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In Reply to: RE: Thank you Bill ... posted by andyr on October 06, 2014 at 00:22:38
andyr
Let us call the support 7.5" away as A, 8" away as B and 10" away as C. The triangle ABC is right angled at B and has side AB 15.1", BC 8 and AC 16.9" in length.
From my calculations I find Reaction at A as 4.3 lbs, at B as 2.61 lbs and at C as 1.53 lbs with the total load being 8.44 lbs.
Had to refer back to old textbooks like Timoshenko's Plates and Shells and the two other books he wrote with Young and Goodyear. I had to do some derivation to get the values for the triangular shape. It all turned into a simple equation of the ratio of the distance of the load to the opposite side of the triangle to the distance of the support to the same side. Thus it is a matter of 3 equations. Interestingly the sum of these 3 ratios add up to one in any triangle.
Thanks for the opportunity to exercise the old grey cells with some structural engineering.
Regards
Bill
Follow Ups:
I intuited that the answer lay in the concept you said ( the ratio of the distance of the load to the opposite side of the triangle to the distance of the support to the same side ) but I didn't know how to express it, mathematically.
OK, so:
* 4.30 @ A
* 2.61 @ B, and
* 1.53 @ C.
That was the simple case ! :-)) For the real-life situation, we need to get more complicated ... and allow for the added affect of 2 arm weights near B and C!! :-))
See my modified sketch:
It seems to me that if the arms were placed at apex B (arm weight = 0.99 lb) and apex C (arm weight = 1.65 lb) then the weight distribution would simply become:
* 4.30 @ A
* 3.60 @ B, and
* 3.18 @ C.
But because the arms are cantilevered out from B & C, there is a negative action on the apex which is at the other end of the particular triangle side?
So:
* the 0.99 lb arm outboard from B reduces the weight at C, and
* the 1.65 lb arm outboard from C reduces the weight at A?
But how to calculate the resulting apex totals, with these cantilevered weights? :-))
FYI, here is a pic of the 1st version of my 'SkeletaLinn' subchassis - which I completed in July, last year. This has the bearing positioned closer to A, causing an excessive compression of the spring at that apex (so I had to get a custom-made spring made up, which was 30% stiffer than the Linn springs).
Hence the weight analysis for v2! :-))
Thanks, Bill,
Andy
A + B + C MUST = 9 By definition I got 4.62# for A(7.5"); 2.81# for B(8"); and 1.57# for C (10")
The problem I solved is the one framed for Krieger below and I thought the weight was 9# but I see he changed that to 8.44 #. Therefore, if I ratio my solution from 9# to 8.44#, I get the same results you did. You're correct - my bad!
Edits: 10/06/14 10/06/14 10/06/14
Hey thats wonderful. The answers match which means they are correct. Great.
Cheers
Bill
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