Relationship Between Radial Compressive Modulus of Elasticity and Shear Modulus of Wood


  • Jen Y. Liu
  • Robert J. Ross


Anisotropic material, elasticity, shear modulus, shear test, tensor transformation, wood


Wood properties in transverse compression are difficult to determine because of such factors as anatomical complexity, specimen geometry, and loading conditions. The mechanical properties of wood, considered as an anisotropic or orthotropic material, are related by certain tensor transformation rules when the reference coordinate system changes its orientation. In this paper, we used our verified shear modulus model to estimate compressive modulus of elasticity in the radial direction by means of certain established tensor transformation rules. The obtained basic engineering constants form a viable set that agrees with reliable test data and the anisotropic elasticity theory.


American Society for Testing and Materials (ASTM). 1996. Standard methods of testing small clear specimens of timber. ASTM D143-83. American Society for Testing and Materials, West Conshohocken, PA.nArcan, M., Z. Hashin, and A. Voloshin. 1978. A method to produce uniform plane-stress states with application to fiber-reinforced materials. Exper. Mech. 18(4):141-146.nBodig, J. 1965. The effect of anatomy on the initial stress-strain relationship in transverse compression. Forest Prod. J. 15(5):197-202.nBodig, J. 1966. Stress-strain relationship of wood in transverse compression. J. Mater. 1(13):645-666.nBodig, J. 1969. Improved load-carrying capacity of wood in transverse compression. Forest Prod. J. 19(12):39-44.nBodig, J., and J. R. Goodman. 1969. A new apparatus for compression testing of wood. Wood Fiber 1(2):146-153.nDaniel, I. M., and O. Ishai, 1994. Engineering mechanics of composite materials. Oxford Press, Oxford, UK.nDoyle, D. V., J. T. Drow, and R. S. McBurney. 1956. Elastic properties of wood—The Young's moduli, moduli of rigidity, and Poisson's ratios of Balsa and Quipo. Rep. No. 1528, USDA Forest Serv., Forest Prod. Lab., Madison, WI.nIfju, P. G. 1994. The shear gauge: For reliable shear modulus measurements of composite materials. Exper. Mech. 34(4):369-378.nJones, R. M. 1975. Mechanics of composite materials. Scripta Book Co., Washington, DC.nKennedy, R. W. 1967. Wood in transverse compression: Influence of some anatomical variables and density on behavior. Forest Prod. J. 18(3):36-40.nKobayashi, S. 1962. Restraint in compression test of orthotropic materials. Forest Prod. J. 12(4):89-92.nKollmann, F. F. P., and W. A. Côté, Jr. 1968. Principles of wood science and technology. I. Solid wood. Springer-Verlag, Inc., New York, NY.nKubojima, Y., H. Yoshihara, M. Ohta, and T. Okano. 1996. Examination of the method of measuring the shear modulus of wood based on the Timoshenko theory of bending. Mokuzai Gakkaishi 42(12):1170-1176.nLang, E. M., L. Bejo, J. Szalai, Z. Kovacs, and R. B. Anderson. 2002. Orthotropic strength and elasticity of hardwoods in relation to composite manufacture. Part II. Orthotropy of compression strength and elasticity. Wood Fiber Sci. 34(2):350-365.nLiu, J. Y. 2002. Analysis of off-axis tension test of wood specimens. Wood Fiber Sci. 34(2): 205-211.nLiu, J. Y. and R. Ross. 1997. Shear modulus variation with grain slope. Pages 107-111 in R. Perkins, ed. Mechanics of cellulosic materials, American Society of Mechanical Engineers, AMD-Vol. 221/MD-Vol. 77.nMarch, H. W., E. W. Kuenzi, and W. J. Kommers. 1942. Method of measuring the shearing moduli in wood. Rep. No. 1301, USDA Forest Serv., Forest Prod. Lab., Madison, WI.nNorris, C. B. 1955. Strength of orthotropic materials subjected to combined stresses. Report 1816, USDA Forest Serv., Forest Prod. Lab., Madison, WI.nPellicane, P. J., J. Bodig, and A. L. Mrema. 1994. Behavior of wood in transverse compression. J. Testing Eval. 22(4):383-387.nReiterer, A., I. Burgert, G. Sinn, and S. Tschegy. 2002. The radial reinforcement of the wood structure and its implication on mechanical and fracture mechanical properties. A comparison between two tree species. J. Mater. Sci. 37(5):935-940.nSchniewind, A. P. 1979. Mechanical behavior and properties of wood. Pages 233-270 in F. F. Wangaard, ed. Wood: Its structure and properties. Educational modules for materials science and engineering (EMMSE) project, Materials Research Laboratory, Pennsylvania State University, PA. Vol. 11979.nTsai, S. W. 1965. Experimental determination of the elastic behavior of orthotropic plates. J. Eng. Ind. 87(3):315-318.nWu, E. M., K L. Jerina, and R. E. Lavengood. 1973. Data averaging of anisotropic composite material constants. Pages 229-252 in J. M. Whitney, ed. Analysis of test methods for high modulus fibers and composites. ASTM STP 521.n






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