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Area moment inertia, curved, non-straight beam

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Area moment inertia, curved, non-straight beam

Trying to determine the bending stiffness (2nd moment of area, or section modulus, etc) for this non-straight beam.  Part is basically a corrugated piece of sheet metal.

cd_iso.jpg

Interested in stiffness when part is loaded a la:

cd_fbd.jpg

 

More precisely, I want to determine how the stiffness varies with changes in dimension "D".

 

cd_sketch.jpg

I suppose I could run a bunch of simple mechanica/Simulate analyses, while varying dimension "D", then extrapolate the correlation between stiffness and "D".  This might suffice in the end...  However I'm wondering if anyone has insight into a more direct (analytical, symbolic) approach

Any ideas on how to figure this out would be greatly appreciated!

Thanks

1 REPLY 1

Re: Area moment inertia, curved, non-straight beam

My initial simplification would be that the compliance (= 1/stiffness) increases in proportion to the total length of the sheet metal - a bit like a clock spring.  This may not be exact, as the bending moment varies linearly along the 71" and not along the 'developed' length of the sheet, but it should give a good first indication.