Foundation Design 3

[LeonhardEuler]

Hello,

I am analyzing what I believe to be a mat foundation, or large spread footing? It is approximately 40'x20' and is loaded via two concrete "walls", or "pedestals", that sit 25' apart and each run the full width of the slab. The structure the pedestals support is subjected to wind load as well as 500 kips of gravity load. The foundation itself is over 6 foot in height, but no part of it is below grade...

From what I am seeing in Das foundation design book I can find bearing pressure on soil by simply dividing gravity load by area i.e. P/A. Easy enough. However, I am having difficulty defining the applied soil pressure resulting from the moment caused by wind loads. I have seen on here assume infinitely rigid slab and use M/S is this accurate?

What I am looking for is a good design procedure and/or reference for designing this type of foundation.

 

[Lomarandil]

Yes, for your dimensions I would begin assuming a rigid foundation (e.g. triangular/trapezoidal soil pressure distribution) and go from there. If your design isn't pushing anything too hard, that assumption and the corresponding methods from Das or any other reference for shallow foundations should be fine.

If you're really pushing things, first, go to your geotech. Then come back here with the details and we can point you in the right direction.

----
The name is a long story -- just call me Lo.

 

[oldestguy]

Is this existing? If so, what do you hope to find? Settlement? Uneven soil pressure? Overloading of reinforcing?

 

[LeonhardEuler]

It is existing. There is a water tank on it that currently weighs ~350 kip and will be increased to ~550 kip (The slab itself weighs 830 kip!). The diameter is increasing by a couple feet, so wind load and subsequently moment will increase. I'm not worried about settlement, but am tasked with checking bearing failure of the foundation and strength of the concrete itself.I don't have a soil boring in this location, but have several close by and have medium dense coarse grained sand down 40 feet in every boring. I have the blow counts in these locations, but they are very high ~40 blows per foot with standard SPT, so I am using building code presumptive value of 2000 psf to be more conservative.

I've attached a rough calc. I converted moment into an eccentric load and came out with 1,860 psf. Slightly more than the 1,750 psf found with gravity load only P/A. I know it's not the best quality picture, but perhaps you can advise if this process, with the assumption of infinitely rigid foundation, is acceptable given the margin and site conditions.

 

[LeonhardEuler]

I have seen that I can model this in an FEA as a concrete plate with soil springs, but with only two walls being supported on this foundation I assume that it is a simple enough model to make some assumptions and hand calc it. I am interested to see more experienced engineers opinions on my calculation procedure.

 

[LeonhardEuler]

I got the equation for qmax from Braja M Das page attached. It is peculiar that in this books combined footing chapter they don't consider moments at all. I take that to mean that the moments can be dealt with similarly to other shallow footings and used his shallow footing ultimate bearing capacity chapter to run the hand calc.

 

[Ron]

Yes, I agree that a rigid foundation model is correct; however, you also have to consider the wind in at least two directions with different kern values for the foundation. This might result in a bearing pressure more like P/.33A rather than P/A, depending on whether the load resolution results in a net uplift on one side of the foundation.

 

[LeonhardEuler]

I checked both wind directions individually and both resulted in an eccentricity well within the "kern" (if I'm using that correctly) anyways the foundation maintains compression on the soil for each wind direction.

With that known I should only have to check the bearing pressure with wind in the critical direction (strongest wind/ shortest side of foundation), correct?

 

[SlideRuleEra]

1) ...advise if this process, with the assumption of infinitely rigid foundation, is acceptable given the margin and site conditions.
2) I am interested to see more experienced engineers opinions on my calculation procedure.

1) Agree with Lo and Ron, rigid. The reason "why" is independent of site conditions... it's all about geometry, math and physics... and the logic has nothing to do with "concrete foundations", it applies to steel, wood, etc. beams, too:

Consider "Section Modulus" (S), for any shape. "S" is proportional to (depth of section... squared). Think of "S" as a measure of "strength".

Now, "Moment of Inertia" (I) for any shape. "I" is proportional to (depth of section... cubed). "I" is a measure of "rigidity".

As a structural section (concrete, steel, wood, etc.) with a constant length gets deeper, "I" increases more rapidly than "S". Turns out that a ratio of of about 10 units length: 1 unit depth is approximately where the value of "I" is high enough for the section to be consider "rigid" when compared to the section's "Strength" (S).

The ratios for this project are 3.3 (20' width / 6' depth) and 6.7 (40' length / 6' depth). Both values are well under a ratio of 10... rigid in both directions, by inspection.

Modern codes totally obscure the significance of the relationship between "S" and "I", but it was not always that way.

2) I went through your math... looks good to me. Although, how you got there took me a while to figure out... I don't (routinely) use a slide rule any more but still handle the math the same way that was practical back then.

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[LeonhardEuler]

Slideruleera,

That was a great explanation of why it can be assumed rigid and I would like to borrow it to explain to others in the future. But I'm a little confused would S not be depth cubed and I depth ^4? Instead of S being depth squared etc

 

[LeonhardEuler]

Ok wow I understand I was omitting the length of base in the equation. Makes perfect sense

 

[SlideRuleEra]

LeonhardEuler - Glad the explanation helps, use it however needed. The AISC "Manual of Steel Construction" has a nice section titled "Properties of Geometric Sections". It begins on page 6-17 of the 9th Edition, don't know exactly where in the more recent editions... but I'm sure it's somewhere in the book. These pages give a concise comparison of squares, rectangle, spaced rectangles (think the the flanges of a W steel member), etc.

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[LeonhardEuler]

Should I analyze this as double symmetric if the moment is from wind load?

 

[SlideRuleEra]

"double symmetric"? Probably just don't understand the terminology.

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[LeonhardEuler]

Sorry I am typing in this while doing other work. I should slow down and pay attention to what I am typing. I meant to say doubly eccentric. I mean by that should I consider a moment from wind in both directions when finding the bearing pressure the foundation puts on the soil. I only considered the wind in the direction that the foundation was shortest, because I was assuming wind will only be blowing in one direction at a time and felt straight onto the long side will be a worse condition than "diagonal". Hopefully this makes more sense. Thank you for the guidance!

 

[SlideRuleEra]

...should I consider a moment from wind in both directions when finding the bearing pressure the foundation puts on the soil.

Yes, but I agree with your observation that overturning in the direction you have calculated will govern. Still, as Ron commented, you should not take that for granted. Make enough preliminary calcs for overturning in the other direction to show that you have not forgotten to check. The answer will not always be obvious as it is this time.

Something else that I would not take for granted is sliding... you mention that "no part of it [foundation] is below grade". It will be straightforward to show sliding is not a problem, horizontal force divided by the vertical force to determine the coefficient of friction (cof) needed to prevent sliding. I expect the cof value calculated will be well below a reasonable cof for concrete on soil. For the horizontal force, be sure to include wind force not only on the tank, but also the worse case foundation profile (40' x 6').

Note: Wind force on the foundation probably should be included for overturning... but the lever arm is so short (3') than neglecting it is minor.

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[Lomarandil]

SRE is right to be cautious and thorough (nothing sinks a project faster than an unexplained and unwritten wrong assumption) but in this case, your instincts are working well.

Given the dimensions and weights mentioned, sliding will be OK by inspection unless you have some unusually high lateral loads. Similarly, it wouldn't take much to convince me that wind in the direction of the short dimension will control, as you've found.
And yes, FEA and soil springs are overly complex to be used here. Hand methods are fine (preferred, actually, as there's less room for black box user error).



----
The name is a long story -- just call me Lo.

 

[Settingsun]

Us structural engineers tend to like the trapezoidal pressure distribution since it is familiar to us (P/A +/- My/I). However, when I talk to geotechnical engineers about shallow foundations, they want to know what the effective footing area is and the effective uniform bearing pressure. This tends to fit their models and calculation methods better.

The effective bearing area for eccentric loads is a reduced area such that the eccentric load would be centred on the effective area:

B,eff = B - 2*eccentricity

The logic (I believe) is that the real footing, which is larger than the fictional effective footing, should have at least the capacity of the effective footing, ie adding concrete to the 'uplift' side of the concentrically-loaded effective footing shouldn't make things worse.

You also have an inclined load due to the wind. There is a basic form of the bearing capacity equation which does not take this into account (sometimes called the Terzaghi bearing formula). You need a formula that takes this into account, which you can spot because it will have inclination factors.

Below area a couple of links to old articles by Brinch Hansen which cover this. Bulletin 28 is newer and presumably improved, but Bulletin 11 has a better example problem IMO.

Now this water tower footing mightn't be very eccentric or very inclined but it's still good to get into the habit of using the proper formulas.

Bulletin 11 -

https://pdfs.semanticscholar.org/9b73/2ae34d1a78dd0704d894bd2575bd3d07e80d.pdf

Bulletin 28 -

https://pdfs.semanticscholar.org/79ce/368810d0fbe154e2f1a41850e80c8b556b31.pdf

 

[LeonhardEuler]

steveh49 the reason I am not using the classic Brinch Hansen, or Meyerhoff methods, is because I don't have boring data in this specific location. I do have boring data roughly 200 yards away, but I don't know if i'm comfortable enough assuming the soil stratigraphy doesn't vary to this point. So what I was doing to work around using the nearby SPT data was using the state building codes presumptive bearing pressure and comparing that to the applied bearing pressure (e.g. P/A+M/I).

 

[Settingsun]

The trick then is to be certain what assumptions are built into the building code's allowable pressure. If vertical loading is assumed as opposed to inclined, the real capacity may be lower. If smaller footings are assumed, the real capacity may be lower.

On the other hand, they may be conservative by a factor of 10 because that's all the code committee was willing to sign their names to, so it's all academic.

You could turn your SPTs into phi values and do a Brinch Hansen or Meyerhof calculation as a quick check. I think you're implicitly assuming non-cohesive ground, aren't you?