A New Method for Studying the Elastic Behavior of Wood

The “second area moment proposition” was used to determine the modulus of elasticity of wood at various angles to the grain. The second area moment proposition is defined as “The vertical displacement of point A from the tangent to the elastic curve at B equals the moment (with respect of A) of the area of the rest of the bending moment diagram between A and B, divided by EL,” Applied to wood beams, this method allows the calculation of deflection on the basic of known elastic properties, or conversely the calculation of modulus of elasticity of various portions of, the beam from observed deflections. The validity of the Hankinson formula for the calculation of modulus of elasticity values at angles to the grain other than zero to 90 degrees was established in work with specially prepared beams. The relationship between modulus of elasticity perpendicular to the grain and moisture content for yellow birch was found to be logarithmic. Analysis of beams with inserts of local cross grain positioned a various points in the span revealed that theoretically computed deflections check very closely with actual deflections obtained by testing.

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