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Tensions in expanded dugout and cracking threshold

Derivation of tension formula |

As one can see from the formula on the drawing, tension * T* grows proportionally
to thickness of sample walls h and in reverse proportion to
initial radius of the log R. So the bigger a log, and the thinner
it was hollowed, the easier it expands. The member (1-1/k) approaches unity when the
expansion rate k tends to infinity, i.e. when a sample becomes
completely flat.

Flat planks made of log halves approx. 30cm in diameter and 12mm thick walls cracked a lot when drying after expanding, so the tensions must be considered beyond the threshold in this case:

* T* = (12/150)*(1 - 1/∞) = 0.08 ( beyond threshold);

Bottom piece made of 45cm log with ~14mm walls was expanded to approx. 65cm final radius, and cracks were few:

* T* = (14/225)*(1 - 1/(650/225) ) = ~0.038 (below threshold);

So we can assume the threshold tension to be approx. 0.04 for pine wood and for this particular technique.

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