It's neither.
I recently shared this post on social media and thought it might be of
interest to some of you. The size of the files for the 'Why t/R Ratios
Aren't Very Helpful' pdf and Paul Muir's Cross Sectional Area v Section
Modulus graph are too large to share on the UKTC.
...
Recently, I caught a podcast where a tree was declared 'safe' if it's less
than 30% hollow. I think they meant 70% hollow. Either way, this isn't right
for several reasons.
I've posted about this before, but as long as this kind of mistake is being
broadcast I think it's worth repeating so the message gradually gets home.
The heart of the confusion is the t/R = 0.3 fallacy. t/R = 0.3 is when a
residual wall thickness (t) is 30% of the stem radius (R). It's often cited
as a failure threshold. It's not. The 'Why t/R Ratios Aren't Helpful' pdf
explains why in detail and can be downloaded from VALID's website here.
https://valid.tiny.us/v65mz84a
In short, one reason is because of a geometric property called section
modulus. Wind load and material properties remaining equal, if you double
the diameter you increase the load bearing capacity of a tree by 8 times.
To add to the confusion, t/R 0.3 is often referred to as 70% hollow. In
fact, a 0.3 t/R ratio is only 50% hollow. 70% is the radius, which is one
dimension. t/R 0.3 is the area, which is two dimensions.
This graph from Paul Muir shows the relationship of central hollowing on:
A = Cross Sectional Area
Z = Section Modulus
t/R = 0.3
A = 49% loss of cross sectional area
Z = 24% reduction in load bearing capacity
To make matters worse. A tree with a t/R ratio of 0.3 can have a very high
likelihood of failure, or it can have a very low likelihood of failure.
If all that wasn't enough, it's seldom that where decay is of concern we're
dealing with a cross sectional area of a tree that's a circle.
Cheers
Acer Ventura
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