Journal of Arboriculture 18 (4): July 1992
Determining Strength Loss from Decay by E. Thomas Smiley and Bruce R. Fraedrich
SL% = d^4/D^4 x 100 ;Originally developed by engineers to compare the strength of pipes.
SL% = d^3/D^3 x 100 ;Wagener modified it to take into account the irregularity of trees.
SL% = d^3 + R(D^3-d^3) x 100
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D^3
SL = Strength loss
d = Diameter of hollow and/or nonstructurally sound wood
D = Diameter of sound wood
R = Ratio of cavity opening to stem circumference
The R(D^3-d^3) modification was developed by the Bartlett Tree Research Laboratories to account for wood which is "missing" at a cavity opening.
Among trees that broke from internal decay, average strength loss was 33% with a SD of 22% [could be between 11% and 44%].
Severity of decay in the trunk predisposes trees to failure [felling, breaking into half, etc.]. Other factors include crown density, branching structure, leaning, location of decay (e.g., in crotches), site exposure, storm severity, [and might I include inherant wood strength]. A lower threshold (20-25%) may be used for trees that are more predisposed.
Journal of Arboriculture 27(2): March 2001
Comparing Formulae that Assess Strength Loss Due to Decay in Trees by Brian Kane, Dennis Ryan, and David V. Bloniarz
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