Keywords: moisture transfer, timber structures, natural varying humidity, sorption hysteresis, hysteresis model, finite element analysis.

This paper presents numerical analyses of timber elements exposed to natural varying humidity at constant temperature. Safety, serviceability and maintenance requirements for timber structures are all strongly dependent on moisture state and the moisture history of the timber. The moisture state of seasoned timber in natural varying climate, indoor or outdoor, is not governed by the acting levels of humidity and temperature alone. The history of moisture states has an important influence on present moisture state. This is readily seen in a sorption isotherm for wood, where there is a hysteresis relation between moisture equilibrium of wood and ambient humidity.

Models for moisture state prediction in an open porous and hygroscopic material, wood, in a natural varying climate has been presented in [1,2]. In this work a coupled Fickian model for moisture field determination is applied. The coupled model accounts for both vapor transport in pores and bound water transport in wood tissue. These transport processes are modeled by individual transport equations following Fick's law. The transport equations are fully coupled by the process of phase change from vapor to bound water or vice verse, i.e. sorption and desorption. Since moisture state history influences the relationship between moisture state of wood and air humidity, it must therefore be taken into account. In order to include history dependency a hysteresis model is used here.

Moisture states in a timber specimen exposed to daily and hourly cyclic variation of outside humidity of the air are presented. Results from the numerical study show that only certain area near the boundary which is exposed to the variation of outside humidity is noticeably influenced by the rise in moisture content. From the view of designing the timber elements this is important since a change of moisture state alters the material properties as well as induces stresses as a result of shrinkage and the swelling constraint.

1

H.L. Frandsen, S. Svensson, L. Damkilde, "A hysteresis model suitable for numerical simulations of moisture content in wood", Holzforschung, 61, 172-181, 2007. doi:10.1515/HF.2007.031

2

H.L. Frandsne, S. Svensson, "Implementation of sorption hysteresis in multi-Fickian moisture transport", Holzforschung, 61(6), 693-701, 2007. doi:10.1515/HF.2007.113

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