Applying moment to beam on elastic foundation; single point or couple?

[StrEng007]

I got a theoretical question about applying OTM, resulting from a wood shear wall analysis, to the top of a footing modeled as a beam on elastic foundation.

Is it better to apply these moments as single point loads? Or is it best to decouple the moment so you have a local tension force and a short bearing compression force?

For my given scenario, I've got two shear walls on the same foundation. The footings are required to be long enough that they will encroach into each others footprint. So I'm placing these two walls on a single foundations. Applying two point load moments works. However, decoupling the moment creates instability in the footing kern and I feel that it's likely due to an "artificial" uplift. I say artificial, but in reality, I will need to check my anchor bolts for this local force... so it's a reality for local forces. I'm not sure if what I'm saying here is making sense.

Drawings below are not to scale.

Side note: If you only have (1) moment placed concentrically on the footing, your bearing pressure will decrease as you decouple the moment and spread the load out concentrically over it's moment arm. Things go wonky when the loads are eccentric, or if you have two loads with varying magnitudes.

 

[HDStructural]

If you have a long shear wall with the moment in it, it would make sense to me to present it as a force couple as you have shown since the moment is applied over a long distance. If it were from a column, I think a point moment would make the most sense. Just my two cents.

There shouldn't be global instability in the footing one way but not the other. I'm not sure what is causing that since the global forces are the same with each analysis type.

 

[KootK]

I would say that:

1) Splitting the moments into T/C couples is almost always going to be a better reflection of reality.

2) Often, splitting the moments into T/C couples is unnecessary.

3) Sometimes splitting the moment into T/C couples is the only way to capture important aspects of the design.

4) I rarely enforce the kern business for transient loads and, instead, let the foundation go into partial uplift. This is common and it's difficult to be competitive if I stick to the kern thing.

For the particular case that you've illustrated, I would expect this procedure to suit:

a) Design the hold down anchorages.

b) Design a combined footing. Or not, per the sketch below.

c) Design the wall element to transfer the wall loads to the foundation fairly rigidly.

Engineers take a variety of approaches to this. And most produce good results.