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.

 

[haynewp]

Are you implying that because by a short term nature of wind thought?

 

[csd72]

Yes,

The only reason why it may not be a good idea for partial loading is because of settlement. For settlement you need more time than a gust of wind takes.

 

[haynewp]

I can see that but I could also see compaction ocurring at the toe from a footing rocking back and forth under wind to create increasing deflections. But this is better answered by a geotech in my opinion, you may be right because it is not really my cup of tea.

 

[Lion06]

miecz-

I'm looking a little more closely at the sheet you posted. I'm having a hard time following some things. For example, in the bearing pressure calcs, what is "S"? Also, for the Zone II calcs, it has ey in the denominator (which is 0), but the f2 value is the same as I would get by hand (but the equations shown don't work out because of the 0 in the denominator). What is the px in the Zone II calcs?

 

[jike]

Risafoot will solve this problem using FEM.

 

[enginerding]

The AASHTO Code has a method for coming up with the qmax as well. See Figure 4.4.7.1.1.1C in the 17th Edition.

I am not sure if the same figure appears in the new one (LRFD only). I think it is strange that the code includes this figure because elsewhere in the code they do not permit bridge foundations to be loaded outside the kern...

On another note, we design sign and billboard foundations often enough, and it is entirely uneconomical to design a spread foundation with the resultant within the kern for wind load. It would irresponsible of an engineer to require the load to remain within the kern in such a circumstance.

 

[miecz]

StructuralEIT-

The "S" used in the bearing pressure calculations, has no name, it's simply a variable defined by the formula.

You're right, e_y is 0. To avoid dividing by zero, I've adjusted e_y (and e_x) by [ε], as shown in the formulas on sheet 1. [ε] is defined as .001 feet, but that definition is not shown anywhere on the printout.

px is the soil pressure at the center of the footing, if M_x=0k'. I use px to calculate the bending moment at the center of the footing, where I believe it is maximum.

Again, I don't know where the soil pressure formulation comes from. I got it at least 20 years ago and have verified it against many other sources over those 20 years. It is always dead on.

 

[Lion06]

miecz- Thanks.

miecz and willis-

Would it be possible for both of you to plug in the following loads in your respective sheets and tell me what you get?
footing is 9'x9'x2' (but the self weight of the footing is already figured into P - using the 0.6DL factor)
P=18.632K
Mx=71.52k-ft
My=5.646k-ft

Using miecz's formulas I'm coming up with 2306psf (which is roughly what I would expect), but this program I'm checking is showing 3380psf (almost 50% higher). I found another method that I was trying out, but that's only giving me 1330psf (which is way too low, so I'm throwing that out).

 

[BAretired]

With only P and Mx, the eccentricity is 3.84', or 0.66' from the edge of the footing. With a triangular distribution of pressure, the effective width of the footing is 3 * 0.66 = 1.98' and the maximum pressure = 2.09 ksf.

Now, considering My = 5.64k' and a section modulus of S of 1.98*9^2/6 = 26.7 for the effective portion of the footing, the additional stress is M/S = 0.21 ksf.

Adding the two together gives 2.30 ksf.

Best regards,

BA

 

[kslee1000]

Just a reminder, by reading your loads, the resultant force is outside the kern w/r to x-axis (ex = Mx/p > middle third), the footing is not fully engage in bearing, and its geometric properties have changed.

 

[miecz]

Here you go.

 

[Lion06]

kslee- No kidding?! That's been the whole point of this post. It's a piece of cake if there's full bearing.

 

[Lion06]

miecz-
I'd give you a second star if I could. Thanks!

 

[kslee1000]

StructuralEIT:

If you have done hand calculation by defining principle axes, you will know you haven't found/confirmed the maximum stress yet.

 

[Lion06]

What?

 

[WillisV]

2.31

 

[Lion06]

Thanks Willis. I am trusting the formulas for miecz's sheet, but does anyone have an idea where they come from?

 

[kslee1000]

If you have located the principle nutral axis, the area remains in compression is trapezoidal, all forces are shifted as well as the stresses. Check the P/A term, it should reveal something.

 

[miecz]

The AASHTO Standard Specs have Figure 4.4.7.1.1.1C to solve this kind of problem. It comes from the old AREA Railway Manual. It gives the same results, but, because it is a graphical solution, it gives information that formulas do not. Specifically, with the loads and dimensions you have, the bearing pressure is very sensitive to small changes in vertical load or eccentricity. Just reducing P 6% to 17.56 kips raises the bearing pressure to 3380 psf. Could your program be fiddling with your input?

 

[csd72]

The graph and formulii look like the exact same ones that i found in an old foundations text.

They can be back checked when you realise that the resulant is a triangular area with a stress increasing from zero to the maximum in the corner of the footing.

It is really just a geometrical problem with the same principles as the 2d case. e.g. centre of reaction = centre of loads e.t.c.