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Old 8th Mar 2011, 18:03
  #626 (permalink)  
Old Engineer
 
Join Date: Jul 2007
Location: Virginia, USA
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Torsional stiffness

Just as background to the information posted by sound asleep, the torsional stiffness of a hollow prism (such as a wing) would depend on the area enclosed by the structural cross-section of object, in addition to the thicknesses of the enclosing cross-section. Here this would normally be the vertical surfaces of the forward and aft main spars, and the horizontal upper and lower surfaces of the wing between these points.

[Note: To some extent the relatively thick vertical webs of the spars cannot be fully utilized in torsion, as the wing surfaces are not comparably thick; additionally, the square corners on this section add to stresses making these regions less efficient. But these complications are basically the same before and after the incident, and so can be ignored in visualizing the basic problem (if not ignored in analyzing it in detail).]

The problem now is that the forward spar is missing in action to some extent. A tear in a surface loaded in torsion (twisting) is a serious problem, as in general the surface must be continuous to satisfy the mathematical condition of enclosing an area. Discounting the damaged forward spar entirely, the area enclosed would be reduced, perhaps to 3/4 or less compared to the undamaged condition.

This would be so even though the forward spar only carried 5% of the load, as was posted sometime back, IIRC-- presumably the reference was to vertical load. And of course openings in shear surfaces can be reinforced, but this is not easy to calculate. And one can say, well, just plug the geometry, as damaged, into the analysis program. This too can be much more easily said than done, as explained following.

That is, every added node is a problem beyond a certain point. It is always necessary that the load matrix operate on the stiffness matrix in such a way the the output matrix of stresses can, first, actually converge to an answer; and, second, that the output stresses are actually correct values. I omit any references to this as I am speaking from the experience of having had to deal with large-matrix structural grid analyses that did not initially converge, even using very sophisticated programs. One's analysis costs can quickly rise if your repetoire of input tweaks fails. (Well, that's how I did it in my day.) OE
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