- #1
vettett15
- 13
- 0
Hey Guys,
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.
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.