# Modeling reaction forces on a foundation for fences

1. Feb 4, 2019

### Craig91

Hello new to the forum.

I'm a builder by trade and enjoy studying the concepts behind the things I build.

My problem is:

A typical concrete post and base panel with a wooden fence. Unit mass approximately 350kgs including the foundation concrete around the posts.

2.0m wide x 2.0m above ground. 0.5m depth below ground. Figures adjusted for ease.
0.1 x 0.1m concrete posts.

If I take a figure of 0.5kN/m^2 for lateral storm wind load, that gives a lateral load of 2Kn.

How do I model the reaction force from the foundations, such that the unit won't tip over?

If I imagine the problem as a seesaw type arrangement, then where do I put the fulcrum:
• ground level
• opposite diagonal to the pushing force. i.e. opposite bottom corner to push force
• or two thirds depth of embedment as point of rotation (I came across this figure in a couple of old texts)

If I look at it as a seesaw arrangement about ground level, then I get a reaction force of 8kN.
If I look at it from a moment arrangement using a footing width of 0.3m, then I get a reaction force needed of 6.66kN.

Either way the reaction force needed is much bigger than the weight of the unit approx 3.5kN . Therefore how much do the following factors come into play:
• Reaction forces from the soil
Are there any rules of thumb for the above factors - I stumbled across Rankine formulas and realised I was out of my depth - no pun intended!

Also how does the lower centre of gravity due to the concrete base panels affect the system?

Craig

2. Feb 4, 2019

### Astronuc

Staff Emeritus
The fulcrum or pivot would be at the ground, since the concrete base fixes the post, which would rotate about the ground level. Each post is basically a cantilever, or panel subjected to a uniform load vertically, or perhaps a variable load, increasing from ground to top. The maximum shear and bending would be at ground level, and there could be torsion based on lateral load variation along the fence line.

3. Feb 4, 2019

### Dr.D

@Astronuc has said that the fulcrum would be at ground level, which would be true in a rigid soil. In a real soil, it cannot work that way. Look at the hole around an existing fence post sometime; it is usually bigger than the fence post diameter because the soil gives way. That is an appropriate first approximation, but I would not put too much confidence in the result.

In actual fact, this is a very difficult problem because it depends so greatly on the soil mechanics, a very difficult matter to quantify for any particular case. In any event, the lateral loading on the concrete will vary with depth, and the top will certainly not be a point of zero displacement.

4. Feb 5, 2019

### Craig91

Thanks for replies.

With regards to Soil resistance is the following correct:

Using my calculated load of 8kN acting on the foundation. So I have 8000N spread over a face surface area of 300 x 500mm (width of footing x depth of concrete column). = 0.053 N/mm^2

Therefore the Soil Shear Strength need be greater than this. Which for medium soil types seems to be around 0.075N/mm^2??

5. Feb 5, 2019

### Dr.D

I would not touch putting numbers on this problem.

6. Feb 5, 2019

### Tom.G

I suggest you ask to see the Engineering calculations that were done for the design. If you are in the USA they are most likely available because would be needed for the building permit(s).

If that approach doesn't work, find a Structural Engineer that does the engineering for homes or commercial buildings; he may want \$ for detailed calculations, or lunch at the local hamburger joint for an informal tutorial.

Let us know what you find out.

Cheers,
Tom

7. Feb 6, 2019

### Dr.D

Is there an existing design? I must have missed that.

8. Feb 6, 2019

### tech99

I have met this problem before and it is a conundrum. I think a reasonable approach is to work out the stability of the system if the block was standing on a hard surface. Then check that the soil loading is reasonable, making assumptions about load distribution.
In practice, the block will try to rotate in the soil, so some soil is helping the mass of the block whilst soil beneath it may start to yield.

9. Feb 8, 2019

### tech99

I notice that the concrete is just a slender cylinder surrounding the pole. In this case the soil is doing everything. You can take the weight of soil in a prism shape where it would be lifted up by the concrete during failure.
I notice that the wind load you give looks a if it is in a 70mph wind. May be a bit low. Also notice that the centre of pressure is half way up the panel.

10. Feb 9, 2019

### Dr.D

Is there ever a case where this is not true? Ultimately, no matter what sort of foundation block we create (concrete, cast iron, whatever), ultimately the soil always bears the load.

Actually, the center of pressure should be higher than the midpoint. The wind speed right at the ground is zero, so this skews the pressure distribution upward.