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pic: Beam Bending Example
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Re: pic: Beam Bending Example
So basically what I am seeing here is that most of the stress results along the sides, which are forced to stretch when a force is applied. Right? So there really isn't that much stress on the top? How would it look if there were a bunch of holes everywhere (on the top and sides)?
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Re: pic: Beam Bending Example
what software was this done with? Inventor maybe???
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Re: pic: Beam Bending Example
For the sake of making the discussion even more interesting, how about making several different shapes and sizes of beam, and applying the same (relatively small) load to them and showing them all? For example, you might have rectangular tubing with the load applied to the narrow side, and to the wide side, and round and square tubing, and an I beam, and a channel.
Also it would be nice if you'd give a quick explanation of how to set up the constraints in Inventor so others can do this, as it's not obvious to the novice Inventor user. |
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Re: pic: Beam Bending Example
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Holes will have a different effect depending on where they are placed. If in the blue areas, hardly any effect (so long as structrual rigidity is maintained) - while along the red areas (top and bottom) these holes will affect the strength of the beam, depending on their size and shape. |
Re: pic: Beam Bending Example
The question on holes got me curious. Here is a summary of my test and results
1"x1"x1/16" wall 6061 Aluminum Box Tube, 18" long. 0.625" holes down opposite sides, spaced at 1" centers End faces fixed constraint 500 psi pressure applied to a 2" long patch, on the top side center of the tube. For the given loading and fixed constraints, the part exhibited a 29% higher maximum stress with the holes than without. The part with holes had approximately 15% less mass than the part with holes. Anyhow, if your holes are on the faces 90 degrees to the one the force is being applied, you don't lose all that much strength. This is the principal behind I-beams. The more cross sectional area you put further from the center, the stronger the beam will be, because it will have a higher moment of inertia. This is why beams with a taller cross section are much stronger in bending, and why I beams have so much material so far away from the center. |
Re: pic: Beam Bending Example
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http://en.wikipedia.org/wiki/List_of...nts_of_inertia http://web.mst.edu/~mecmovie/index.html |
Re: pic: Beam Bending Example
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Holes would create 'stress concentrators' where the lines of flux (stress) would be concentrated between the edges of the holes and the sidewall. The stress loads here would be the same as in the full part but that section would only have the strength of the, now smaller, width. |
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Is the "strength" of the beam the same as "bending resistance?" I read in Dave Gerr's book on boat design that the stiffness (which I would think is the same as bending resistance) of a beam, all else being equal, goes up with the fourth power of thickness, not the third power. Of course, the failure strength might go up as the third power -- about this I know nothing. |
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I'm not familiar with Gerr's book, so I can't speak to the context. <speculation> Since you reference 'thickness' he may be experiencing both an increase in height and width of the section, but I can't be certain.</speculation> Not sure if I am clarifying or confusing things... pics to follow. |
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Attached is the deflection diagram that goes with the original post... 3.475 lbm 8643 psi max stress .133 in max deflection |
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OK, I'm posting each of the beam sections seperately because I think it organizes the data better... holler if I should stop.
4" x 2" aluminum tube (wide) 1/8" wall 1000 lbf uniform load 5.3283 lbm 5158 psi max stress .078 in max deflection |
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Last one of this batch...
2" x 4" aluminum tube (tall) 1/8" wall 1000 lbf uniform load 5.3283 lbm 5096 psi max stress - Note this is a singularity out at the support where as the others are in the middle. The middle of this is somewhat lower than 3400psi .026 in max deflection Are we getting anything out of this? (i.e. Keep going?) |
Re: pic: Beam Bending Example
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Don Rotolo's post talked about the stresses being greatest on the top and bottom, which doesn't match how I read the picture it's referring to. The recent images use the words "wide" and "tall", but the pictures associated with those words seem to be swapped. Help? |
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Thanks for saying something. This conversation started from another thread discussing frame rails getting hit from the side which is why I modeled the beam with the load from the side and now we're mixing that convention with the typical beam loaded from top convention. I'll correct the images so that the load is on top since that seems to be the easiest to understand for anybody wandering in to this thread. *sigh* Once again, I'm making the simple complicated. |
Re: pic: Beam Bending Example
Um, sorry about that, I accept the responsibility for confusing the directions. When I wrote I was thinking of deflection force from above, but of course the image shows (showed?) the force from the side.
Just think in 4 dimensions and it'll all make sense. Don |
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Is this what your looking for.....
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It looks like three smaller loads, 2 up and 1 down, with fixed end faces on a shorter beam. |
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i put equal weight in each place but in differing directions....like you said the two going up are equal to the one going down all forces are equal to 200 lbs.
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I also did a different one with the exact same force and placement as you and it still worked out. ( like the one you started off with )
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So from looking at the previous images I think we can safely conclude that
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1/8" wall 1000 lbf uniform load 2.674 lbm 20318 psi max stress - Gee, why is that so much higher than the others? :rolleyes: .243 in max deflection |
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