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Improved models for predicting the modulus of rupture of lumber under third point loading


Frank C. Owens
Rubin Shmulsky



Publication type:

Research Paper (RP)

Primary Station(s):

Forest Products Laboratory


FS Research Paper


To properly evaluate the reliability of lumber structures, good models for the strength distributions of their components are needed. Modulus of rupture (MOR) distributions of structural lumber grades have often been modeled as two-parameter Weibulls. However, in a series of papers, Verrill and others have established that strength properties of visual and machine stress rated grades of lumber are not distributed as two-parameter Weibulls and that modeling them as two-parameter Weibulls can yield large over- or underestimates of probabilities of breakage. Instead, grades of lumber have “pseudo-truncated” distributions. Recent research also established that the appropriate MOR model can change significantly with location and time and that model differences have practical significance. Verrill and others concluded that “there may be significant efficiencies that can be obtained through the development of computer models that yield real-time in-line estimates of lumber properties based on measurements of stiffness, specific gravity, knot size and location, slope of grain, and other strength predictors.” In this paper, we discuss models that predict the MOR of a piece of lumber from modulus of elasticity, specific gravity, slope of grain, and knot data.


Verrill, Steve P.; Owens, Frank C.; Shmulsky, Rubin; Ross, Robert J. 2021. Improved models for predicting the modulus of rupture of lumber under third point loading. Research Paper FPL-RP-712. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 38 p.

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