Roll Stability of static structures

[antons]

Hi,

Maybe someone remembers how to determine the necessary conditions for a static structure to be stable and not to roll over. I know about the method when you imagine the structure has been rotated back an forth, and depending on how the center of mass takes higher or lower state the structure is considered stable or not. But it is a little bit vague and I am interested in more precise definition. Something from vector mechanics would be enough.

Best Regards,
Anton

 

[haruspex]

Hi,

Maybe someone remembers how to determine the necessary conditions for a static structure to be stable and not to roll over. I know about the method when you imagine the structure has been rotated back an forth, and depending on how the center of mass takes higher or lower state the structure is considered stable or not. But it is a little bit vague and I am interested in more precise definition. Something from vector mechanics would be enough.

Best Regards,
Anton

It is not a simple question. You need to specify the nature of the perturbation. One measure would be the energy investment needed to tip it over; another would be the angle through which its base would need to be rotated; another, the force applied steadily at some point.

 

[antons]

It is not a simple question. You need to specify the nature of the perturbation. One measure would be the energy investment needed to tip it over; another would be the angle through which its base would need to be rotated; another, the force applied steadily at some point.

Hi haruspex,

Did you mean that there is an overall tendency to acquire the lowest state (or level) of potential energy in nature? Like structure's stability depends on how much effort you need to make to shift the center of gravity of a body, so that it could take the most stable position? My thoughts were on something like this: imagine a tripod standing on the ground with some kind of object placed on it, somewhere on the border of a tripod's plate. Assuming that the tripod with an object on it is stable, a question arises: how much force is needed to tip tripod over? (assuming of course that the force is applied where the structure is the most unstable). That is the question I cannot answer myself. The perturbation could be just a simple push, an impulse.

 

[haruspex]

Did you mean that there is an overall tendency to acquire the lowest state (or level) of potential energy in nature?

That is of course the case, but I meant that the measure of stability depends on the nature of the perturbation.
A structure might be able to withstand a wind up to a certain speed, no matter how long the wind blows, so that is not a matter of the energy of the perturbation, as that is unlimited. Or it may withstand an impulse of a certain energy or momentum. Or it may withstand its base being tipped through some angle, without necessarily much energy being involved.
If you can be specific about the nature of the perturbation then I might be able to help you come to a suitable measure.

 

[CWatters]

You basically need to work out if the input will give the structure enough energy to keep it moving beyond the point at which gravity takes over. Typically as the structure tips it's centre of mass will rise giving it PE. Perhaps draw the structure tipped over until the centre of mass is just outside it's footprint an work out the gain in PE. If the input can supply that much energy watch out.