Checking furniture for overturn?

After drawing models of furniture in Rhino, if they were ecccentric I used to do an analysis for for overturning effect of chairs/benches/tables by hand until now. But only for objects in 2d plane. This is an example of bench or chair:

(“A” point represents the reference point for overturning)

Overturn condition:
F1 * a ≤ 1.5 * F2 *b

But what should I do when objects are not planar (planar but extruded in third dimension like this bench)?

Here is an example of a 3d irregular shaped table/chair:

It is not possible to check for overturn this kind of irregular shaped object by hand. Because forces/momentums no longer lie in the same plane:

Some other combinations:

Does anyone know how in this cases an overturn check will be calculated?

Thank you.

here is .3ds file of this object:

Make a plane perpendicular to the two points of contact that form the pivot. Project the forces and moments onto that plane.

I feel like some scale models would help.

Thank you for the reply both of you.

Scott there is one problem - the point A can no longer be considered as a point. But as an axis/line. But not a vertical one.

I’m having a hard time figuring out what’s going on in your model. But- I think- any normally stable piece of furniture is going to have a tipover axis formed by the points along its forwardmost edge- the front two legs of a chair, the leading edge of a bookcase, and so on. You have a considerably more complicated shape than either of those, but the principle still applies. You just need to calculate the tipover moment on a plane perpendicular to that axis.

All that said, I would just simulate it in Solidworks Motion or print out a quick 3D part. Trying to calculate this stuff is more trouble than it’s likely worth.

Clorenzetti has a good point. What are you trying to validate here?

I remember UL for floor lights tests a fixture by placing it on a plane that is at a 10 degree incline. The fixture must not fall over. Could you accept something similar?

Also, you can always use weight to your advantage. I don’t know how you are making this, but you can put heavy weights in the legs to help hold it down.

Thank you for the replies both of you.

I do not own a 3d printer, not Solidworks application knowledge.

I wanted to check this by hand calculation.

Scott you mentioned the forwardmost edge of the objects. Can you explain this a little bit please? If my understanding of this term is correct, is the the furthest edge? Furthest in comparison to what?

Forwardmost relative to the direction of the force vector. Extend the force vector to the floor, if it intersects within the contact points of the legs, it’s stable. If it intersects outside, the stability will depend on the force exerted by the mass of the object. This is really just a free body diagram problem. Project those two forces (tipover force and gravitational force due to mass) to the ground, and draw a line between them. The point where that line intersects the axis of the legs nearest to the tipover force vector is your fulcrum point. Simple calculation from there.

Why not just make a quick scale model out of balsa wood?