Foundation Design
Foundation Design
(OP)
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.
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.





RE: Foundation Design
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.
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The name is a long story -- just call me Lo.
RE: Foundation Design
RE: Foundation Design
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.
RE: Foundation Design
RE: Foundation Design
RE: Foundation Design
RE: Foundation Design
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?
RE: Foundation Design
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.
www.SlideRuleEra.net
www.VacuumTubeEra.net
RE: Foundation Design
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
RE: Foundation Design
RE: Foundation Design
www.SlideRuleEra.net
www.VacuumTubeEra.net
RE: Foundation Design
RE: Foundation Design
www.SlideRuleEra.net
www.VacuumTubeEra.net
RE: Foundation Design
RE: Foundation Design
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.
www.SlideRuleEra.net
www.VacuumTubeEra.net
RE: Foundation Design
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).
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The name is a long story -- just call me Lo.
RE: Foundation Design
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/9b73/2ae34d1a78dd...
Bulletin 28 - https://pdfs.semanticscholar.org/79ce/368810d0fbe1...
RE: Foundation Design
RE: Foundation Design
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?
RE: Foundation Design
RE: Foundation Design
RE: Foundation Design
RE: Foundation Design
oldestguy I did see those and from what I have gathered there are SPT conversions from Hough that give an allowable soil bearing pressure that results in 1 inch of immediate settlement. I would imagine the Florida Building Code's number is derived from settlement as well, but it is impossible to tell, because they don't offer their calculation procedure. If I am remembering right from my foundation design classes I believe terzaghi offers some settlement procedures for cohesionless soil.
RE: Foundation Design
RE: Foundation Design
If so and there are no signs of excessive or differential settlement, you're unlikely to have any significant problems with the 17% load increase which is still essentially centred on the footing. Just another level of confidence on top of the building code allowable pressure and your Meyerhof calc.
RE: Foundation Design
RE: Foundation Design
RE: Foundation Design