t/R = 0.3 | 70% hollow or 30% solid?

[Acer ventura]

I thought some of you might find this post from VALID's News page useful, so am sharing it.

 

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 Very Helpful' pdf explains why in detail.

 

 

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.

Why tR ratios are not very helpful v5.0.pdf

[Khriss]

To be fair to Matthecks work and others, his data did see failures outside the guide t/r , so by averaging its a sound guide, but quite literally can fall down on individual trees.   K

[Acer ventura]

3 minutes ago, Khriss said:

so by averaging its a sound guide

Hi Khriss

 

Sorry, t/R 0.3 isn't a sound guide at all.  It's pretty much useless and incredibly misleading.

[Khriss]

Well Matthecks research was quite extensive, however i condemned  a line of Lombardys couple years ago, well beyond the limit t/R 30% of decay and annoyingly the buggers are still standing,  but wont be parking my car under them. Case by case will always throw up exceptions and Mattheck himself told me any tree within strike distance of a Rail line should be felled  😮  so what do you do  😯 K

[Paul Cleaver]

Ive only just found this thread by chance.

Tree surveyors shoud not use Matthecks equation literally, just a guide 

A big factor for me with hollow trees, is the trees vitality. Has the hollow tree had the vitality ( stored energy) to produce adaptive growth - butresses to compensate for strength loss in the trunk? Is the tree still producing adaptive growth? This can  be visable in the the summer with lighter wood. 

If it hasnt produced adaptive growth in the current year , you have to decide whether the tree has produce enough adaptive growth already  and doesnt need anymore, or the trees vitality is low and is not able to produce it.

 

[AA Teccie (Paul)]

10 hours ago, Paul Cleaver said:

Ive only just found this thread by chance.

Tree surveyors shoud not use Matthecks equation literally, just a guide 

A big factor for me with hollow trees, is the trees vitality. Has the hollow tree had the vitality ( stored energy) to produce adaptive growth - butresses to compensate for strength loss in the trunk? Is the tree still producing adaptive growth? This can  be visable in the the summer with lighter wood. 

If it hasnt produced adaptive growth in the current year , you have to decide whether the tree has produce enough adaptive growth already  and doesnt need anymore, or the trees vitality is low and is not able to produce it.

 

A big factor for me is the size, and form, of the tree crown - once had an application to fell ("remove") a vet Oak on a development site based purely on the 'T/R' factor - the form of the tree with very low major limbs meant it couldn't fall over if it wanted to  

Whether T/R is valid or not (apologies for the pun, unintended) it has brought the issue of hollowness not being solely a reason to remove a tree to the fore...no bad thing.

Thanks..

[daltontrees]

On 06/12/2023 at 08:15, AA Teccie (Paul) said:

A big factor for me is the size, and form, of the tree crown - once had an application to fell ("remove") a vet Oak on a development site based purely on the 'T/R' factor - the form of the tree with very low major limbs meant it couldn't fall over if it wanted to  

Whether T/R is valid or not (apologies for the pun, unintended) it has brought the issue of hollowness not being solely a reason to remove a tree to the fore...no bad thing.

Thanks..

Agreed, there's always other factors, which can be more important than strength loss through hollowing. It stmulates debate, which is good, but is followed blindly by some as if it is a rule, which is a bad thing.

 

Inserted is what I think is a slightly more intuitive graph of the same subject matter. It shows that as t/R ratio decreases the cross sectional area doesn't decrease so quicky and the strength decreases even more slowly. So at Mattheck's fabled t/R = 0.3, half the cross sectional area is still present and 3/4 of the strength (measured by 'modulus') is still there.

The strength doesn't drop to half until only 15% of the stem remains!

 

In reality, stem buckling will probably cause failure first before tensile breakage.

 

Edited December 7, 2023 by daltontrees

[jfc]

Ok, opinions on this stem? On another forum some people felt it was retainable.

[Mick Dempsey]

Is that a Horse Chestnut? 
Isn’t species important in these decisions?

[jfc]

15 minutes ago, Mick Dempsey said:

Is that a Horse Chestnut? 
Isn’t species important in these decisions?

Sycamore. Was decay by dryad's saddle.