptive deformations, shrinkage due to changes of water content, stresses and time. The displacements and stress distribution at some characteristic cross-sections are presented. The temperature distribution may also have a significant effect on water content distribution, as well as on deformation of the structure. However, since the experiment used for comparison was held at constant temperature, the effect of changing temperature was not taken into account.

In the literature several reports about mechano-sorptive effect evaluation based on extremely small wood specimens can be found. We decided to perform experiments on relatively large specimens. Therefore, long-term tests of straight glulam beams of size 5 by 10 by 180 cm in different constant and changing climatic conditions were completed in January 2000. The specimens were made from European spruce (Abies alba Mill.) and glued with resorcyn-phenol-formaldehide type of glue. Each beam consists of 7 laminations. Some control specimens were kept at constant humidity, others were exposed to changing humidity but were not loaded.

The effect of the permeability of glue in glulam beams is examined. Two extreme cases were taken in consideration: the permeability of glue is equal to permeability of wood, the permeability of glue is equal zero - impermeable layer of glue. It was found that the differences between the two extreme cases are significant only in the second laminate from the top and the bottom. As a result the effect of permeability of glue does not have a significant effect on displacements of the beam.

The comparison between numerical and experimental results indicates that it is possible to obtain a successful mathematical model for the moisture diffusion as well as mechanical behaviour. The analysis of contributions of different strains to the total strain implies that all effects induced by water content changes are more pronounced in beams with relatively small cross-sections. The main problem in mechanical analysis remains the experimental evaluation and verification of parameters involved in numerical procedures.

1

Hearmon, R.F.S., Paton, J.M., "Moisture content changes and creep of wood", Forest Products Journal, 14, 357-359, 1964.

2

Hunt, D.G., Shelton, C.F., "Progress in the analysis of creep in wood during concurrent moisture changes", Journal of Materials Science, 22, 313-320, 1987. doi:10.1007/BF01160586

3

Ranta-Maunus, A., "Creep and effects of moisture in timber", Informationsdienst Holz, Düsseldorf, Germany, 3.4, 1-21, 1995.

4

T. Toratti, T., "Creep of timber beams in a variable environment", Helsinki University of Technology, Laboratory for Structural Engineering and Building Physics, Report 31, 1992.

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