Finding forces in a wall of a trailer box filled with mass

[Silentnox]

Trying to calculate the forces against the wall of a trailer and not sure how to do that in the case of it being filled with grain. Any help would be appreciated. I know the weight and volume and the wall profile just not sure how to find the force acting straight out against the wall. The grain is just piled in there and the trailer is open.

Thanks for the help in advance,

-Jason

 

[handleman]

I would probably start by calculating as though the trailer were filled with a liquid of the same density as the grain. It seems like that would be a reasonable worst-case scenario.

 

[Silentnox]

Ya thats what I was thinking, but I am a little new to this game and wasn't sure if that would be a proper assumption.

Thanks

 

[MintJulep]

I think that the liquid assumption would be extremely conservative.

I suspect that the angle of repose is involved in the solution.

 

[GregLocock]

I don't think it is very conservative, as the trailer rides over bumps it'll behave much more like a fluid than an earthbank.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[GregLocock]

Incidentally, if your trailer rides over a half g bump, it'll change the pressure exerted by the grain by 50%.

If it doesn't have suspension then half a g is a low estimate.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[MintJulep]

I am right and I am wrong.

Hydrostatic assumption is conservative, but angle of repose is not apparently involved.

Slides 40 to 50 of this very nice power point presentation:

http://www.engineering.uakron.edu/~chem/fclty/chase/Solids/Bin and Hopper Design Lecture.ppt

 

[Silentnox]

Thanks for the help so far. I am only done 3/4 of my degree and currently on an internship. I dont really have anyone to ask whether my calculations/logic are correct. I appreciate the feedback.

Okay well I treated it like water and ended up a saftey of 15 so I guess its over built. This is what I did you guys can tell me if Im off the track a little:

1) Treated the grain like water using rho * g *h where h is the height of the trailer

2) after finding the force for the grain that would be used I applied a non-uniform sloped load over a flat surface and did bending-moment diagrams.

3) from the moment diagrams found the location that would be under the greatest stress

4) calculate my moment of inertia for the cross section at the point under the most stress

5) Used the M and the I to calculate the maximum pressure the wall should be exposed to.

6) Using that new force re-enter it into F = rho * g * h and calculate a new height and new volume of grain.



However would it not be better to use a FEA method since there is actually bending occuring along the height and the length of the trailer?


Thanks again

-Jason

 

[MintJulep]

I dont really have anyone to ask whether my calculations/logic are correct

Isn't the whole point of an internship to gain knowledge and experience under the tutelage and supervision of a mentor? Perhaps you need to speak with your internship program director.

Your approach seems ok up to step 4, if you are trying to look at the trailer as a whole. You seem to be treating the entire trailer as a beam. (I assume that your moment of inertia is for the cross section of the whole trailer?).

Things seem to fall apart in steps 5 and 6 however.

To use FEA you first must understand the problem, and the limits and capabilities of the program.

 

[Silentnox]

Well I chose to sacrifice my short term "engineering" education to be in a field that interests me. Not to mention that the amount that I am learning from the non engineers that have been doing this for a long time is unreal.

My intent wasnt to model the trailer as a whole since I am just looking into changing the side walls at this time. The front and back walls of the trailer are solid and would not be a problem.

As for the moment of inertia that I calculated it was for the length of one wall. Which bothers me because the wall is supported at each end (front and back).

When doing the bending moment diagram I also assumed it was the classic example of a pin on one side a roller on the other. Im not sure this was a correct assumption either.

 

[MintJulep]

I don't know that you can get away with looking at only the walls. The walls are connected to the bottom, so the bottom deflection in effect puts a load on the bottom edge of the walls, and vice-versa.

This seems like a non-trivial problem, and one that is well outside my area of expertise.

 

[GregLocock]

If I were investigating the side only I'd treat it as a plate, simply supported on 3 sides, with a non uniform load. Then I'd realise that to all intents and purposes that is not solvable by hand (it's a PDE), so a better approach might be moment plasticity theory, in which you work out the work done to fail the structure using an assumed mechanism. It is a simple elegant method, but it is non-conservative. And it is not so simple that I'm going to explain it in a post.

FEA would be fine but an uncorrelated FEA model is of limited use. I'd be fairly sure of getting it right (having been involved with FEA for 25 years off and on), but would still do handcalcs of simpler load cases to back it up.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[GregLocock]

Incidentally this specific load case is not covered in Roark, but Chapter 11 will give you some insight into the general problem.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[PeterCharles]

The classic work on grain pressures in bins was by Janssen, see link below

http://arxiv.org/PS_cache/cond-mat/pdf/0511/0511618.pdf

The subject of pressures in bins, hoppers and silo's has generated a lot of PhD's for a lot of people!

 

[zcp]

Silentnox,

Are you modifying the design of the side walls or just doing a quick check to see if the current design will handle the loads?

ZCP

http://www.phoenix-engineer.com

 

[Silentnox]

Thanks for all the advice so far. I read a couple of documents on Janessen and silos and found them interesting. What I was able to take from them that the bulk solid force on the wall is not dependent on height but instead diameter (or in my case width) with an asymptotic behavior. Which tells me that treating the grain in my case as water is not correct but at least its on the safe end.

I have never heard of, or dont recall hearing of plastic deformation theory but I will look into it. I was hoping I would use this problem as an excuse to force my employer into getting us a FEA program but I have limited to no experience with it outside using SOLID WORKS.

To answer zcp, yes I am modifying the wall and have a few designs in mind. We are basically doubling the length of the wall and playing around with supports other then a simple beam that separates two sheets. My calculations though were for a worst case unsupported wall so that we could have a base line to work from.

 

[vonlueke]

Silentnox: Is your beam that separates the wall into two sheets a vertical beam, or a horizontal beam? If it's vertical, is it simply supported at the bottom end, or clamped? What is the sheet thickness? I assume these sheets are steel. Are they just flat sheets, or do they have ribs running in the horizontal or vertical direction?

 

[arto]

Chapter 7 of Troitskys "Tubular Steel Structures" is on Bins & Bunkers - lotsa good stuff that might be helpful.
Available from

https://ssl.lincolnelectric.com/foundation/item.asp?prodnum=TS&PID=16

 

[Silentnox]

Well Im removing the vertical beam that seperates the two sheets and switching to one single sheet so that eliminates that problem. The wall is welded to the floor about a foot from the bottom of the wall (which I would consider completely fixed) the top end is reinforced with a 3/16" formed gusset and cross braced between the two walls of the bin (Im not sure what to consider this) The wall profile is complicated, it has 3 formed trapazoidal channals running the entire length horizontaly. The walls themselves are 12GA.
______
/ \
/ \

However, the horizontal channles add very little strength in the plane that I am looking at.

 

[vonlueke]

I think if I had to make a rough initial guess in a very short time without any access to FEA, since the upper edge is supported by cross members, I might assume one half of the maximum hydrostatic pressure, for an acceleration of a = 1.5 g (if you have suspension), is exerted on the middle rib over a beam width equal to the rib spacing (s = h/3), modeling the middle rib as a simply-supported beam; i.e., beam uniform load, w = 0.5*rho*a*h*s = 0.1667*rho*a*h^2. Then, ignoring any edge support from the adjacent ribs, this beam's midspan moment would be M = 0.125*w*L^2, and stress, sigma = M*c/I, where I = moment of inertia of one rib over a width of s = h/3, and L = wall length.

If I can, I'll try to check if this very rough estimate comes anywhere near the plate maximum stress, with the two ends of the wall simply supported, the bottom edge of the wall clamped, and assuming you have three simply-supported cross members. Or is that one cross member?