Stability Calculations

[DanielMeidan]

Hi everybody,
I designed a single post table consists of the following:
1 - Base plate with 4 glides.
2 - Post connected rigidly to the base plate with connection plate at the top.
3 - Table top plate (round).

This table is tested for stability by placing a weight off center.
The weight location around the center at the most unstable location.
ONLY vertical forces exist in this stability test (NO HORIZONTAL FORCES).
The loading force is known, marked as L.
Stability is measured as the ratio of required force to tip over the table, to the loading load L.
The requirement is to exceed the load L by minimum of 25%.

My question is:
Does stability depends in the height of the the table top from the floor.
Attached a PDF picture of the tested table.
According to my calculations height is not the factor, however test results given to me claim that the higher the table the lower the stability.
Can someone provide me with the static equations of the stability.
Thank for support

Daniel Meidan P.Eng.

 

[DanielMeidan]

Center of mass height will have a factor when horizontal forces will exist.
In this case there are only vertical forces.
thnx

Daniel Meidan P.Eng.

 

[rb1957]

oh, so the table is resting on two supports ?

don't understand the tangent comment ... it'll tip when the CG is outside the supports ... back to LR/(G+L) > X

another day in paradise, or is paradise one day closer ?

 

[IRstuff]

"Center of mass height will have a factor when horizontal forces will exist.
In this case there are only vertical forces."

The applied forces may be vertical, but their interactions with the table are not solely vertical. The fact that you can tip the table given sufficient weight vertically applied to the edge of the table should be readily apparent, and should tell you that your assertion is either incomplete, or invalid. Run your calculation with the CM placed halfway up the post and see what happens.

TTFN
faq731-376

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Of course I can. I can do anything. I can do absolutely anything. I'm an expert!

 

[Dougt115]

The net horizontal force is zero. If this were not the case then a table with wheels would roll across the room if a load was placed on it. So would your office chair when you leaned back. The horizontal forces you are looking at are countered by the bending moment.

In a rigid table the CM of the table will remain inline with the centerline of the table. Height will factor in only after the table has started to tip.

Height is only a factor in the analysis if deflection is permitted in the assumptions. Bending of the table would result in the CM of the table to move off of the center line of the table and add to the tipping force. A taller table of the same material would have greater bending under the same loading and therefore a greater displacement of the CM increasing the chance to tip.

 

[rb1957]

in your orinigal post you mentioned four guides (i hadn't divined their purpose till a couple posts back).

we're saying the same thing .. FR/(G+F) = x is the same as Gx = F(R-x)

another day in paradise, or is paradise one day closer ?

 

[prex]

DanielMeidan, I think you had sufficient consensus on the (obvious) fact that height is not a factor under your conditions (no horizontal forces, no significant deflections under the applied load).

prex
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