Failure Modeling: A Basis for Strength Prediction of Lumber

Authors

  • Steven M. Cramer
  • James R. Goodman

Keywords:

Strength prediction, lumber strength, failure modeling, mathematical models, fracture mechanics, knot effects

Abstract

Failure modeling of knot-containing wood members was investigated as a means to predict member tensile strength. A finite element/fracture mechanics model was developed to model the progressive fracture process observed during failure of wood members. The failure modeling process yields predicted tensile strengths for members that contain knots in the wide face. Predicted strengths compared favorably with tensile strength data measured in initial experimental tests. Predicted strengths are generated from basic engineering computation and are not derived or adjusted by any empirical factors. With further research and verification, the concepts presented hold promise for use in lumber grading and quality assurance.

References

American Society of Testing and Materials. 1984. Standard methods for establishing structural grades and related allowable properties for visually graded lumber. ASTM designation: D 245-81.nAnthony, R. 1985. Experimental data for the tension behavior of Douglas-fir with defects. M.S. thesis, Dept. of Forest and Wood Sciences, Colorado State University, Ft. Collins, CO.nAtluri, S. N., A. S. Kobayashi, and M. Nakagaki. 1975. An assumed displacement hybrid finite element model for linear fracture mechanics. Int. J. Fract. Mech. 10:1281-1287.nBodig, J., and J. R. Goodman. 1973. Prediction of elastic parameters for wood. Wood Sci. 5(4): 249-264.nCramer, S. M. 1984. Failure modeling of wood structural members. Ph.D. dissertation, Department of Civil Engineering, Colorado State University, Ft. Collins, CO.nCramer, S. M. and J. R. Goodman. 1983. Model for stress analysis and strength prediction of lumber. Wood Fiber Sci. 15(4):338-349.nCramer, S. M. and J. R. Goodman. 1984. Modeling material failure with a vectorized routine. CYBER 200 Applications Seminar. NASA Conference Publication 2295. Pp. 259-271.nDabholkar, A. Y. 1980. Analysis of wood with knots and cross grain. Ph.D. dissertation, Department of Civil Engineering, Colorado State University, Ft. Collins, CO.nDoyle, D. V., and L. J. Markwardt. 1967. Tension parallel-to-grain properties of southern pine dimension lumber. Research Paper FPL 84. U.S. Products Forest Laboratory.nGoodman, J. R., and J. Bodig. 1980. Tension behavior of wood—An anisotropic, inhomogeneous material. Final Report to the National Science Foundation. Colorado State University, Ft. Collins, CO.nGreen, A. E., and W. Zerna. 1968. Theoretical elasticity, 2nd ed. Oxford University Press. Pp. 322-368.nKunesh, R. W., and J. W. Johnson. 1972. Effects of single knots on tension strength of 2- by 8-inch Douglas-fir dimension lumber. For. Prod. J. 22(1):32-36.nLeicester, R. H. 1974. Applications of linear fracture mechanics in the design of limber structures. Proceedings of the 1974 Conference of the Australian Fracture Group, Melbourne, Australia 23:156-164.nMcGowan, W. M. 1968. Parallel-to-grain tensile properties of visually graded 2 x 6-inch Douglas-fir. Information Report VP-X-46. Forest Products Laboratory, Vancouver, BC.nNewlin, F. A., and R. P. A. Johnson. 1923. Basic grading rules and working stresses for structural timbers. United States Dept. of Agriculture, Dept. Circular 295.nPearson, R. G. 1974. Application of fracture mechanics to the study of tensile strength of structural lumber. Holzforschung 28(1):11-19.nPetterson, R. W., and J. Bodig. 1983. Prediction of fracture toughness of conifers. Wood Fiber Sci. 15(4):302-316.nPhillips, G. E., J. Bodig, and J. R. Goodman. 1981. Flow-grain analogy. Wood Sci. 14(2):55-64.nPugel, A. D. 1980. Evaluation of selected mechanical properties of coniferous knotwood. M.S. thesis, Dept. of Forest and Wood Sciences, Colorado State University, Ft. Collins, CO.nTang, R. C. 1984. Stress concentration around knots in laminated beams. Wood Fiber Sci. 16(1):57-71.nWilson, T. R. C. 1934. Guide to the grading of structural timbers and the determination of working stresses. United States Department of Agriculture. Misc. Publication No. 185.nWu, E. M. 1967. Application of fracture mechanics to orthotropic plates. J. Appl. Mech. 12-1967:967-974.nZandbergs, J. 1985. Finite element fracture prediction of orthotropic inhomogeneous materials. M.S. thesis, Dept. of Mechanical Engineering, Colorado State University, Ft. Collins, CO.n

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Published

2007-06-28

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Section

Research Contributions