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

• Tirijazzmanray
In summary, Ignacio Pérez, a mining engineering student from Spain, is seeking help in analyzing the stability of a slab with rounded edges against toppling failure. The slab is rectangular-prism shaped with rounded edges of a particular radius, r. He is wondering whether he should consider the moments of every piece of the block or just calculate moments from a selected origin when the block is resting on an inclined plane. Another colleague suggests that if the mass distribution is uniform, there is no need to divide it up and the center of mass and toppling pivot can be used. Ignacio has already calculated all moments with respect to the rotation pivot and found slight differences when considering only the weight projections at the center of mass. He is seeking further
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

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Tirijazzmanray said:
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.

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

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## 1. What is stability analysis and why is it important in this context?

Stability analysis is the process of determining whether a structure or object is able to maintain its equilibrium and resist external forces. In the context of a slab resting on an incline, stability analysis is important because it ensures that the slab will not tip over or collapse, which could pose a safety hazard.

## 2. How do you calculate the stability of a slab resting on an incline?

To calculate the stability of a slab resting on an incline, you will need to consider the weight of the slab, the angle of the incline, and any external forces acting on the slab. Using principles of statics, you can determine the forces acting on the slab and analyze their effects on its stability.

## 3. What factors can affect the stability of a slab resting on an incline?

The stability of a slab resting on an incline can be affected by a variety of factors such as the weight and distribution of the load on the slab, the angle of the incline, the material properties of the slab and the incline, and any external forces acting on the slab.

## 4. What is the difference between static and dynamic stability analysis?

Static stability analysis is concerned with determining whether a structure or object is able to remain in equilibrium under external forces. Dynamic stability analysis, on the other hand, considers the effects of motion and acceleration on the stability of a structure or object.

## 5. How can stability analysis be used in real-world applications?

Stability analysis is used in a variety of real-world applications such as building and structural design, transportation engineering, and product design. It is crucial in ensuring the safety and functionality of structures and objects in various environments and conditions.

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