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Simple analytical methods to predict one- and two-dimensional drying stresses and deformations in lumber

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Abstract

This study was conducted to develop analytical models for the prediction of drying stresses and defomations in lumber. Both one- and two-dimensional analytical models were developed with two assumptions: the visco-elastic creep could be neglected, and the diffusion coefficient is constant with moisture changes. The method developed in this study showed that the drying stress of lumber with symmetric moisture profile could be approximately predicted using one-dimensional (1D) and two-dimensional (2D) models. In the case of the 1D model, drying deformations could be determined rather easy and the drying stress can even be predicted by hand calculation. The results of this study might be used for lumber with an asymmetric moisture profile. In order to predict more accurately drying stress and deformation across overall moisture changes, however, this procedure should be incorporated with the other moisture transport models and might be extended to a 3D model.

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Abbreviations

u, v:

displacement in width and thickness directions, respectively

E :

Young’s modulus

σ :

stress

ε :

strain

α :

free shrinkage coefficient

M 0 :

initial moisture content

M s :

surface moisture content

ΔM:

moisture content change below fiber saturation point (FSP), ΔM≤FSP

ψ :

moisture characteristic function

F :

mass transfer Fourier number

t :

time

ν :

Poisson’s ratio

κ :

mechano-sorptive coefficient, MPa-1

μ :

mechano-sorptive coupling coefficient

D :

diffusion coefficient

E TR :

ET/ER

α TR :

αT/αR

R :

radial direction

T :

tangential direction

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Acknowledements

The authors thank Dr. R. Keey of the University of Canturbury, New Zealand for his valuable advice and discussions, and Prof. Y. Fortin of Laval University, Canada for his kind discussions. This work was supported by the grant of Post-Doc Program, Chonbuk National University in Korea (2000).

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Authors and Affiliations

  1. Department of Forest Products College of Agriculture, Chunbuk National University, 561–756, Chonju, Chonbuk, Republic of Korea

    Wook Kang

  2. Department of Forest Products College of Life Sciences and Agriculture, Seoul National University, 441–744, Suwon, Republic of Korea

    Hee-Suk Jung

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  1. Wook Kang
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  2. Nam-Ho Lee
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  3. Hee-Suk Jung
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Correspondence to Wook Kang.

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Kang, W., Lee, NH. & Jung, HS. Simple analytical methods to predict one- and two-dimensional drying stresses and deformations in lumber. Wood Sci Technol 38, 417–428 (2004). https://doi.org/10.1007/s00226-004-0230-z

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  • DOI: https://doi.org/10.1007/s00226-004-0230-z

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