Transformation of Elastic Properties for Lumber with Cross Grain
Publication: Journal of Structural Engineering
Volume 123, Issue 10
Abstract
Application of orthotropic constitutive models to lumber with cross grain requires transformation of coordinates when material axes are not aligned with board axes. This paper presents a procedure to construct the coordinate transformation matrix using angles measured on the surface of a board for any orientation of wood fibers and growth rings within the board. Procedures in the literature are limited to special orientations of the wood material, although their authors have not always recognized the limitations. The key to the present method is the recognition that for each set of three independent surface angles there corresponds a set of Euler angles that can be used in the coordinate transformation matrix. Numerical examples show that the procedure identifies significant variations in board elastic properties for changes in the grain and ring angles. The examples also reveal potentially critical material shear stresses in uniaxial situations following stress transformations associated with combinations of seemingly small angles.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
ANSYS engineering analysis system user's manual (ver. 4.3). (1987). Swanson Analysis Systems, Inc. Houston, Pa.
2.
Bindzi, I., and Samson, M.(1995). “New formula for influence of spiral grain on bending stiffness of wooden beams.”J. Struct. Engrg., ASCE, 121(11), 1541–1546.
3.
Bodig, J., and Jayne, B. A. (1982). Mechanics of wood and wood composites. Van Nostrand, New York, N.Y.
4.
Cook, R. D., Malkus, D. S., and Plesha, M. E. (1989). Concepts and applications of finite element analysis. John Wiley and Sons, New York, N.Y.
5.
Foschi, R. O.(1977). “Analysis of wood diaphragms and trusses. Part II: Truss-plate connections.”Can. J. Civ. Engrg., Ottawa, Canada, 4(3), 353–362.
6.
Goodman, J. R., and Bodig, J.(1970). “Orthotropic elastic properties of wood.”J. Struct. Div., ASCE, 96(11), 2301–2319.
7.
Hearmon, R. F. S. (1948). “The elasticity of wood and plywood.”Forest Products Res. Special Rep. No. 7, Dept. of Scientific and Industrial Res., London, U.K.
8.
Love, A. E. H. (1944). A treatise on the mathematical theory of elasticity. Dover Publications, Inc., New York, N.Y.
9.
Malvern, L. E. (1969). Introduction to the mechanics of a continuous medium. Prentice-Hall, Inc., Englewood Cliffs, N.J.
10.
March, H. W. (1944). “Stress-strain relations in wood and plywood considered as orthotropic materials.”Rep. No. 1503. U.S.D.A. Forest Service Forest Products Lab., Madison, Wis.
11.
Myklestad, N. O. (1967). Cartesian tensors. D. Van Nostrand Co., Inc., Princeton, N.J.
12.
“Standard practice for establishing structural grades and related properties for visually graded lumber.” (1993). D 245, ASTM, West Conshohocken, Pa.
13.
Suo, S., and Bowyer, J. L.(1995). “Modeling of strength properties of structural particleboard.”Wood and Fiber Sci., 27(1), 84–94.
14.
Wood handbook: Wood as an engineering material, Agricultural Handbook 72 (1987). U.S. Dept. of Agr., Washington, D.C.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 123 • Issue 10 • October 1997
Pages: 1402 - 1408
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Oct 1, 1997
Published in print: Oct 1997
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.