internal forces when steam bending wood

Jun 2019
10
1
uk
Hi all, first of all is this the most appropriate forum of the many options to pose some questions relating to the forces created when wood steam bent .

I understand the practical aspects but I cant get the relevant maths to tally,
thanks I post the qu. when I know where to post .
 
Jun 2019
10
1
uk
is it ok to post in more than one forum area ?
 
Jun 2019
10
1
uk
a few facts first ..

when bending the wood the outside surface is totally restricted from expanding by the green strap with end blocks . so as the wood bend the inside surface is compressed. the force to compress the wood is a constant . a value i have practically tested. the strap has a tension gauge at G. so i know the tension force being exerted within the restraining strap.
It seems logical that the force in the strap should be equal to the compression constant x area,
However the the force within the strap is far less than this figure , only about 30% . can anyone explain where the force is coming from to compress quite a the timber without an equal and opposite force on the strap. ( without he strap the timber would break across the outer surface as it is relatively weak in tension.)
IMG_ arc.jpg
 
Jun 2019
10
1
uk
I will give more details of my particular problem later ,
but if anyone is a little intrigued by the topic then a look at the maths in 'the mechanics of bending wood ' page 31 on the link below may help in forming an answer to my issue.
As said previously I am not a mathematician but still need help with what seems to be an anomaly . but it cant be ...some how the physics of what is happening must be able to be explained . Only then can I improve the bending machine and successful bends.

https://www.fpl.fs.fed.us/documnts/usda/ah125.pdf
 
Jun 2019
10
1
uk
The board i am bending is approx 10" wide so the forces involved here are very high .
the board is approx 1" thick . the distance between the point of contact of the wood and the former starts at 50 " but reduces as the wood is bent around the former. so if my understanding is correct there is about a 50 : 1 MA with the point on the strap vertically above the point of contact with the former acting as the fulcrum point.
The comprehensive force required to compress oak is 6720 psi this is reduced by approx 30% when steamed so approx 4700 psi x10 for the board width = 47000lbs.
The max load detected in the gauge in the steel strap is 7000lb. nothing near 47000.
This is the anomaly I question , the wood does bend and it does compress , so 47000lb is being exerted but the rule of equal and opposite reaction doesn't seem tie up,
Any thoughts as to what I am missing here ?
 
Apr 2014
1,013
348
UK
Ah-ha, some details!
While I don't have a full answer, what I think is happening is that since the compression isn't even over the whole cross section (10 x 1 inch), the psi will be less. The outer part of the bend has no compression at all, only the innermost part has the maximum compression, so the result must be somewhere between 0 and 47000lbs.
 
Jun 2019
10
1
uk
hi thanks Dave for the reply ...however once wood starts to compress the force on it cannot be increased, it self regulates so to speak so since all the wood has compressed across its thickness or lets say 95% of its thickness then the figure are in the realm outlined.

I have tried compressing a sample and as soon as it starts compressing the gauge stops rising however much more the 'screw is turned ' so to speak