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.