Equations used to evaluate strength loss associated with wood decay, adapted from (5).
| Source | Equation | Strength loss threshold | Strength loss calculated for section A (below) | Strength loss calculated for section B (below) | Comments |
|---|---|---|---|---|---|
| Coder (1989) | (d/D)*100 | 220–44% caution > 50% hazard | 13% | 4% | Does not account for asymmetric decay |
| Wagener (1963) | (d/D)*100 | 33% | 22% | 9% | Does not account for asymmetric decay |
| Smiley & Freadrich (1992) | (d + r[D-d])/D * 100 | 33% | 22% | 14% | Accounts for lateral decay, but underestimates strength if internal decay is larger than indicated by external cavity opening |
| Mattheck, et al. (1992) | t/R | <0.30 | 0.45 | n/a | Formula is not applicable to trees with open cavities. For these trees, the strength loss threshold is a cavity occupying >120 degrees of the stem circumference |
| Percent loss in I | I decay / 1 trunk * 100 | see comment | 12% | 28% | No failure criteria. Accounts for irregularly shaped decay |
| Percent area of | a/A * 100 | 35% | 18% | Does not account for asymmetric decay |
Where:
d = diameter of decayed wood
D = diameter of trunk
t = width of sound wood
r = size of cavity opening/circumference of trunk
R = radius of trunk
I = second moment of area a =
area of decay
A = area of trunk