Estimating Local Compliance in a Beam from Bending Measurements Part I. Computing "Span Function"
Keywords:Span function, local modulus of elasticity, local compliance, stress-rated, MOE, MEL, MSR, beam
Bending modulus of elasticity measurements have been useful and profitable for decades in the sorting of dimension lumber for its structural quality. Bending and tensile strengths of lumber are known to be correlated with modulus of elasticity. Previous research indicates that bending elasticity on short spans, shorter than can be practically measured with precision, may improve correlation with strength. It is expected, therefore, that the optimal estimation method of the present two-part paper will be applied in the machine stress rating (MSR) process for more accurate sorting of dimension lumber into MSR grades.
Using weighting functions called "span functions," the estimation method processes a sequence of bending measurements from overlapping spans, such as those obtained from equipment for MSR lumber production. A span function is specific to the support configuration of a particular bending span and defines how much the local elastic properties along a beam contribute to a measurement. Intuitively, the local elasticity values of a beam near span center affect the measurement more than values near span ends. Span function defines this effect as a function of position along the bending span. In Part I, a procedure is developed for computing span function of a general bending span configuration. Span functions are graphed for bending spans of a production-line machine used in MSR lumber production and for other bending span configurations. In Part II, use of span functions in optimal estimation of local elasticity is described.
American Society for Testing and Materials. (ASTM). 2005. Standard Test Methods of Static Tests of Lumber in Structural Sizes. D198-05a. American Society for Testing and Materials, West Conshohocken, PA.nBechtel, F. K. 1985. Beam stiffness as a function of pointwise E, with application to machine stress rating. Proc. Int'l Symp. on Forest Products Research. CSIR. Pretoria, South Africa.nBechtel, F. K., C. S. Hsu, and T. C. Hanshaw. 2006. Method for estimating compliance at points along a beam from bending measurements. U.S. Patent No. 7,047,156.nBechtel, F. K., C. S. Hsu, and T. C. Hanshaw. 2007. Estimating local modulus of elasticity in a beam from bending measurements, an overview. Forest Prod. J.57(1/2):118-126.nHigdon, A., E. H. Ohlsen, and W. B. Stiles. 1960. Mechanics of materials. Wiley & Sons, New York, NY. 502 pp.nKass, A. J. 1975. Middle ordinate method measures stiffness variation within pieces of lumber. Forest Prod. J.25(3):33-41.nOrosz, I. 1976. Relationship between apparent modulus of elasticity, gage length, and tensile strength of lumber. Wood Sci. Technol.10:273-291.n
The copyright of an article published in Wood and Fiber Science is transferred to the Society of Wood Science and Technology (for U. S. Government employees: to the extent transferable), effective if and when the article is accepted for publication. This transfer grants the Society of Wood Science and Technology permission to republish all or any part of the article in any form, e.g., reprints for sale, microfiche, proceedings, etc. However, the authors reserve the following as set forth in the Copyright Law:
1. All proprietary rights other than copyright, such as patent rights.
2. The right to grant or refuse permission to third parties to republish all or part of the article or translations thereof. In the case of whole articles, such third parties must obtain Society of Wood Science and Technology written permission as well. However, the Society may grant rights with respect to Journal issues as a whole.
3. The right to use all or part of this article in future works of their own, such as lectures, press releases, reviews, text books, or reprint books.