Open-Cavity Trunk Strength Loss (Smiley & Fraedrich)
Strength loss in a trunk with an OPEN cavity.
Example
You enter
- Trunk diameter (in, inside bark) 24
- Sound-shell (wall) thickness (in) 3
- Open cavity face width (in, 0 = closed hollow) 8
You get
- Closed-hollow loss (Wagener) 42.1875
- Open-cavity strength loss 48.3216
- Penalty for the opening 6.1341
Checked against published worked examples from: Smiley & Fraedrich (1992) open-cavity strength-loss formula.
Details, formula, and sources
Scopean open face (wound, seam, fire scar) makes the ring a broken tube, far weaker than a closed hollow. loss = (hollow_d^3 + R x (D^3 - hollow_d^3)) / D^3 x 100, where R is the opening arc / circumference (Smiley & Fraedrich 1992). Collapses to Wagener at R = 0; validated against the paper's example (4-in stem 70% hollow, 2-in opening -> 45%). A 24-in trunk with a 3-in wall and an 8-in opening loses 48% vs the 42% a closed hollow shows. A screen, not a load rating.
Formula or tablehollow_d = D - 2t; R = min(1, opening_width / (pi x D)); closed_loss = (hollow_d^3 / D^3) x 100; open_loss = (hollow_d^3 + R x (D^3 - hollow_d^3)) / D^3 x 100.
Source and editionSmiley & Fraedrich (1992) open-cavity strength-loss formula, by name.
Free accessThe Smiley & Fraedrich open-cavity relation is published arboriculture research (ISA Arboriculture & Urban Forestry); a qualified arborist governs the assessment.
What governsEstimate. AHJ and licensed professional govern.
API field namesdiameter_in, shell_thick_in, opening_width_in, closed_loss_pct, open_loss_pct, opening_penalty_pct
- Opening ratio R = opening arc / circumference; the opening adds R of the remaining sound wood (D^3 - hollow_d^3) to the lossSmiley & Fraedrich 1992
- Collapses to Wagener at R = 0 (closed hollow) the formula equals the Wagener (hollow_d/D)^3 lossSmiley & Fraedrich 1992