Geometry Problem: Preventing a Heavy Table from Tipping

      Furniture makers ponder how to determine the base dimensions required to ensure that a heavy table will not tip over. October 14, 2010

Question
I am building a conference table that will be a circle 84" in diameter. The top will be 3" thick and weigh about 475 lbs. I want to do a single large cylinder base and would like it to be 4' or less in diameter. Is there a formula for calculating the minimum base width that will keep it from tipping over with XYZ weight placed on a single edge?

Forum Responses
(Furniture Making Forum)
From contributor M:
That's heavier than solid MDF. Lighten it up a bit and divulge some construction details and we'll see about a formula.



From contributor J:
If your base is 48", your overhang is only 18" - I think you'd be okay. If in doubt, bolt it to the floor, or put a bottom in the base and fill it with sand.


From the original questioner:
The top will be concrete. On top of the base I will make a 2.5" support frame that will hold the top. The top will be 1" thick with a 4" folded edge, leaving a 3" void to hide the support frame. More worried about the tipping. I guess I can build the base at 48" and if needed, put some feet on it. Was just wondering if there was a mathematical formula to determine the balance maximums, i.e. 18" overhang would equal XYZ lbs. of weight placed on it before it tips.


From contributor O:
It would require a fairly sophisticated formula to figure this out, but it's certainly doable. In any case, you wouldn't want to cut it at all close, since such a heavy table could be lethal if it fell over.


From contributor W:
The problem is not just the mass of the top and tipping over. The fact is that people will look at it being big and thick, and then lean on the outer edge, screwing up the balance.
I would put 12" feet on the base, and no less than 5, but probably 6 or 8, because you do not know where someone will lean on it.


From contributor G:
I’m feeling mathy this morning. Here’s what I come up with. Basically, you have a teeter-totter, with the fulcrum being the edge of the base at the floor. The plank is 7’ across. The fulcrum is 1.5’ from the edge of the plank. Skinny little you is pushing down on your edge. Fat Albert is on the other side, waiting for you to lever him into the air.

1.5 ft is some 21% of the 7 ft diameter
21% of 475 lb is 102 lb
79% of 475 is 373 lb

The difference is 271 lb. You have to generate 271 lb of force just to lever the top. This is not including the weight of the base.

Disclaimer: I just made all this up and I don’t claim it is accurate or even meaningful. You may want to consult a structural engineer. You can also Google “mechanical advantage lever” to find formulae.



From contributor T:
That's straightforward plane geometry, but I flunked it! Have some fun with a mockup. 7' 2x4 on a 4' plywood panel (or 2) and lean on 1 end of the 2x4. I bet you'll be surprised how much force is needed to teeter that totter. Note that the mass of the top is moot, but the mass of the base is/could be, as per the "sand in the bottom" idea.


From the original questioner:
Contributor T is right. The last time I built a conference table past logical boundaries, I was uncertain of the outcome until it was finished. Once finished it took a great deal of weight to move and I had no worries. However, it was not round. Not to mention he wanted it sex proof - that created a little stress. FYI, always design office furniture for this certain possibility. I guess I will build it at 5’ and add feet if needed. Once again the outcome will be uncertain until complete.


From contributor P:
If you have a CAD program, you can map it out pretty easily. I think it will show you that contributor G's approach is on the right track. You need to know the percentage of the area of the circle that's on the other side of the tip line. Counterbalancing that would be the weight of the smaller portion, plus the lever arm of the sitting person (or people?). That assumes static loading - if they aren't perfectly still, it gets a lot more complex. My gut tells me you will have no problem.


From contributor Z:
How do you plan on building the base? The tipping point would be where the base meets the floor. I think that bolting the base down is a good idea. If that is not possible, make sure there is enough weight at the bottom. I think the base being properly weighted is more important than the size.

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