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# #2 -- Box Tipping

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Mechanics Corner

A Journal of Applied Mechanics and Mathematics by DrD, No. 2

© Machinery Dynamics Research, LLC, 2015

It is a common practice for manufacturers to ship their products in packing crates that are strapped down on pallets for handling. There is often concern about the stability of this package as it is handled in transit to the purchaser. For this problem, we understand that the manufacturer wants to perform a simple test on each package shipped to assure that it will not tip over in transit. The test will consist of tipping the package slightly to the left and placing a block under the right edge of the pallet. The block is then quickly pulled out and the question is whether or not the package will fall over to the right. The answer depends upon the amount of the initial tip to the left and the location of the center of mass of the combined packing crate and pallet.

It is clear that the falling box impacts the floor, causing an impulsive distributed load to act on the bottom of the package. This will apply both an impulsive upward force and an impulsive moment to act on the box. Since the actual distribution of the force is unknown (and unknowable), an impulse--momentum approach to this problem is not likely to get very far. There is, however, a much simpler energy analysis available. Go on over to the attached PDF for more details.

In an actual case, the center of mass might not be a constant. The movement of products inside the box may cause the shift in CG.

Also after the pallet touches the ground, the impact energy may travel through the box and cause the damage of the product, and not cause a RCC. This will not be captured in the analysis given above. So the actual test becomes essential. please explain.

A simple, methodical and very understanding approach to the testing of box tipping. Please also share the experimental test results of this method.

Ah, Umama! If only I had experimental results, I would be happy to share them. Unfortunately, I have no capability to run the necessary experiments, so I have no data.

About all I can do is make a careful analysis, mathematically correct, and following the laws of physics. I hope someone else will provide us with the experimental results.

Balagopal, what you say is entirely true. There may be many things happening when the crate/pallet is dropped, and this only addresses the question of tipping.

If the CG shifts, that suggests that the packing was inadequate. This is a note to the shipper that he needs to pack better. If the shift is due to something breaking, the we have real problems!

I don't know what you mean by an "RCC." Can you fill me in, please?

Your closing comment, "So the actual test becomes essential," is interesting. Without a doubt, we would like to test everything. But there is the little matter of money. In almost all cases, calculation is less expensive than testing, so questions that can be answered by calculation are almost always done that way.

Quite a few years ago, I worked company that needed to qualify some products seismically for nuclear plant service. I looked and looked for a test facility that could do the necessary shake table testing for us. I found one, and only one, that could do a very limited form of the required test, not really what was desired. Their fee was a young fortune. The problem: our product weighted a little over 250,000 lb. Testing is not always an option.

• Balagopal, what you say is entirely true. There may be many things happening when the crate/pallet is dropped, and this only addresses the question of tipping.

If the CG shifts, that suggests that the packing was inadequate. This is a note to the shipper that he needs to pack better. If the shift is due to something breaking, the we have real problems!

I don't know what you mean by an "RCC." Can you fill me in, please?

Your closing comment, "So the actual test becomes essential," is interesting. Without a doubt, we would like to test everything. But there is the little matter of money. In almost all cases, calculation is less expensive than testing, so questions that can be answered by calculation are almost always done that way.

Quite a few years ago, I worked company that needed to qualify some products seismically for nuclear plant service. I looked and looked for a test facility that could do the necessary shake table testing for us. I found one, and only one, that could do a very limited form of the required test, not really what was desired. Their fee was a young fortune. The problem: our product weighted a little over 250,000 lb. Testing is not always an option.

by RCC i meant right critical condition

Balagopal, thanks for clarifying RCC for me (tripped up by my own terminology -- how embarrassing!).

The Right Critical Condition always exists; it is the state where the box is about tip to the right. In most cases that do not involve tipping, it will not be reached at all. If the box gets to the RCC with zero velocity, then it is balanced on the corner and is in unstable equilibrium; it could go either way.

Thanks for the comment.

I just use a simple rule of thumb of 2 x height to 1 pallet maximum. If it exceeds 2.5 to 1, weight jacking occurs and the package becomes unstable. If the forces are shear to the jacking forces it will slide. Box tipping to me is not a science. It is just common sense. It is also appropriate to know the load centres and COG of the part that is put on the pallet to effectively know where the inertia is going to be at it's most vulnerable. If this is the case you may need to position the part off centre to maintain a good COG on the pallet. Nice information DrD.

Dear Paul,

Thanks for the comment. I'm sorry for the delayed response; I was not aware of your comment until late July.

Your comment is common sense, and will be valuable to many. Only in exceptional cases is it necessary to make calculations.

DrD