The Modulus of Elasticity of Hybrid Larch Predicted By Density, Rings Per Centimeter, and Age
Keywords:Modulus of elasticity, wood density, age, rings per centimeter, larch, <i>Larix X eurolepis</i>
AbstractA total of 492 specimens from eighteen trees representing fast-growth larch were studied. The mean values of the modulus of elasticity (MOE), density, age, and rings per centimeter were determined for each. Mathematical models were developed to predict the MOE from the other parameters. Linear models are first presented showing the dependence of MOE on each of the three parameters, density, age, and rings per centimeter. A multivariate linear regression model is then developed for MOE as a function of all three parameters. The correlation coefficient of this model is 0.66, an improvement over each of the models for which each parameter is taken individually. A prediction of MOE by visual means alone, i.e., using only age and rings per centimeter in a linear model, is also presented. The correlation coefficient of this model is 0.58, which is superior to any of the parameters taken individually. In order to develop a model useful for extrapolation beyond the range of test data, a nonlinear model is presented. The parameters of this nonlinear model can easily be interpreted in terms of (1) the maximum attainable stiffness, (2) the ring age for maximum MOE growth rate vs. age, and (3) the shape parameter of the model. We found that the nonlinear model matched the data well and incorporated the realistic conditions of zero MOE at zero ring age and a limit on the maximum attainable MOE.
Ashby, M. F. 1992. Material selection in mechanical design. Pergamon Press. Oxford, UK. 311 pp.nBodig, J., and J. R. Goodman. 1973. Prediction of clastic properties for wood. Wood Science 5(4):249-261.nBodig, J., and B. A. Jayne. 1982. Mechanics of wood and wood composites. Van Nostrand Reinhold, New York. NY. 712 pp.nGuitard, D., and F. El Amri. 1987. Modèles prévisionnels de comportement élastique tridimensionnel pour les bois feuilles et les bois résineux. Annales des Sciences Forestières 44(3):335-358.nHaines, D. W., J.-M. Leban, and C. Herbé. 1996. Determination of Young's modulus for spruce, fir and isotropic materials by the resonance flexure method with comparisons to static flexure and other dynamic methods. Wood Sci and Technol. 30:253-263.nHaines, D. W., J.-M. Leban, and C. Herbé. 1997. Evaluation of the MOE of Norway spruce by the resonance flexure method. Forest Prod. J. 47(10):90-94.nHervé, J. C. 1998. Personal communication.nLeban, J. M., and F. Mothe. 1996. La qualité du bois de Douglas. Forêt Enterprise 108:22-25.nPâques, L. E. 1996. Variabilité naturelle du mélèze d'Europe: Bilan de 34 ans de test comparatif de provenances. Annales des Sciences Forestières 53:51-67.nRichards, F. J. 1959. A flexible growth function for empirical use. J. Exp. Bot. 10(29):290-300.nSYSTAT for Windows. 1992. Statistics, Version 5 Edition. SYSTAT, Inc. Evanston, IL. 750 pp.nZhang, S-Y. 1994. Mechanical properties in relation to specific gravity in 342 Chinese woods. Wood Fiber Sci. 26(4):512-526.nZhang, S-Y. 1997. Wood specific gravity-mechanical property relationship at species level. Wood Sci. Technol. 31: 181-191.n
The copyright of an article published in Wood and Fiber Science is transferred to the Society of Wood Science and Technology (for U. S. Government employees: to the extent transferable), effective if and when the article is accepted for publication. This transfer grants the Society of Wood Science and Technology permission to republish all or any part of the article in any form, e.g., reprints for sale, microfiche, proceedings, etc. However, the authors reserve the following as set forth in the Copyright Law:
1. All proprietary rights other than copyright, such as patent rights.
2. The right to grant or refuse permission to third parties to republish all or part of the article or translations thereof. In the case of whole articles, such third parties must obtain Society of Wood Science and Technology written permission as well. However, the Society may grant rights with respect to Journal issues as a whole.
3. The right to use all or part of this article in future works of their own, such as lectures, press releases, reviews, text books, or reprint books.