Optimizing structure for toppling

[Harsh188]

Hi! everyone...

I'm a building a standing frame for disabled children, the structure in elemental form is shown in picture.
https://drive.google.com/file/d/0B60ALttRvwKmdzRGc0pGWlN5Z3c/edit?usp=sharing
link to picture - https://drive.google.com/file/d/0B60ALttRvwKmdzRGc0pGWlN5Z3c/edit?usp=sharing

Now, I want to optimize the structure for toppling, let's say a force, F is acting on the top most part, fig(a).
I can change dimensions but there are certain limitations like minimum length of the frame, maximum width and maximum weight of the plate. So, how do I optimize all these things keeping in condition that frame doesn't topple??

Also, can I do better optimization by changing structure as shown in fig(b), and fig(c)? if yes, how?

 

[A.T.]

The vector sum of frame weight and F must go though the frame's base, to prevent toppling.

Your a,b,c variants have different structural stability, but the same toppling stability, as long h & W as the same. Unless the weight of the frame or its center of mass position change significantly.

 

[Harsh188]

The vector sum of frame weight and F must go though the frame's base, to prevent toppling.

Your a,b,c variants have different structural stability, but the same toppling stability, as long h & W as the same. Unless the weight of the frame or its center of mass position change significantly.

hmm... toppling stability actually makes sense.
So, can I just say, FcosA*h=mg*W/2? (neglecting the mass of vertical bar)