Statics problem -- Stability analysis of a slab resting on an incline

[Tirijazzmanray]

Dear colleagues:

My name is Ignacio Pérez, a mining engineering student from Spain. I am trying to analyze the stability of a slab with rounded edges against a toppling failure. The slab can be considered rectangular-prism shaped (I provide a rectangular section in the enclosed picture) but the edges are rounded with a particular radius, r.

My question is, how could I analyse the stability of this block when resting on a plane inclined alpha degrees? Should I considered the moments of every "pieces" in which I have divided the block or just calculating moments from the selected origin?

Any kind of help is acknowledge...

Ignacio

 

[A.T.]

Should I considered the moments of every "pieces" in which I have divided the block or just
View attachment 222515

If the mass distribution is uniform, there is no need to divide it up. Just use the center of mass, and the toppling pivot.

 

[Tirijazzmanray]

First of all, ,many thanks for your prompt reply and explanation!

The point is that I have calculated all moments with respect to the rotation pivot (marked in red) and I have also calculated the stability of this block by considering only the weight projections (normal and shear forces) applied at the center of mass. I have found slight differences when computing a, let's say, Factor of Safety defined as the ratio between moments which contribute to overturn the block and moments which tend to stabilize it (please, see equations below).

Maybe I made some mistakes...could you help me with this problem?

Ignacio