Bearing Pressure Under Eccentrically Loaded Footings 2

[labeattie]

Hi all,

I'm having a frustrating problem that I would think has an easy answer. I'm designing a wall footing for bearing pressure right now, and can only increase the footing dimension in one direction. Imagine my surprise when my calculations say adding a foot in one direction of a footing increases the maximum pressure. I don't really believe this can be true. So I attached a basic calculation showing 3 cases, all with the load inside or at the kern point, that show adding footing area is increasing my applied bearing pressure. Please tell me what I'm doing wrong here, unless the calculations are correct, in which case I would need some hard convincing that more footing means more pressure.

http://files.engineering.com/getfil...11c-bdcd-a3df8ec82ffc&file=20150806110730.pdf

Thanks in advance,
labeattie

 

[JoshPlumSE]

Your calculations look correct to me. But, that assumes RIGID footing behavior. That's what I always assume, but there are other ways to do the calculation. Soil isn't neat and linear the way we always assume it to be in these calculations. And, the footings aren't really rigid. In my opinion, as long as you obey statics, you should have a reasonable method.

You can use a constant soil pressure that only extends partial length under the footing. This would give you the same soil bearing in all three cases.

You could use a more complex curved or multi-linear profile.... as long as the centroid of the pressure resistance coincides with the point of the applied load.

 

[Once20036]

Looks correct to me, but I`m not sure that I can provide the "hard convincing" that you need.
It will help if you include some dead load over the top of the footing. The dead load of the soil and (assumed) concrete slab over the footing will help create a more balanced load - thus less eccentricity and less of a spike in the bearing pressure as you approach the outside edge.

 

[manstrom]

That's correct. Increasing the size in one direction doesn't help you unless you can counteract it with other loads or moment.

Stand in a canoe on a lake. The best place for you is dead center. You can't sit on the edge unless you have a similar load on the other side of the boat.

When I am working on a problem, I never think about beauty but when I have finished, if the solution is not beautiful, I know it is wrong.

-R. Buckminster Fuller

 

[JoshPlumSE]

Love the canoe example! That makes it clear why the calculations are correct.

Tt also highlights the Rigid Footing + flexible soil assumptions that we're making for soil /footing interaction. Which means the reality may be slightly different than what we assumed.

 

[Signious]

Not sure how to give you hard convincing evidence, but lets give it a try. See attached.

[URL unfurl="true"]https://res.cloudinary.com/engineering-com/image/upload/v1438886105/tips/SBizHubC22-15080600430_vflrf4.pdf[/url]
td:dr; The total bearing reaction stays the same (no increase in stress), but the distribution changes. Any eccentricity is going to increase your maximum pressure. See manstroms post for the great boat analogy.

 

[labeattie]

Thanks everybody for the responses. I'm starting to buy it. The canoe example was a real brain buster, but is really bringing me around. I will add that the maximum bearing pressure being greater than allowable doesn't necessarily constitute instability or failure, as the pressure would redistribute based on the soil's post-failure resistance, which is why I think other assumptions for static analyses end up working fine, as JoshPlum suggested. I won't be getting into any stress-strain curves for the soil though so I'll just try and minimize the eccentricity and proceed. Thanks!

 

[labeattie]

And regarding the canoe analogy, I was imagining standing in the middle of a canoe, and then one side begins to get wider. The side that I am now farther toward would poke further down into the water. Don't know if that illuminated or obfuscated the issue, but it was how my thinking progressed!

 

[CANPRO]

it looks as though you're not accounting for the weight of the footing itself. Your larger footing will pull the net reaction slightly closer to the center compared to what you have shown. Depending on the thickness of your footing this may not be significant...but if you need to split hairs to make it work, it may help. For example, when designing the footing for a tower crane, the self weight of the footing is significant.

 

[labeattie]

I had the self-weight in my real calc, just added in via superposition of a constant, rectangular amount. This should give the same result (I think) as using that equation with an adjusted eccentricity, and just increases the maximum pressure a little. So according to the numbers I'm still better off not adding concrete in only a single dimension. Let me know if I'm wrong though, and thanks for the response!

 

[KootK]

A useful trick is to recognize that, in many cases, you can exceed your allowable stress at the edge of the footing. Most shallow foundation allowable stresses are determined based on settlement concerns rather than true failure. And you don't care how much the footing edge settles. You care how much the supported structure settles. As such, it often makes more sense to compare your allowable bearing pressure to something closer to the average bearing stress rather than the peak. I'll often combine this with Once2006's recommendation to extract the maximum benefit from a seemingly unhelpful footing extension.

As a matter of principle, I don't for a second believe that adding more footing actually makes the situation worse out there in the wild.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[labeattie]

KootK: You don't think the extra footing on a single side could resist settlement greater on that side and cause the whole thing to begin to tilt? Anyways I'm sure that effect is small or at least nowhere near what my rigid footing calcs show. And great point about the settlement.

 

[KootK]

You don't think the extra footing on a single side could resist settlement greater on that side and cause the whole thing to begin to tilt?

The linearly varying soil stress certainly does imply tilt. But then, eccentric footings are a pretty regular occurrence and we're rarely bothered by the degree of tilt in those instances.

There's kind of a catch 22 at play with the supported structure. If the supported structure and its connection to the footing were stiff enough to be adversely affected by small footing rotations, that same supported structure would probably be stiff enough to help resist that footing rotation. A shear wall or a beefy fixed base moment frame might be stiff enough to offset some rotation whereas a simple gravity column probably would not.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[BAretired]

I have used eccentric wall footings where the exterior face of the walls was on the property line. The walls were not free to rotate because there was a floor located ten feet above the footing. If the walls are designed to carry the eccentricity, the pressure on the underside of footing is almost uniform.

BA

 

[RPMG]

I agree that adding footing does not decrease stability. In the canoe example, I consider this adding a log on one side 3'-0" away. It doesn't make it less stable, only that instability can only occur at one side.

I have never done this, but I have considered this for a small moment frame where the post had to be at the end of the footing. I'm curious to what others think this in application. I had to "find" a horizontal force at the anchors for it to work. However, it seems to fit the discussion that if you permit bearing pressures greater than allowable, you should find a stabilizing force elsewhere. Otherwise, you violate the sum of all moments equals zero.

 

[Lion06]

It doesn't surprise me that the maximum bearing pressure increases while the average decreases. It's similar to a column with an axial load only. If you increase the column size and make the load eccentric then the maximum compressive stress will increase (in most cases).

There are a couple ways to look at this one. If you look at adding 1' of length to any size footing with a 0.5' eccentricity, then the max bearing pressure will asymptotically approach the bearing pressure for the concentric case that is 1' smaller as the footing size increases and P is constant.
If you look at keeping the original size constant, and increasing the footing size in 1' increments, then it's all over the map, because at some point you'll be outside the kern and also the larger the original size, the closer you'll be to q average right off the bat.