Relationship between apparent modulus of elasticity,gage length,and tensile strength of lumber

The percent explained variation (r²) of tensile strength (T) of dimension lumber can be accounted for primarily by apparent modulus of elasticity (E_a).Tensile strength ratio, a good index of T of structural lumber, and E_a are both dependent on relative knot size, making T a function of E_a. This theoretical relationship helps to increase r² when T is regressed on E_a and gives the cause and effect for some multiple regression analyses. An independent variable was identified on the basis of this theory.Shortening the gage length enhances ability to predict T when flatwise bending E_a or tension E_a is used as an independent variable, but not when edgewise bending E_a is used.Two single variables not previously reported, E_a measured in flatwise bending on 16-inch gage length (EF 16) and E_a measured in tension on 6-inch gage length (ET 6) (based solely on deformation measurements), are individually able to explain approximately as much variation of T (r²=0.75) as the combination of E_a measured flatwise on 48-inch gage length (span length for the existing American grading machines), and ASTM bending strength ratio. The combination of EF 16 and ET6 can explain 85% of the variation of T. The highest r² (0.87) was obtained when a modified bending strength ratio was added to these new variables.This research was done in partial fulfillment for the degree of Master of Science, Department of Civil Engineering, University of Wisconsin, Madison, Wis., May 1971.