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footing with biaxial moment 5

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Lion06

Structural
Nov 17, 2006
4,238
I've been looking for a reference as to how to determine the max soil pressure for a footing that has moments in both directions, but only has partial bearing. The moment in one direction would the load in the kern (if it were the only moment), and the moment in the other direction would put the load outside the kern. I can't find a reference on this in my foundations book, and I could go through the math of it (but that would take a REALLY long time, and I honestly don't want to spend an entire day to figure it out), but I figured someone else has to have done this before.

My first inclination was to take the max pressure of the moment causing partial bearing and adding that to the max pressure caused by the full bearing (M/S), then I realized that I couldn't us the full S of the footing (for the smaller moment) because the whole footing isn't in bearing anymore. I tried estimating the amount of the footing that would be in bearing and using that S. That would get me close, but I'm really trying to be exact because I'm evaluating a program. The line of zero bearing stress is not perpendicular to either edge of the footing because of the moments in both directions, but again, I don't know how to address this without a day-long geometry session.
 
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csd-

Can you tell me what text that was?

I know it is a geometric exercise (and not difficult to work through), but is very time consuming to work through from scratch.
 
The book was 'Foundation Design' By Wayne C Teng, Prentice Hall 1962.
 
That book is going for $325.00 online. Is there any chance you have those pages scanned?
 
It must be out of print as it is selling as a collectors item. I see no issue with providing copies of 46 year old out of print books so I will scan and post it on Monday.
 
Hey! I mentioned the Teng text way back at the beginning of this thread (on January 29).

No one gave me a star [sadeyes]

DaveAtkins
 
Dave-
You're right. Here you go.

The AASHTO spec does give equations that are less straightforward, but will get you the answer. I'm anxious to see the equations out of the Teng text.
 
Here is one way to do it.

On the attached sketch, Vol. abcd is the volume under the stress block.

Cx and Cy are measured from the edge of footing to the centroid of the stress block.

h is the height at point a.
kh is height at point c.
0 is the height at b, c and e.

Using Excel, one can experiment with different x and k values until Cx = A/2 - P/Mx and Cy = A/2 - P/My.

Finally, calculate "h" to satisfy the equation that the volume under the stress block is equal to P, the applied load.


Best regards,

BA
 
 http://files.engineering.com/getfile.aspx?folder=f4e03566-ee8e-4ad6-a7e9-012df081141f&file=Biaxial.pdf
Oops, I meant to say:
until Cx = A/2 - Mx/P and Cy = A/2 - My/P.

Best regards,

BA
 
Is there anyone that has the Teng text who can scan and post the relevant pages?
 
I have a copy of Teng at home. I'll bring it in and scan it in the morning.
 
If anyone is interested, the RISAFoot program (even the free Demo version) provides information that can be used to verify a bi-axial soil bearing profile.

That program will show you the soil bearing pressure at each of the 4 corners and will also display the distace from the point of maximum compression to the neutral axis location.

If you know that information it is not all that difficult to verify that the total pressure load equals the applied vertical load. I did this for one of our users yesterday. It takes me awhile to remember how to do the integration, but once I remember then it's not that bad.

You can even use this same information to verify that the centroid of the soil pressure corresponds to the load eccentricity location. But, the integration gets more complicated, and I tend to "guesstimate" it for my hand calculations instead.
 
In the attached diagram, the pressure at corner b and d is zero. The pressure at c is k times the pressure at a, namely h. The volume abcd is actually a truncated triangular pyramid, so can be expressed as abe - cde. The volume and centroid of a regular pyramid is well known, so no need to integrate.

The procedure is to guess at x and k and iterate to a correct solution such that Cx and Cy correspond to the known location of the load P. When this has been found, the highest pressure, h (at point a) can be found by equating the volume of abcd to applied load P.

A bit messy, but it can be done.

Best regards,

BA
 
 http://files.engineering.com/getfile.aspx?folder=c96af9cf-a458-4aa9-9104-d8e6148b18c8&file=Biaxial.pdf
Bendog,

Thanks for sharing this. It is is a very comprehensive treatment of the subject of eccentric loads on rectangular footings.

By the way, my solution given in my last post agrees precisely with Case III from Teng.

Best regards,

BA
 
Viewing the soil pressure as a truncated pyramid makes it seem so easy.... At least in comparison to all the integration that I've been doing.

Now I'm embarassed that I never made that connection. But, am very thankful to BAretired (and EngTips in general) for showing me the light. :)

Thanks!
 
JoshPlum,

There is one slight disadvantage to the truncated pyramid model. That is, when My = 0, k is 1.0 and the expressions for Cx and Cy become indeterminate (0/0).

With the Teng model, D and A may be evaluated when R is 1.0.

Of course, when My is zero, it is not biaxial moment?

Best regards,

BA
 
StructuralEIT, I don't know if this would influence your decision, but I found the book by Teng for about $150 here:


Its used of course, but I have usually found their prices to be somewhat lower than others. Never actually bought from them before though. Just search "Teng Foundation" in the books tab.
 
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