Simple over-turning question

[gharli]

Hi All,

Simple question (hopefully).

If there is a continuous system with a discreet point load, over what length would it be reasonable to calculate over-turning stability?

For e.g. a rigid wall that is continuous and has a continuous overturning force induced by soil pressure. This is easy, take a 1 m strip and do the math(s). Brackets if you're British.

But if the wall is continuous and flexible (say a steel mesh) and the load is a discreet point load, what length of wall would you consider for the stabilizing effect of self-weight? The wall in this case could fall over locally, i.e. twist from being vertical far away from the load to horizontally flat where it has fallen over. My feeling is that the length is a function of the torsional stiffness of the wall. If this is the case, then how to we solve this problem practically?

I hope the question is clear, would appreciate your thoughts/views.

Thanks

 

[jayrod12]

I feel it's less the torsional stiffness and more a function of the horizontal spanning capability of the wall in question. So the horizontal spanning capability will have an effect on how much wall, and therefore footing, could be engaged to resist the point load overturning.

 

[gharli]

Good point Jayrod. I'm wondering if one considers say an infinitely long plate fixed on one edge with a perpendicular point load, the angle of force distribution will be such that at some point the wall doesn't feel the point load. Perhaps the length that the angle subtends at the fixed edge of the wall is what should be considered?

 

[phamENG]

This has been tossed around a bit before. It depends a good bit on what the wall's made of and how it's built. If you're looking at an isotropic solid wall (think giant steel plate), then your question is no different that how you approach a point load on a beam web (out of plane of the web). That's often approached with a 30 or 45 degree angle (I think some will go as far as 60) to determine the effective width for your calculation. A wood soldier pile wall with timber lagging would be quite a different story.

In a practical scenario, you might look at it this way:

- Look at it as though only one foot of length is resisting that point load (sort of like the uniform load). Is the design reasonable (i.e., does your "typical" design for that kind of wall work?)? If the answer is yes, you can be confident that it'll work without issue because that is incredibly conservative (depending on the wall construction, of course).
- If it didn't, then start spreading out until you find an area that makes for a reasonable design.
- Now look at your design and see if it makes sense. Are you having to use 15 feet of a 6 foot tall wall? Maybe not realistic. Using 6 feet of a 15 foot tall wall? I could probably get behind that. Keep iterating until you're satisfied.

In the end, there's no great approximation. FEA is your friend if you need really accurate results to this kind of question in a hurry.

 

[r13]

I think there are two approaches to look into discretely loaded flexible wall. 1) Consider arching effect between point loads, and 2) similar to phamENG's idea, assume a failure wedge behind the point load, and use soil internal friction angle for the spread. The analysis and design is similar to the design of sheeting piling wall with soldier beams in between.