Rectangular Footing Aspect Ratio

[labeattie]

Hi all,

I feel sure this is an easy question, but I can't seem to find an answer in ACI 318 or my concrete textbook. But when calculating applied pressure to the soil through a rectangular footing, I'm sure you cant count on your whole footing area to bear evenly if it's 2'x10' for example. In my specific problem I'm trying to find a required footing width for a strip footing with axial loads of about 20-kips every 10 feet, with qa=2000psf. So if i choose 18" for the width, the problem works out if you have a bearing area of 1.5'x10', but I'm sure that extreme of an aspect ratio doesn't bear evenly. Are there any provisions or rules of thumb you all could direct me to?

 

[KootK]

The answer to your specific question is that you can use any aspect ratio so long as your footing is strong and stiff enough. Economics becomes the limiting factor. For a rectangular footing supporting a concentrated load, ACI prescribes concentrating the short direction rebar a bit.

I've heard it proposed that a "rigid" footing with uniform soul stress assumed ought not cantilever more than 5X the footing thickness.

This sounds like a one way footing to me. A real strip footing in the conventional sense. Are your loads transmitted to the footing through a continuous wall? Is it a basement wall situation with columns on top?

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[labeattie]

KootK, thanks. I will use your 5X rule for my preliminary design spreadsheet and use something more sophisticated for the final calc. But no it is not a continuous load, but rather point loads at a given spacing (10-ft in my example). The point loads are on a 6"x6" square if that is of interest. I'm varying the spacing in my spreadsheet to try and get idea of what is economical, so just from the judgment test, I was thinking I could count on the full length of the 1.5' wide footing at like 4' spacing but not so much at around 10'. The footing depth is also variable, but right now I'm considering a 18" wide and 12" thick strip footing.

 

[spats]

It seems to me you would be better off analyzing it as a beam on elastic foundation. An excellent spreadsheet that does this is BOEF by Alex Tomanovich. You'll find it at

http://www.steeltools.org.

 

[SlideRuleEra]

labeattie - As KootK stated, the stiffness of the footing is most important for uniform load distribution to the soil. Its relatively easy to make it strong enough by proper selection of rebar. Footing stiffness is roughly proportion the cube of the footing depth (the moment of inertia). Since you can vary the depth, a small increase in depth will make a significant increase in stiffness. For example, going with 15" depth instead of 12" depth will almost double the stiffness: 15^3 / 12^3 = 1.95 increased stiffness. You may not need to do this for your situation, but that is an easy way to approximate the benefit of thickness.

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[labeattie]

Thanks! Very useful tip SlideRuleEra. I will be sure to keep that in mind. And I actually have seen that spreadsheet before spats, but did not think of it. I will have to try it out!

 

[KootK]

Canada's concrete handbook has a blurb that says: "the assumption of an infinitely rigid footing (uniform soil stress distribution) is acceptable for combined footings where the column spacing to footing shear depth ratio does not exceed approximately 4:1". That's all that I've been able to find in print.

Now that I know that there's not a concrete wall on your footing, the 18" width makes me a bit nervous. Small accidental eccentricities in the cross footing locations of those 20 kip loads may have significant impacts. At potentially 18"W x 30"H, your footing is starting to feel more like a grade beam or a stocky wall. I'd hate to see it roll over.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[Hokie93]

I manually ran a quick beam on elastic foundation calculation for a concentrated load (20 kips) acting at the center of a 10'-0 long, 18" wide continuous footing. Assuming the footing is 12" thick with concrete compressive strength equal to 3000 psi and a subgrade modulus equal to 200 pci, the results indicate a maximum pressure of 1740 psf and an average pressure of 1158 psf. Since these values are less than 2000 psf and 1333 psf, respectively, it would appear you can safely base your design on a uniform distribution of pressure. I ran through this very quickly so you should definitely verify these results for yourself. To follow up on KootK's comment, the 18" width does seem rather narrow for a continuous footing subject to concentrated loads.

 

[labeattie]

Thanks all! KootK, thanks for finding that rule of thumb. I'm not sure where the 30" comes in (maybe I'm missing something) but I will pay close attention to eccentricity demands and will make it a little wider too probably. And Hokie, thank you for the investigation, I really appreciate it. I think I'll be playing around with Tomanovich's spreadsheet today.

 

[KootK]

30" was just a guess at the depth based on the rules of thumb that we've been kicking around. Pay no heed to it if you've got something else in mind.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.