Measuring Modulus of Elasticity along and across the Grain

The Modulus of Elasticity can be calculated from a measurement of the deflection of the wood as a free-free beam loaded at its center.


Once the deflection for a given load is measured, the Modulus of Elasticity can be calculated from these expressions.


where I is the Moment of Inertia for the cross section of the beam.

These are the definitions of the variables used and the SAE units in which they are measured to obtain the Modulus of Elasticity in lbs per sq. in.

These tables from the Machinery's Handbook 2001 Ed. list Moment of Inertia expressions for different beam cross-sections.Page 219     Page 220     Page 221

So, the complete expression for the Modulus of Elasticity is



The Xcel spreadsheet (right-click "Save Content As") is set up to average 8-9 measurements of thickness from 2 micrometers: a small one that reaches only 1" from the edge and a larger home-made "deep-throat" caliper that is less accurate. The computation is carried out in duplicate. The results differ by ~6.5% due to the different results from these two sets of thickness measurements.The bold font cells are inputs to the calculation.
Western softwoods tend to have along/across ratios of ~5.8 while European spruces have ratios of ~4.5 but this is just one of several parameters that define the differences between these woods.
I favor length measurements in inches over millimeters because inexpensive micrometers, calipers and dial indicators are available that measure 0.001 inch lenghts which is 4 times more precise than 0.1 mm. The same argument applies to temperature where there are 180 Fahrenheit degrees between freezing and boiling water but only 100 Centigrade degrees. The reverse is true for the measurement of weight or force.