Stability Calculations
Stability Calculations
(OP)
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
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.





RE: Stability Calculations
stability would be critical if the pressure from the table base onto the floor went to zero. this should be enough for a P.Eng to figure out the details.
another day in paradise, or is paradise one day closer ?
RE: Stability Calculations
In reality, if your test arrangement is not perfectly level, if deflections are sufficiently large under test loads, there will be horizontal reactions at the base.
RE: Stability Calculations
δ = ε*(1 - cos(p*L))/cos(p*L) where ε = eccentricity, L = column length and p = (P/E*I)0.5
RE: Stability Calculations
Have you tried drawing a 2D orthogonal free body diagram? We all were taught this for a reason.
Have you considered the dynamic case in which your mass decelerates to a halt when it makes contact with the table top?
--
JHG
RE: Stability Calculations
could you repost your test results ... this is a purely static problem, right?
it sounds odd that for two tables identical except for height, that the taller one is more unstable (unless the table top is rotating significantly.
another day in paradise, or is paradise one day closer ?
RE: Stability Calculations
RE: Stability Calculations
Thanks everybody.
This is a simple static case, no moving parts and the table is horizontal.
From the equations that I used the height is not a factor.
As for test results, I get tip over or not, no numbers.
Please your comments.
Thnx
Daniel Meidan P.Eng.
RE: Stability Calculations
you have the weight of the table (Wt) acting on the table center, the load (L) at some distance X, and the radius of the baseplate,(R). the CG of the two weights (table + load) should be inside the baseplate ...
CG = LX/(Wt+L) < R
another day in paradise, or is paradise one day closer ?
RE: Stability Calculations
The weight of the table without the weight is G, and it acts along the table center line.
The weight is located at the distance R from the Table center line.
The distance X is the fulcrum which is a tangent line between two glides.
When the moment that the table provides (G * X) is greater then the load L applies L*(R-X) the table is stable.
I calculated the required load to tip over and the ratio to the test load is the stability.
In other words the over capacity that the table weight provides to overcome the eccentric load.
Hope I provided the full picture,
Please comment.
Thank you.
Daniel Meidan P.Eng.
RE: Stability Calculations
RE: Stability Calculations
where's the CG of the two weights ? one weight(G) is at zero, the other (L) is at X ... G*0+L*X = (L+G)*cg
the only way i see height entering into it is if the floor (that the table is standing on) isn't horizontal.
another day in paradise, or is paradise one day closer ?
RE: Stability Calculations
TTFN

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RE: Stability Calculations
thinking about it, the imbalance moment, Lx, is reacted by a "bending" stress at the baseplate, peak = (Lx)*R/(pi*R^4/4)
and when this equals the deadweight pressure, (G+L)/(pi*R^2), so it should start to tip when ...
4Lx/R = (G+L) ... Lx/(G+L) = R/4 ... that's a bit of a surprise ... if G = 3*L, then x = R ...
higher tables are less stable when you apply horizontal loads
another day in paradise, or is paradise one day closer ?
RE: Stability Calculations
There are two ways to calculate this stability case.
They both and in the same equation where the height is not a factor in the equations.
Please see the attachment.
From all the discussions today I may come to the conclusion that the test was not performed in the same way and details for all heights.
Thanks for the support
Daniel Meidan
Daniel Meidan P.Eng.
RE: Stability Calculations
This is a simple problem of moments. Sum of the moments equal zero to balance the table on the edge of the base. Using the edge of the base as the zero distance.
Weight of table * Radius of base - Load * (X-radius) = 0
where X-Radius is the overhang of the load in relationship to the base radius and X>Radius for instability.
or
G*R-L(x-R)=0
for balance G*R=L(x-R) Looking at the equation, if X<R then stable, if X=R it is stable.
Solving for R to get the Radius of the base as a function of the load and distance from the central support.
R=LX/(G+L)
To fall over G*R-L(x-R)<0
and G*R < L(x-R)
R < L*X/(G+L)
RE: Stability Calculations
based on my "bending stress for imbalance moment" = dead weight "pressure" ... (Lx)*R/(pi*R^4/4) = (G+L)/(pi*R^2) ...
I realize this is the onset of tipping, that you can use a partial disc with a linearly varying pressure to react the dead weight and the imbalance moment (basically having the resultant act at the CG).
I think it'll tip before Lx/(G+L) = R
another day in paradise, or is paradise one day closer ?
RE: Stability Calculations
Here are some clarifications
1 - The table will tip over around the line tangent between two glides.
This is the pivot line or the fulcrum.
This is the point A shown in the sketch.
The distance from this line to the center of the table is X.
2 - The total weight of the table G (without the test load L), applies a moment of M1=G*X
3 - The test load L is located in the distance of R from the table center.
The distance of the test load L to the pivot line or fulcrum is R-X
The test load L applies a moment of M2=L*(R-X)
The table will start to tip over when M1=M2
If M1>M2 then the table will not tip over.
In this case, the center of gravity of the table with the test load, is between the table center line, and the pivot line.
I hope this explains my calculations.
The point of this discussion was to get other professional opinion that the height does not affect stability.
Thanks.
Daniel Meidan P.Eng.
RE: Stability Calculations
TTFN

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RE: Stability Calculations
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RE: Stability Calculations
In this case there are only vertical forces.
thnx
Daniel Meidan P.Eng.
RE: Stability Calculations
don't understand the tangent comment ... it'll tip when the CG is outside the supports ... back to LR/(G+L) > X
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RE: Stability Calculations
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.
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RE: Stability Calculations
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.
RE: Stability Calculations
we're saying the same thing .. FR/(G+F) = x is the same as Gx = F(R-x)
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RE: Stability Calculations
prex
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