Circular Footing with eccentric load and "negative" soil pressure (Flagpole)

[mastruc]

Hi all:

I'm a bit confused about the approach for flagpole foundation designs. I designed a pole foundation based on IBC's straightforward approach in Section 1807 (Unconstrained round piers subject to lateral load). It was relatively narrow and deep (~2.25' wide and ~7.5' deep.) The contractor then prepared on-site an excavation for a premade "kit" which is wider and shallower with flared ends, which subsequently failed inspection. This off-the-shelf solution fails the IBC equation badly at the given dimensions (and doing some research it looks like flagpole foundations are often this odd shallow, nearly square "plug".) Are any of you familiar with how these foundations are justified? Since the steel for the kit is currently in the ground, the contractor wants to keep the shallow depth and widen the foundation to our satisfaction. Doing this with the pole-foundation equation gives huge diameters, and the only other method I'm familiar with is treating it as a bottom-supported spread footing with an eccentric load. I'm not aware of any design approach that combines ground-support with lateral moment resistance.

A constructably-reasonable circular spread footing results in there being negative soil pressure at the heel. So the actual pressure distribution would be circular with a "chord" missing in plan view. I don't have the time to relearn the calculus needed to do derive that from scratch. Are any of you familiar with a design approach or approximation that would give the actual toe pressure under those conditions?

 

[Once20036]

Personally, I'd approximate the round foundation as an equivalent square foundation, with the area of the square matching the area of the circle.
Negative pressure on the heel isn't a deal breaker for me - but obviously it's not possible. I'd use a different pressure distribution - triangular - instead of trapezoidal. You still have 2 unknowns - the pressure at the toe and the width over which the pressure acts. Pressure at the heel is zero.
I look to keep bearing pressure over ~2/3 the width of the footing.

Where I think your question gets a little trickier is flexural reinforcing of the footing - given that the wind can blow from any direction.

 

[DaveAtkins]

I agree--check the bearing pressure under a square footing with area and section modulus less than or equal to the area and section modulus of the round footing.

The bearing pressure due to an eccentric load is equal to (2*P)/(3*a*B), where a is the distance from the leading edge of the footing to the load, and B is the width of the footing.

DaveAtkins

 

[WinelandV]

Here's a pdf of a few pages from a textbook by Teng. I found in the geo forums here a few years ago. It was from a bi-axial bending on a footing post, but the pages also include a round footing with e outside of the kern - which sounds like your situation. Maybe if one of the geotechs stop by this, they can fill in more of the details on the reference. Hope this helps.

 

[JStephen]

If you do integrate the expressions for force and moment on a circular slab, they're kind of a mess and still require iteration to find the point of uplift.
The simplest approach to that problem if you're starting from scratch:
Assume linear bearing distribution y=Ax+B.
Assume a point of loss of contact, from which you can find A/B by setting y = 0.
Use Simpson's rule in a spreadsheet to integrate bearing over the area and compare to total weight. That'll let you find A and B.
Use Simpson's rule to integrate bearing x moment arm over the area to find the resulting moment. Compare that to the actual moment. And adjust point of uplift and repeat until you hit the solution.

 

[DaveAtkins]

This just occurred to me--if you have RISA-3D (or some other FEA software), you can model the round footing with soil springs below.

DaveAtkins