Structural strength of timber
The Evaluation of current rigging and dismantling practices used in arboriculture ( 2008 ) notes that tree stems which fail under load usually experience rupture on the compressive side first . The authors thereby propose the following method of deriving an approximation of the strength of a stem when it is subject to load .
Where :
F &'( * π 4 × d + , × σ - ./ 0 # − ( H − 1 ) × ρ × g
cos α + 8 × sin α × H − Z 1 d +
Fmax is the maximum load tolerable at anchor height H under the angle a before primary compression failure of marginal fibres occurs , d1 is the representative diameter of the stem at 1m height σcompr is the compressive strength of green fibres at the elastic limit ( yield strength – species dependant but using a value of 20MPa for Australian and New Zealand native species will provide a margin for error in most cases )
Z0 is the height of the representative diameter ( 1m ) ρ is the density of green wood ( species dependant but using a value of 1000kg / m 3 for Australian and New Zealand native species will provide a margin for error in most cases ) g is the acceleration due to gravity ( 9.81ms 2 )
We can simplify the equation by incorporating the ‘ generic ’ values for Australian and New Zealand timber suggested above and multiplying out the constants :
F &'( * d +
,
×
20 , 000 , 000 − ( H − 1 ) × 7 , 700
cos α + 8 × sin α × H − 1 d +
This method is specifically intended for use in tree rigging operations and may not be useful for the evaluation of most anchor points used for climbing and rescue . Whole-stem failure is unlikely in any rescue operation unless tensioned high-lines are to be used , or unless the tree structure is significantly compromised .
Where failure of a tree does occur , it is likely to be at a weak spot such as an area of decay , insect damage , mechanical damage or poor structure .
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