Middle Ordinate Method Measures Stiffness Variation Within Pieces of Lumber

This paper describes a laboratory instrument capable of detecting stiffness variations within boards over lengthwise regions of less than 2 feet. The magnitude of the lowest stiffness is presumed to be a better nondestructive indicator of strength than is the full-length stiffness of the piece. Stiffness calculations are based upon the assumption that short segments of a board undergoing bending approximate arcs of circles with varying radii. The middle ordinate measuring instrument measures, either continuously or in discrete steps, the perpendicular distance between the midpoint of a chord and its arc. This deflection, here referred to as a “middle ordinate,” is geometrically related to the radius of curvature which is inversely related to the modulus of elasticity. The minimum useful gage length of the device is between 8 and 12 inches. Differences in modulus of elasticity of better than 200,000 psi can be discriminated in 2 by 6 lumber having an outer fiber stress of about 750 psi. For a selected sample of 80 pieces of 16-foot southern pine lumber, maximum compression strength correlated with the lowest middle ordinate modulus of elasticity better than with specific gravity, compression strength ratio, or compression modulus of elasticity. In 69 of the pieces, failure occurred within the central 13 feet tested with the middle ordinate measuring instrument. Of those, 86 percent of the failure coincided with the region of lowest modulus of elasticity or in a region with a modulus within 10 percent of the lowest value. Although the middle ordinate measuring instrument cannot be considered a mechanical grading device from a practical standpoint, it does provide another means of assessing objectively the strength-reducing potential of defects in lumber. It can be employed in the laboratory environment to test whether utilization of the stiffness of individual defect regions will significantly improve strength-predicting capabilities. Firm verification of this principle should lead to improve lumber grading processes.

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