Overturning stability for footing with biaxial moment

[ars13]

I have a footing with biaxial moment. How do I go about finding a "toe" or moment arm distance for calculating my resistance to overturning? Thanks

 

[Lion06]

See this thread javascriptpenindex(450,450,'

http://www.tipmaster.com/includes/refinfo.cfm?w=450&h=450')

a few threads down on this page.

 

[Lion06]

Let's try that again.
thread507-236147

 

[ars13]

I'm not sure if I'm missing something in that thread. I've gone through my process of calculating my effective area and found my maximum soil pressue. Now I want to satisfy my overturning stability. For footing with single eccentricity I take my overturning moment about my "toe" or the outermost edge where the footing will actually overturn. Like I said maybe I missed something in that thread but where does that location occur with two way eccentricity?

 

[JoshPlumSE]

I just calculate the OTM safety factor independently about each axis. If they are both good, then I consider the overall footing to be good.

I suppose you could calculate the stability ratio about a line perpendicular to your eccentricity which starts at the corner of your footing.... that might end up being more accurate. But, I've never seen anyone do it that way.

 

[BAretired]

With two way eccentricity, there are two toes, one for Mx and one for My. If the footing is square, you need only consider the maximum moment. But if the footing is rectangular, you must consider both.

Best regards,

BA

 

[ars13]

Simple enough. Thank you.

 

[miecz]

Take a look at the thread referenced by StrucuralEIT. The sixth post is mine and contains an attached PDF of a mathcad file I wrote for footings with biaxial moments. Sheet 3 has an interaction formula for overturning stability. I wrote this interaction myself so you won't find it in any literature. It combines the overturning effects in the two directions. Ignore the "0.75" factor in the test to the right of the interaction formula as it no longer applies.

 

[BAretired]

miecz,

I do not understand your last comment. Please elucidate.

Best regards,

BA

 

[BAretired]

miecz,

Okay, sorry I was not able to find the file you were talking about. Now I have found it. And, having found it, I still don't understand it. So far as I am concerned, it is a pile of garbage.

Overturning may occur in either the X of the Y direction. The expression given in your file for Safety Factor on Overturning has no merit whatever!

Best regards,

BA

 

[miecz]

BA,

The expression that I wrote for overturning safety is not based on experimental test. So, I agree, it has little merit. That's why I didn't offer it up at the beginning of this thread.

Having read the other responses, I see that none of them are based on experimental evidence, or come from the literature. So, as I see it, we're into the realm of measured opinion here.

When I imagine a footing with overturning moment in one direction with some safety factor against overturning, and then add a force in the other direction, I feel that there is a reduced safety against overturning resulting from the additional moment. So, I don't believe the safety factors are independant.

The formula is my attempt to quantify the interaction. Constructive criticism is always welcome.

 

[BAretired]

miecz,

Both Mx and My contribute to the maximum pressure in the corner, but there are two possibilities for overturning. If Mx/B is greater than My/A, the Mx determines the safety factor against overturning. It would be V*B/2Mx. 'My' does not enter into the calculation because it has no effect about the edge in question.

It is based on the definition of overturning, not experimentation.

Best regards,

BA

 

[miecz]

BA-

Ah, therein lies my problem - the definition of overturning. It assumes the footing will tip on an edge. I don't believe a footing will tip on the edge, as the bearing pressure would have to be infinite. I see the footing rotating about some point in from the edge. The location of that point would depend on the bearing pressure, and the bearing pressure would change if there were moment in the other direction.

 

[BAretired]

miecz,

Sorry, but you are not being consistent. If My = 0, your own formula for safety factor against overturning boils down to the behavior you say you don't believe in, i.e. the footing tipping on one edge.






Best regards,

BA

 

[miecz]

BA-

You're right. If M_y=0, my calculated "safety factor" is identical to the behavior I don't believe in. I believe that my real safety factor is something less than that, but I adhere to the traditional calculation of overturning safety factor for the case of uniaxial moment in either direction. This is the long recognized method of calculating the overturning safety factor for uniaxial moment and I tend to stick to tried and true design methods. In the case of biaxial moments, I don't have so much confidence in the assumption of dual knife edge bearing, so I devised this garbage method to increase my safety factor.

 

[BAretired]

Okay with me. I have no quarrel with you increasing your safety factor. I just don't believe it has a sound basis in theory.

If you put a wood cube on the floor with a long nail projecting upwards, then apply moment be pushing the nail head horizontally, the block may slide along the floor, but if friction is enough to prevent sliding, does the block not tip about one edge? How is it different?

Best regards,

BA

 

[miecz]

BA-

I agree, my formula has no basis in theory. And, it has no basis in experimentation. This comes straight out of my gut, and I've devised a mathematical formula to reflect my gut feeling, which is, that a footing with moments in two directions will overturn before a footing with moment in one direction.

Fot the case of the wood block on a floor, the difference is that the floor is hard enough so that the block will indeed tip over it's edge. This models a footing on a mud slab. For a footing on soil, you would have to put the block on something soft, like a thick wet sponge.

 

[JoshPlumSE]

Miecz -

Personally, I like your attempt at establishing a formula for this. I think one of its strengths is that it condenses into the uni-axial case when only one moment is present.

You're using, essentialy, an SRSS (square root sum of the squares) for compbining the two overturning moment safety factors. That was my first thought as well as it is a common statistical combination.

Seeing as those two moments act at the same time. then I would think that something closer to a CQC (complete quadratic combination) method would make more sense. Per your terminology:

0.5*V / [sqrt ((Mx/B)^2 + 2Mx*My/A*B + (My/A)^2)]

or

0.5V / (Mx/B + My/A)

I haven't run any numbers (or conducted any experiments). But, like your original method, it does reduce down to the uni-axial case.

If you looked at overturning resistance as a function of rotation direction, both methods give the knows value for the uni-axial cases. But, your method assumes an elliptical interpolation between the known cases and mine should be a straight line interpolation..... at little bit more conservative.

 

[miecz]

JoshPlum-

Thanks. Without published information or experimental evidence, we're pretty much left to whatever feels right. Your method seems as reasonable to me (though I like mine a wee bit better). Careful, though. We're at the point is this thread where one of the heavy hitters usually posts overwhelming evidence that blows my silly theory out of the water.

 

[kslee1000]

For typical building with more than 4 columns, please do not take OT due to biaxial loadings to extreme - simply check each direction is adequate. The inherent Conservatism include:

1. Code specified safety factor.
2. Typical practice - ignoring passive pressure.
3. Group effect - typically analysis is performed on one of the worst case that happened to one of the footing out of many, not all the footings experience the same loading, nor behave the same simultaneously.

Throughout my practice, I prefer to emphasis stability in the construction stage, new or re-construction, during which the footing is isolated from others, the failure rates are high.