Forces in Walls? Pressure Uniform?

[TriKri]

Hi!

I have a question about forces inside of walls.

When you consider the walls of a house, they have a certain density $$\delta$$ and they create a force downwards, which becomes bigger closer to the ground. Assume we don't need to care about the weight of the roof or that of the atmosphere. The force in each wall, will be

$$\overbrace{\underbrace{w\cdot h\cdot t}_\texttt{total volume}\cdot \delta}^\texttt{total weight}\cdot g$$

where w is the width of the wall, h is the heigth up to the top of the wall, and t is the thickness of the wall. So, independent of the width and the thickness of the wall, the pressure create by the wall above will be

$$h\cdot\delta\cdot g$$

Now to my question: Is the pressure uniform? That is, will the pressure be the same in all directions, vertically as horizontally? The pressure vertically will be $$h\cdot\delta\cdot g$$, since when the material gets squeezed from the top and the bottom, it gets compressed vertically, so it creates a pressure vertically since it wants to expand in that direction. Besides, it needs to support its own weigth. But what about horizontally, does it want to expand it that direction as well? How big will the pressure be in that direction? Near to the pressure vertically, or almost zero? Does it depend on the material of the wall? (wood/concrete/metal?)

Thanks in advance!

 

[Mapes]

Let's approximate the wall as a uniform solid (no 2x4s, no plaster layer, etc.) and let's assume that the wall is much taller and wider than it is wide (this is typical, of course).

Then at the bottom of the wall the height is compressed by a strain

$$-\frac{1-\nu^2}{E}h\delta g\mathrm{,}$$

(where $E$ and $\nu$ are the Young's elastic modulus and Poisson's ratio, respectively, of the wall material) and the wall expands outward with a strain of

[tex]\frac{\nu(1+\nu)}{E}h\delta g\mathrm{,}[/itex]

which corresponds to thickness increase of

[tex]\frac{\nu(1+\nu)}{E}ht\delta g\mathrm{.}[/itex]

To first order, there is no pressure on the face of the wall, and that's why it's free to expand in that direction.

I wrote a note a little while ago discussing these types of analyses.

 

[charng]

Hello!

I can provide some insights into the forces within walls and the uniformity of pressure in walls. The concept of pressure is defined as the force exerted per unit area. In the case of walls, the force exerted is the weight of the wall itself, which is dependent on its density, height, and thickness. This force is distributed over the surface area of the wall, resulting in a pressure.

In terms of the uniformity of pressure, it is important to consider the direction of the force and the structure of the wall. In the vertical direction, the pressure will be uniform as the force is evenly distributed over the entire surface area of the wall. However, in the horizontal direction, the pressure may not be uniform as it depends on the structural integrity of the wall and the direction of the force.

For example, in a solid concrete wall, the pressure will be uniform in all directions as the material is able to withstand and distribute the force evenly. However, in a wooden or metal wall, the pressure may not be as uniform as these materials may have weaker points where the force is not evenly distributed.

In conclusion, the pressure in walls is dependent on the material, structure, and direction of the force. In most cases, the pressure will be uniform in the vertical direction, but may vary in the horizontal direction depending on the material and structural integrity of the wall. I hope this helps to answer your question!