Biaxial Overturning Factor of Safety
Biaxial Overturning Factor of Safety
(OP)
I am looking at a footing that has biaxial overturning. The footing is not symmetrical and I have found that the factor of safety about each direction to be adequate but of course if the moments occur simultaneously I do not want to double count the resisting moments due to gravity loads, intertia of the footing. Thus I was thinking the formula below may be appropriate, thoughts please...
(1/FS)lateral + (1/FS)longitudinal = (1/FS)total
The idea here is that the resisting moment relative to the overturning moments is effectively the common denominator and thus not double counted in the total FS.
(1/FS)lateral + (1/FS)longitudinal = (1/FS)total
The idea here is that the resisting moment relative to the overturning moments is effectively the common denominator and thus not double counted in the total FS.






RE: Biaxial Overturning Factor of Safety
RE: Biaxial Overturning Factor of Safety
(1/FSlat)^2+(1/FSlong)^2=(1/FStot)^2
RE: Biaxial Overturning Factor of Safety
RE: Biaxial Overturning Factor of Safety
A more important check may be the bearing stress that occurs at each corner of the footing and verification if uplift is occuring at any of the corners.
RE: Biaxial Overturning Factor of Safety
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: Biaxial Overturning Factor of Safety
I only checked overturning in each direction independently.
The more difficult task is determining the bearing pressures and % bearing area for a footing with biaxial moments. It can turn into a bit of a science project.
Checking overturning in the resultant direction may be even more difficult. About which point does one sum moments for the resultant direction?
RE: Biaxial Overturning Factor of Safety
RE: Biaxial Overturning Factor of Safety
Though, I agree with PaddingtonGreen that the exact way would be to resolve this into a single moment along an inclined plane. Then calculate the overturning and resistance relative to that inclined axis.
RE: Biaxial Overturning Factor of Safety
RE: Biaxial Overturning Factor of Safety
I had to pull up a spreadsheet and play with the numbers a bit.
It looks like for a rectangular footing, the combined safety factor will always be in between the safety factors in the two principle directions, so if they're both okay, the combination is okay. This is for checking rigid-body overturning about a point, only.
Note that in the first case above, the soil bearing due to moment is doubled at that corner, so if that's the limiting factor, it's different.
For a round footing, the moment arm doesn't change, so checking in two directions is unconservative.