footing with biaxial moment 5

[Lion06]

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.

 

[ash060]

My foundation design textbook has a method for calculating effective widths and lengths for biaxial footings, but the solutions result in charts that you have to read.

I have attached a link to a website that has an excel spreadsheet with sited references that will do a biaxial footing

http://www.seaofsc.org/Alex's Corner.htm

 

[WillisV]

There are various solutions but a trial and error approach as outlined in Peck/Hanson/Thornburg "Foundation Engineering" (Mine is 2nd ed. -1974 p391) is rather straight-forward.

 

[msquared48]

StructuralEIT:

Any chance of using grade beams to avoid the problem? I always like to KISS the situation, if you know what I mean. Not that the solution you are looking for is hard, but it could save you concrete in the footing.

Mike McCann
MMC Engineering

 

[oneintheeye]

i have worked out eccentricity for both directions. If one will mean pad is non bearing for a length (say due mx) I have used that bearing pressure in my P/A +- Mx/Zy +- My/Zx formula then for the other way applied the reduced bearing area to work out my Z in other direction.

Sorry if the symbols are different from USA but you get the idea.

 

[miecz]

Here's a PDF of my standard mathcad file. The approach is simple. Determine the zone from the eccentricity and then determine the pressure from the formula for that zone. Unfortunately, I didn't record where this was published (duh), and the engineer who gave it to me has passed away. If anyone knows where this comes from, I would appreciate that info.

 

[BAretired]

As a first approximation, calculate the resultant moment acting on the footing, i.e. the vector sum of the two moments. Assume the line of zero pressure occurs parallel to the resultant moment (using the right hand rule). Take an educated guess where the zero pressure line is and determine whether the resulting stress block satisfies both load and moment. Modify the position of the zero pressure line until load and moment are approximately satisfied.

Then check the moment normal to the resultant vector. If it is not zero, modify the direction of the zero pressure line until it is close enough.

Best regards,

BA

 

[JLNJ]

Last one of these I did I modeled in RISA3D on compression-only springs. Took me all of 20 minutes.

Once you get outside the kern in one or both directions things go haywire for bi-directional bending.

 

[kslee1000]

From personal experience, here are my views:
1. As suggested by MSQUARED48, avoid the situation to the best you can.
2. As JLNJ pointed out, use FEM with compression only spring.
3. For personal satisfaction, you can write your own spreadsheet program assuming the footing and soil both are linear elastic (linear stresses). The difficult part is once a corner has developed negative pressure (uplift), the bearing area is reduced, and the new bearing area/neutral axes need to be found, its properties re-calculated (quite mathematically challenging), and load redistributed. The iteration process stops when the footing is fully in bearing.
Have fun.

 

[Lion06]

Well, I'm just evaluating software, so I think it important to check by hand.

 

[Ron]

StructuralEIT...good point...most states require hand check on the software, or at least same model run through two or more software programs.

 

[BAretired]

Are we talking about a square footing? Why not give us the load, P also Mx and My and see how we might deal with it?

Best regards,

BA

 

[msquared48]

Do the moments happen at the same time or independently?

If they happen independently, then use the worst case of two conditions, P + Mx and P + My.

If they happen concurrently, then resolve the moments to a Mxy and rotate the square footing to the axis of the combined moment, allowing a solution similar to a simple P + M solution for inside or outside of the kern.

Mike McCann
MMC Engineering

 

[Lion06]

The moments are concurrent. These are all service loads using the appropriate load combinations.
P=20k
Mx=88k-ft
My=4k-ft

The shears are already included in the moments (that's why they're not included above), and the footing weight is included in P (at the appropriate DL factor). The progam is spitting out a 10'x10'x2'thick footing.

 

[Lion06]

I can get within 100 psf (of the max bearing pressure spit out by the program) using the method I stated above, but I'd really like to use a more rational approach and see where I get.

 

[oneintheeye]

can someone convert k to kg or KN for me and tell you what I get using spreadsheet

 

[WillisV]

That size seems about right. qmax = 2.36ksf is what I'm getting with that size footing.

 

[Lion06]

Willis, can you try it with P = 20.818k, Mx=87.842 k-ft, and My=4.226k-ft?

 

[DaveAtkins]

When I add in the weight of the footing, P = 50 kips. The My moment is so small it is basically negligible. And so q = 2P/3aB = 1.03 ksf. I think you can make the footing smaller.

For those cases where the biaxial moments are both large, I use the graph on page 133 of Foundation Design by Teng.

DaveAtkins

 

[Lion06]

my P had the footing weight added in already. I think I noted that in the post.