Distributions of modulus of elasticity and modulus of rupture in four mill-run lumber populations

Frank C. Owens, Steve P. Verrill, Rubin Shmulsky, Robert J. Ross

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2 Scopus citations


The modulus of elasticity (MOE) and modulus of rupture (MOR) of graded lumber populations are commonly modeled by normal, lognormal, or Weibull distributions, but recent research has cast doubt on the appropriateness of these models. Such modeling has implications for ultimate performance and efficiency of resource use. It has been shown mathematically that the distribution of MOR in a graded subpopulation does not have the same theoretical form as the full, ungraded (or "mill-run") population from which it was drawn; rather, its form is pseudo-truncated, exhibiting thinned tails. Although the phenomenon of pseudo-truncation in graded populations has been well substantiated, the form of the underlying full distribution-an essential factor in characterizing the distribution of the graded population-remains unsettled. The objective of this study was to characterize the distributions of both MOE and MOR in four diverse mill-run lumber populations to determine if and to what extent the distributions of strength and stiffness in mill-run lumber are similar from mill to mill. The authors collected a mill-run sample of 200 southern pine 2 × 4 specimens from each of four sawmills, for a total of 800 test pieces. After measuring MOE and MOR, they fit candidate distributions to those data by mill and evaluated each distribution for goodness of fit. Results suggest that perhaps none of the traditional distributions of normal, lognormal, or Weibull is adequate to model MOE or MOR across all four mills; rather, MOE and MOR in full lumber populations might be better modeled by skew normal or mixed normal distributions.

Original languageEnglish (US)
Pages (from-to)183-192
Number of pages10
JournalWood and Fiber Science
Issue number2
StatePublished - 2019
Externally publishedYes

Bibliographical note

Funding Information:
This research was made possible by funding from the US Department of Agriculture Forest Service Forest Products Laboratory under Agreement No. 17-JV-11111133-035. Any opinions, findings, conclusion, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the view of the US Department of Agriculture. The authors wish to acknowledge and thank the Southern Pine Inspection Bureau for their gracious contributions to this research.

Publisher Copyright:
© 2019 by the Society of Wood Science and Technology.


  • Full lumber population
  • Mill run
  • Modulus of elasticity
  • Modulus of rupture
  • Normal distribution
  • Pseudo-truncated
  • Weibull

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