Buried Cantilevered Concrete Column Maximum Moment Location

[Renderuru]

Hello. I have a 10" diameter concrete Column buried 6 FT (anchored to footing at bottom). The pier protrudes 5FT above ground. Assuming I have a simple horizontal load at the top of the column, is there a method or rule of thumb to estimate the location of the maximum moment? Or, is the assumption that the column is completely encased at ground level a common acceptable assumption? Intuitively, I added an extra foot to my lever (so 6FT), but I would like to understand how this is normally done.

Thanks.

 

[JAE]

Depends on the inherent stiffness of the soil around the column.

I would say the answer is somewhere between assuming fixity 1 ft. below the soil level and assuming fixity at the top of footing.

You can model the soil's stiffness - but that would be a bit of a guess - depends on soil characteristics and level of compaction - not to mention the variations over time due to freeze-thaw (if you are in cold country).

We sometimes use 50 pci lateral soil stiffness as a start in modeling below grade concrete piers.

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[WARose]

Assuming I have a simple horizontal load at the top of the column, is there a method or rule of thumb to estimate the location of the maximum moment? Or, is the assumption that the column is completely encased at ground level a common acceptable assumption? Intuitively, I added an extra foot to my lever (so 6FT), but I would like to understand how this is normally done.

I believe another way to pose the question would be: What is the unsupported length of a buried column?

Those are actually 2 different questions.

As far as the first question goes: that is going to depend on the stiffness of your fill around it. But with such a shallow embedment.....I think you might as well just do a straight cantilever to the top of the footing. (I.e. your horizontal load x 6'.) Especially if we are talking a high shear.

Many would take the unsupported length as 0. (If you are in competent fill.) It would be conservative just to take the full length and account for any P-Delta by magnifying the moments.

 

[Renderuru]

Thanks WARose. I realized my error and tried to edit the post in time.

If I take the moment to the footing it more than doubles my lever. If somewhat accurate I'll do that but I feel like it would be too conservative.

 

[WARose]

If I take the moment to the footing it more than doubles my lever. If somewhat accurate I'll do that but I feel like it would be too conservative.

There are a lot of variables here. (A big one being the kind of max. shear we are talking about.) But to give you an idea: most geotechnical reports will tell you to not even consider the first several feet of embedment for a laterally loaded situation. The "depth to fixity" I am use to getting from those guys typically varies from 8 to 15'. (And you don't even have 6.)

Bottom line: if it's a significant shear.....it's probably nothing the soil can stop......and if it's low, it's nothing the footing and column probably can't take anyway with minimum steel.

 

[KootK]

Find yourself a copy of ANSI/ASAE EP486.3 Shallow Post Foundation Design. It seems to be about all that there is for quick and dirty assessment of this kind of thing. It's got diagrams similar to that shown below for a number of cases. You wind up with a point of rotation not all that far from the footing. The forces acting opposite to the applied shear will reduce your moment some though. If you've got hardscape restraining the top of the piers, that's potentially another case altogether.

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.

 

[JAE]

KootK - I think that the use of pier-type designs like that are fine but I wonder if the presence of a large footing at the bottom changes the behavior a bit by lowering, or potentially eliminating the inflection point due to the much larger interface with the soil across the footing face.

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[jayrod12]

JAE,

They actually have formulas that take that into account as well in that standard. They call it a collar but essentially the same thing.

 

[dik]

You might take a gander at the attached.

KootK: Can you include the portion of your posting to include beyond 'where'?

Thanks, Dik

 

[dik]

A 10" pier is pretty flexible... and I cannot imagine it being attached to a large footing... the junction of the pier to the footing I would consider being fixed due to the relative stiffness, if the footing were large.

Dik

 

[dik]

KootK:
I'm working on a program that has all the post embedment formulae that I can find.

 

[Renderuru]

Does anyone know why there would be a maximum foundation depth (see Kootk post)?

 

[MotorCity]

There is a maximum depth, because at some depth, it "sees" no effects of the load. Take an extreme......say the post was embedded 200'. At that depth, there would be virtually no stress on the post due to the lateral load

 

[Renderuru]

I worked out the minimum depth using the above formula and I got a surprisingly short depth (compared to my actual 6FT depth.

I assume the value b is the diameter of my post (12")? with a soil pressure of 13psi (clay, worse case), Va=1000lbs, and Ma=60,000 lb-in, my minimum depth is only about 15"! Does that make sense? I assume that in my case, the bottom condition would be more of a pinned condition. Nevertheless, this does give me some confidence in the 6FT depth.

Thanks.

 

[jayrod12]

In our office we have a magic rule d= (10M/d)^(1/3). M in ft kips, d in feet. I usually use that formula and the above and take whichever is deeper.

but you may want to double check your calcs, I checked your inputs using a spreadsheet I created for the EP486 formulas and calculate approximately 7 ft of embedment. My magic formula results in a 4 ft embedment, either way, it's more than your calc.

You also indicated your pier was 10" in your original post, which results in my calcs being more than 7 ft embedment using EP486.

 

[Renderuru]

Thanks I've changed it to 12" now. I will recheck my calcs. I appreciate the additional formula.

 

[KootK]

KootK - I think that the use of pier-type designs like that are fine but I wonder if the presence of a large footing at the bottom changes the behavior a bit by lowering, or potentially eliminating the inflection point due to the much larger interface with the soil across the footing face.

Yes, there is that potential. As jayrod pointed out, the source document covers these conditions. When I do this myself, I consider a few permutations and come up with an approximation that I feel is appropriate. Some judgment is required as it's not a situation conducive to a lot of "knowing" unless you're willing to get good geotechnical parameters and make a thesis out of it.

KootK: Can you include the portion of your posting to include beyond 'where'?

Anything for you. Google is your friend here, trust me.

KootK:I'm working on a program that has all the post embedment formulae that I can find.

Neat. Is that the faux MathCAD alternative that I've heard you mention in the past? There is a brand new version of that ANSI standard out which, supposedly, contains significant updates: Link. Might be worth incorporating into your spreadsheet effort.

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.

 

[Renderuru]

Thank you

 

[Shu Jiang PEng SE]

The geotechnical report normally gives subgrade modulus of elasticity of soil (unit: kip/ft^3). You can treat the soil as lateral springs to the pile and derived the spring stiffness per the pile diameter and subgrade modulus of elasticity of soil. Then you get pile internal forces and deflection information with the help of structural analysis software.

 

[jdgengineer]

For shallow embedment, I would consider the pier to be "rigid" and use traditional soil pressure diagrams similar to drawn by KootK.

The USS Sheet Pile Design Manual has good example of the approach (Document should be available online). While intended for retaining wall equations the logic can be applied to other loading conditions. You'll also need to retool for piers rather than continuous sheet piles but the logic is the same. See Design Example No 1 at the end of the manual for a sample calculation.