Force & Deflection While Dumping Material Into Bin
Force & Deflection While Dumping Material Into Bin
(OP)
I am designing a 5' diameter bin which will be filled from a larger bin above. We will dump 75 cu. ft., or approx. 3000 lb., of material into the lower bin in around 5 seconds. I know the normal calculations for sudden impact, but how do you calculate the force and deflection for a falling mass when it is a flowing material instead of all one chunck of mass?
Phil
Phil





RE: Force & Deflection While Dumping Material Into Bin
That's your worst case scenario, isn't it?
V
RE: Force & Deflection While Dumping Material Into Bin
If the material fell as a solid chunk, according to Roark the ratio of the stress as the product hit the bottom of the bin compared to the stress of the static load is 1 + sqrt(1 + 2h/d), where h = height of fall and d is displacement during static loading. Since the material doesn't fall as a solid chunk, this equation can't be used.
Phil
RE: Force & Deflection While Dumping Material Into Bin
I'm sorry if I'm missing something.
V
RE: Force & Deflection While Dumping Material Into Bin
Something falling onto a surface imparts a much higher force on the surface than if it is just sitting on the surface. The farther it drops, the higher velocity it has and the higher force it causes.
Phil
RE: Force & Deflection While Dumping Material Into Bin
A compromise approach would be to treat the dump as a series of small chunks, each impacting immediately after the other, spread out over 5 seconds.
TTFN
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RE: Force & Deflection While Dumping Material Into Bin
I knew that the longer it takes for all of the material to fall in the bin, the less impact the fall would have. However, I didn't know if 5 seconds was long enough.
I might try your suggestion of treating it as a bunch of small chunks and see how chunk size affects the force.
Phil
RE: Force & Deflection While Dumping Material Into Bin
So, even with small, solid chunks, there'll be some degree of overdesign.
TTFN
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RE: Force & Deflection While Dumping Material Into Bin
I've just had another thought while writing this, consider it as a fluid mass flow rate impacting a surface.
The force is the mass flow rate x impact velocity.
So estimate the time to discharge the 3000 lb into the lower bin to give the mass flow rate. The impact velocity is
v^2 = 2 x g x h . There's an estimate of the impact force.
RE: Force & Deflection While Dumping Material Into Bin
RE: Force & Deflection While Dumping Material Into Bin
W/gt*V
and V is the free fall velocity on impact.
W=weight
g = grav constant
t = time of evacuation of mass
F=3000/(32.2*5)*sqrt(2*32.2*7)=395
So at the end of the flow the total force would be
3395lb
RE: Force & Deflection While Dumping Material Into Bin
RE: Force & Deflection While Dumping Material Into Bin
If you knew what the recoil time of the lower hopper was, you could break up the Roark into a series of events:
If you take your Roark eq factor, which is somewhat constant (although the height of fall will decrease as the bin fills), and have = x, then the force of a 3000 lbs. chuck falling would be 3000x. If you then broke this up into a series of events, each the length of the recoil time, with the total time of the series of events equally 5 seconds, you have an analysis that comes closer to describing reality.
The recoil time, however (a factor associated with the damping of the bin) will change as the bin fills. We see this all the time with the application of rotary electric vibrators. If operated on a full bin, such a vibrator will draw 70-80% of its FLA, but if the bin is empty, then the amp draw will double to triple, sometimes worse. (Without good O/L protection, the vibrator burns up.)
Also, the effective impact area of the material on the bin will expand as the material accumulates. You can estimate how much if you have the "angle of repose" data of the material, which is the angle the material mound will form as it accumulates. That is who many of the participants rightly believe this is not a big deal; there would be many more broken hoppers if their observations did not apply.
Thus, the hopper is likely subjected to something like impacting in the early part of the 5 second pour.
No sub for testing thou, to see what model appears to describe the real world.
BK
RE: Force & Deflection While Dumping Material Into Bin
The responses regarding impact force and momentum are exactly what I was looking for.
Phil