Calculating Overturning / Resisting Moments of a gravity Wall.

[MatthewMansfield]

Hello all

I was wondering if anyone could help me with the following problem.

I am digging a hole in the ground that is 1.946m deep and erecting a wall.

I am trying to work out whether my overturning moment of the wall is greater than the sum of all the resisting moments.

Below is an image of my wall.

As you can see that my over turning moment is 7.781kN and the total sum of my resisting moment is 4.7kN however I am not sure if my math is correct.

The only thing that I am certain of is that I have 11.99kN/m acting 0.649m from the base of the wall.

I was hoping if anyone could cast their eye and give any pointers or advice.

The green circle is the point of rotation.

Thank you.

 

[Settingsun]

The point of rotation should be under the toe of the footing (bottom right corner). Then you also take the loads down to bottom of footing (2.196m) instead of to top of footing.

Assuming the footing is 0.25 + 0.222 + 0.25m wide, that's quite a narrow footing for that wall height.

 

[MatthewMansfield]

Hi Steveh49

Thanks for the response, I do agree but this is not a real structure, it is just for my understanding.

The reason why I picked the point of rotation as shown on the sketch is because that the point i just wanted to calculate from.

But is the math correct or am i missing something?

If the math is correct then it means that my structure wall will collapse?????

 

[JoshPlumSE]

I'll re-iterate what steve said:

1) Overturning moment should based on the point at the bottom of the toe of the footing.
Overturning moment = 11.99 kN * (0.649m + 0.25m)

2) Soil Resisting moment should be based on that same point:
Soil Resisting Moment = 9.24 kN/m * ( 0.25/2 + 0.22 + 0.25)

3) Wall Resisting moment
9.07kN/m* (0.22/2 + 0.25)

4) Footing or slab resisting moment
1.5 kN/m * (0.25+0.22+0.25)/2

 

[JoshPlumSE]

This is not the same as doing a sum of the moments = zero about any point like we do demonstrate that a structure is in equilibrium. Also, note that we're NOT doing a free body diagram because we're ignoring the soil pressure at the bottom of the slab. Right?

We're checking if there is enough moment to flip the retaining wall about the toe of the footing, so we have to take the moments about that point.

If we had more backfill on the toe side, we'd include that in the resistance as well. Heck, we might even include passive pressure from that soil as a resistance moment as well.

 

[Settingsun]

this is not a real structure, it is just for my understanding.

The reason why I picked the point of rotation as shown on the sketch is because that the point i just wanted to calculate from

Ok, understood. So you're just checking the brick stem? Then you don't get to count the footing weight or the soil weight which acts on the footing. You could add soil friction on the back face of the wall.

A stem this thin would need to be tied down. A gravity wall would be something like 1m thick at the base for this wall height.

 

[ProgrammingPE]

If you are checking overturning for the entire wall and footing structure about the bottom right corner (not just checking the stem), then the overturning force would increase and be shifted down since you need to consider the soil pressure on the side of the footing as well.

1) Overturning from soil
Linear Force = 1/2 * 0.333 * 19kN/m^3 * (1.946m + 0.250m)^2 = 15.3kN/m
Overturning Moment = 15.3kN/m * 1/3 * (1.946m + 0.250m) = 11.2kN-m/m

Also you would get to use the weight of the entire footing to resist overturning, not just the area below the soil.

4) Footing or slab resisting moment (assuming your toe length is also 0.250m)
Linear Force = 0.250m * (0.250m + 0.222m + 0.250m) * 24kN/m^3 = 4.33kN/m
Resisting Moment = 4.33kN/m * (0.250m + 0.222m + 0.250m)/2 = 1.56kN-m/m

If your overturning moment is greater than your resisting moment, then the wall and footing will tip over. Typically you want to a Safety Factor of at least 1.5 to prevent this.


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