Hollow / Decayed Trunk Strength Loss
A tree-risk screen for a standing tree with internal decay.
Example
You enter
- Trunk diameter outside bark (in) 24
- Sound-wood shell thickness (in, radial) 4
You get
- Strength loss (Wagener, cube) 29.6
- t/R ratio 0.333
Checked against published worked examples from: Wagener 1963 / Mattheck t/R / ISA TRAQ.
Details, formula, and sources
ScopeThe Wagener strength loss (hollow_d^3 / D^3) x 100 from a central hollow, plus the Mattheck t/R ratio and the t/R < 0.30 concern flag. The cube law keeps loss small until the hollow is large -- a trunk can be two-thirds hollow and keep most of its strength. An open cavity is far weaker.
Formula or tablehollow_d = D - 2t; loss_pct = (hollow_d^3 / D^3) x 100; t_over_R = t / (D / 2); concern when t/R < 0.30.
Source and editionHollow-trunk strength-loss screen (Wagener 1963; Smiley & Fraedrich 1992; Mattheck & Breloer t/R; ISA TRAQ), by name.
Free accessThe Wagener cube-law loss and the Mattheck t/R rule are published arboricultural results; a qualified arborist and a TRAQ assessment govern.
What governsEstimate. AHJ and licensed professional govern.
API field namesdiameter_in, shell_thick_in, loss_pct, t_over_r
- Closed hollow the loss estimate assumes a central closed hollow; an open cavity (slot) is far weakerWagener 1963
- Concern trigger t/R < 0.30 (sound shell below 30% of the radius) flags escalation to a full TRAQ assessmentMattheck & Breloer