Estimating Local Compliance in a Beam from Bending Measurements Part I. Computing "Span Function"

Friend K. Bechtel


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.


Span function;local modulus of elasticity;local compliance;stress-rated;MOE;MEL;MSR;beam

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