UKTC Archive

t/R 0.3 = 30 or 70% Hollowing

Subject: t/R 0.3 = 30 or 70% Hollowing
From: David Evans
Date: Mar 01 2021 16:44:22
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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