Outdoor project - adding stability by filling a column

[RB2314]

TL;DR Summary

Stability of unattached standing column

I have a square column to be filled with gravel to avoid being moved or tipped over by wind. The column is about 1 ft x 1 ft x 8ft tall. It is sheathed with a covering and hollow inside. What is the optimum fill height to avoid the wind tipping over an unattached single column. And the heavier the better for fill material?
Thanks very much. I would love to see an analysis.

 

[berkeman]

Summary:: Stability of unattached standing column

I have a square column to be filled with gravel to avoid being moved or tipped over by wind. The column is about 1 ft x 1 ft x 8ft tall. It is sheathed with a covering and hollow inside. What is the optimum fill height to avoid the wind tipping over an unattached single column. And the heavier the better for fill material?
Thanks very much. I would love to see an analysis.

Welcome to the PF.

Sounds like a very unstable form factor. How is it anchored to the ground? What is the application? What happens if it falls over / fails?

 

[AZFIREBALL]

Is the bottom closed with a welded plate?
Is it setting on a level surface?

 

[Baluncore]

If you can keep it absolutely vertical the centre of mass will be only 6” from an edge.
If it can begin to rock sympathetically, it will certainly fall in a low wind.

Your problem is similar to the computations of brick chimney stability.
What is the maximum wind gust ever recorded in your area.
From that calculate the wind force applied to the column. Expect maybe 100 lbs/sq ft.
That force will act at maybe 2/3 the height of the column. Calculate the torque at the base.

The heavier it is, the harder it will fall.
The column needs to be attached to the ground or have a larger base.
Are there earthquakes in your region?

 

[hmmm27]

If it was in a laboratory, on a micrometer precise level ground, plumbed within a millimeter, capped on the bottom and top, and clear of anything squishable within a 12 foot radius, I'd say top it up.

What's the application ? What kind of ground is it on ? And the other reasonably obvious questions.

The further the column is away from vertical, the lower your fill height is going to have to be. And you're looking at almost half a ton if you fill it right up.

 

[RB2314]

Welcome to the PF.

Sounds like a very unstable form factor. How is it anchored to the ground? What is the application? What happens if it falls over / fails?

It's not anchored and has a solid plate 1 ft x 1ft on the bottom. At this point I would just like to keep it theoretical as to the application. Just a column filled with gravel sitting on a level surface. Many people theorize to fill it half-way, but I'm thinking full. Thank you for your interest.

 

[RB2314]

Is the bottom closed with a welded plate?
Is it setting on a level surface?

Yes to both. Thank you for the questions.

 

[RB2314]

If you can keep it absolutely vertical the centre of mass will be only 6” from an edge.
If it can begin to rock sympathetically, it will certainly fall in a low wind.

Your problem is similar to the computations of brick chimney stability.
What is the maximum wind gust ever recorded in your area.
From that calculate the wind force applied to the column. Expect maybe 100 lbs/sq ft.
That force will act at maybe 2/3 the height of the column. Calculate the torque at the base.

The heavier it is, the harder it will fall.
The column needs to be attached to the ground or have a larger base.
Are there earthquakes in your region?

I would just like to keep it simple at this point, with a column filled partially or fully with gravel, or some other filling, with a cross wind blowing 90 degrees to the column, and how much should I fill it. Thanks very much.

 

[256bits]

If you cannot attach it to a solid base, or dig it into the ground, you can increase the stability by building an enclosure, perhaps 3 foot diameter, and 2 foot high, setting the column in the middle, fill and pack the enclosure with gravel, and fill the column around a third high.
Not sure about the numbers, but you get the idea.

 

[RB2314]

If it was in a laboratory, on a micrometer precise level ground, plumbed within a millimeter, capped on the bottom and top, and clear of anything squishable within a 12 foot radius, I'd say top it up.

What's the application ? What kind of ground is it on ? And the other reasonably obvious questions.

The further the column is away from vertical, the lower your fill height is going to have to be. And you're looking at almost half a ton if you fill it right up.

My intuition is agreeing with you to top it off; but I wish I knew the physics involved. Please ignore the application and other details. Just a vertical column sitting on a hard level surface, with 1ft x 1 ft caps on either end, and the ability to put anywhere from no filler to topping it off, in order to minimize the chances of a crosswind blowing it over. Thanks so much for your interest.

 

[Dullard]

Assuming everything is level/plumb/ideal:

The physics is pretty simple. The force (from wind) required to tip the column increases with the mass of the column - the wind has to rotate the column about the 'downwind' edge of the base. The weight of the column opposes that. More weight, more counter-rotation force.

The assumptions are critical - a little non-ideality goes a long way in this problem.

 

[hmmm27]

My intuition is agreeing with you to top it off; but I wish I knew the physics involved. Please ignore the application and other details. Just a vertical column sitting on a hard level surface, with 1ft x 1 ft caps on either end, and the ability to put anywhere from no filler to topping it off, in order to minimize the chances of a crosswind blowing it over. Thanks so much for your interest.

You've posted a DIY problem in MechEng, but what you seem to want is one of the physics subforums, ie: what basic formulas should be applied, prior to - or perhaps in concert with - dealing with real world issues and the working parameters which you are reticent to supply.

The reason you're getting so many vague answers and all the backfilling with "ideally" and the like, is that in this forum (and in DIY) there's a concern about telling you the wrong thing, or having it taken the wrong way, or having it misread by somebody else a few years from now, and ending up with a squashed forum member. Not so much if we're just talking scribbles on a piece of paper.

 

[hutchphd]

So in the ideal world you want to fill the sucker with spent uranium to the top.
In the real world this is a much more interesting question! I see two modes of failure to be most likely:

1. Nonlinear dynamics (see Tacoma Narrows Bridge) which sets the column to to rocking even in steady wind.
2. Soil subsidence (exacerbated by water) as pressure at the base caused by wind and weight gets large

Of course the combination of two is even worse. And nontrivially difficult to quantify.

 

[Baluncore]

In a steady wind, once the column starts to lean, it will accelerate and cannot be stopped. The movement of the centre of mass, and the collapse of the footing due to rapidly increasing ground pressure, will provide positive feedback.
But the point at which a rigid column on a firm base starts to lean will be dependent only on the total mass and the square of the windspeed.

There is a tipping point, the angle at which the leaning tower would fall independent of the wind pressure. The tipping point is determined by the position of the centre of mass. Filling only the base with lead or DU will give the greatest angle before the tipping point is reached. Filling the column to the top will give the highest centre of mass and the earliest tipping point.

 

[Lnewqban]

It's not anchored and has a solid plate 1 ft x 1ft on the bottom...

During a hurricane in Florida, I have seen a refrigerator slide out of an apartment and keep going over the third floor walkway until hitting a wall.
It was being moved but not tipped over by the hurricane force wind, because it was a heavy object with low center of mass respect to the dimensions of its base.

With enough velocity of wind, your column will fail one way or the other.
Moderate hurricane winds can generate huge amounts of force per square foot of surface being hit perpendicularly.
A column has a coeficient of aerodynamic drag to be considered as well.

Please, see:
https://www.engineeringtoolbox.com/wind-load-d_1775.html

As you see, it is important to determine the maximum velocity of cross-wind that your column will ever see, as well as the amount of available friction between the base plate and the surface.

Friction force between the base plate and the supporting surface is important and anchoring can make that force much higher than weight can.
Three guy wires properly located and grounded can go a long way regarding stability of slender columns: the column and plate go from resisting huge bending forces to resist mild compression ones.

 

[jack action]

Condition to move

To move your column, since it is not anchored, depends only on the friction force $F_f$ between your column and the ground. The condition before it begins to move is:
$$ F_f > \mu W$$
Where $\mu$ is the coefficient of friction (static) and $W$ is the total weight of your column. If the wind (or anything else) pushes harder than $F_f$, the column will slide.

Considering a coefficient of friction of 0.5 (as an example; depends on the materials of the column and the ground) and a weight of 600 lb (= 75 lb/ft³ * 8 ft³) for a completely gravel-filled column, a force of 300 lb would move the column.

Condition to tip

For tipping, you need to consider the moments. The applied force $F_a$ times the height of application $h$ will tip the column if it is greater than the reaction moment of the weight. Since the weight should be acting at the center of the column and the normal force will be at the edge of the column just before tipping, the distance between the two forces is half the width of the column, thus:
$$F_a h > W\frac{d}{2}$$
Or:
$$F_a > W\frac{d}{2h}$$
Where $d$ is the width of the column. If the wind (or anything else) pushes harder than $F_a$, the column will tip. If $F_a$ is greater than $F_f$, then it will slide, and it should never tip.

Considering a weight of 600 lb and a force applied at the tip of the column (8 ft), a force of 37.5 lb would tip the column.

Considering the force is acting at the middle of the column (4 ft), a force of 75 lb would tip the column.

Because the tipping force is less than the friction force, it will tip before it slides.

These numbers are obtained before the application of a safety factor. And with the simplicity of the analysis and the potential risks of an error, I would used a safety factor of at least 5 (maybe 10), i.e. divide these forces by 5.

Even a force of 75 lb @ 4ft high is something that a human can easily produce.

 

[RB2314]

Assuming everything is level/plumb/ideal:

The physics is pretty simple. The force (from wind) required to tip the column increases with the mass of the column - the wind has to rotate the column about the 'downwind' edge of the base. The weight of the column opposes that. More weight, more counter-rotation force.

The assumptions are critical - a little non-ideality goes a long way in this problem.

Thank you. I should not have labeled the problem as an outdoor project. It's actually just a offshoot from a project I was doing, but not much like the actual project. The project just piqued my interest in the theory. It sounds like for any given filler, the column should be filled to the top, and if I'm limited to a given weight, I should place it at the bottom. And the column will tip at an earlier point the higher the center of mass; but it's still better to fill the column to the top to avoid any tipping. In this problem I assumed no sliding would occur, only tipping. The bulk of the answers to my question before asking this forum was to fill the column halfway, which didn't seem right to me. Thanks for all of your time and expertise.