Simple footer question - eccentricity in both axes

[ARS97]

Alright.....this is driving me nuts.

I'm designing a simple square mat subjected to eccentricity in 2 directions and I'd like to permit partial uplift for the load condition, as long as the bearing pressure stays within reason.

First....imagine a basic square/rectangular footer pad subjected to eccentricity in only ONE direction. The resultant vertical downward load falls outside of uni-directional "kern" (middle 1/3 of footer length). This condition no longer allows the use of q = (P/A) + (MC/I) to find the maximum bearing pressure since there will be uplift and a reduced bearing area, however, since it's only 1-axis, it's still easy to find the maximum bearing pressure. I simply find the effective bearing length due to the location of the resultant upward pressure (in-line with the resultant downward load P) and solve for qmax. Easy, right?

Ok...now imagine the same basic square/rectangular footer pad subjected to eccentricity in BOTH directions. The resultant vertical downward load falls outside of the bi-directional diamond shaped "kern" of the footer. Is there a graphical or numerical solution to finding qmax? Can you look at each axis separately and superimpose/add the bearing pressure from each direction? It just seems like the pressure distribution could be very complex, even with linear assumptions.

The conservative thing to do is simply make the mat large enough to eliminate uplift altogether, but I was just trying to save some concrete.

What am I missing here?

 

[structSU10]

This thread has some good reference material, including a PDF of a mathcad program that works well:

http://www.eng-tips.com/viewthread.cfm?qid=236147

 

[Lion06]

Is your eccentricity due to an eccentrically placed, but concentrically loaded column or a concentrically placed column with a base moment?

If given the option, I never design a footing to not have full bearing for anything other than transient load.

Have you taken advantage of the soil overburden weight? That often helps if you have a footing with a large footprint.

 

[ARS97]

structSU10 - Wow.....great thread. Thank you.

Lion06 - it's a 4-column frame centered on the mat. It is transient load. No overburden present.

 

[bkal]

I do not think that you can look separately and then superimpose as the problem is essentially nonlinear.

 

[Ron]

Andy...you're an engineer, not a contractor, so it's a "footing" not a "footer".

From your description you have a concentric application with a base moment. For that, I agree with Lion06...don't lose bearing. Concrete is relatively cheap. If you spend 3 or 4 hours trying to figure it out, that would buy another 5 to 10 cy of concrete. In many cases like this, the overturning moment resistance prevails over the bearing pressure analysis.

 

[ARS97]

Ron - I've checked the overturn & sliding separately...they're fine. I've also just completed a Staadpro FEM that verifies the reduced FOOTING size. I'll probably use the larger option though for the sake of simplicity and considering the application (industrial - conveyor head frame resisting belt pull). Thanks