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I am working on a situation where I have a beam that is simply supported in the middle, and the two ends of the beam are .005" higher than the middle where the support sits. I am trying to figure out with a linearly increasing load what the force is to make the two ends ,which are sitting .005" higher, the same heigh as the middle. Basically I want to flatten the piece.

EI = 731 lbf*in^2

length = 3.522in

width = .404in

So this is what I have:

I broke it down into two beams that are cantilevered

So for each cantilever:

load = (displacement * 81 * EI ) / (7*(Length/2)^4) Length/2 because I broken the simply supported beam into 2 cantilevered beams

load = 4.399 lbf/in

pressure = load/width of beam = 10.9 psi

My problem is assuming the above is correct, why does it not work out the same when I break that linearly increasing load into the resultant force:

resultant force for one of the cantilevered = .5 * L/2 * load = 3.872lbf

So since we need 2 of those forces, one on each end 2/3rds of the way up the linearly increasing triangle, that would equal 7.744 lbf

My problem is now if I say that force (7.744 lbf) / (L*width) = 5.442 psi

5.442 psi doesn't equal the 10.9 psi???

I know it is different but I did the same thing using a uniform pressure, where I broke the uniform pressure into two resultant forces and then divided those forces by the area and got the same pressure as the uniform pressure I had originally calculated.

Any help would be appreciated, thanks.

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# Beam that is simply supported in the middle

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