Eccentically Loaded Pad Footing Design 1

[LTTANG]

In many design examples from the ACI318 Design Handbook (for footing strength design for Vu, Mu), the values of W or E is given in terms of a concentrically load P and subsequent q is derived (with proper load combinations) yielding a simple q=P/A. This q is then used to evaluate Vu and Mu and subsequent As and Av.My question is how can I derive the q in these terms when I have an overturning moment at the footing and essentially an eccentric P? In some cases, applying 0.9D+E or 0.9D+1.6W, yields 'e' larger than the width of the footing (far beyond B/2) and yet q < Q allowable when evaluating stability of footing. Should I just give up trying to figure out what q is and use whatever allowable Q given by the soil engineer or by code since it's a sin to go beyond the Q.I'd greatly appreciate your thoughts.

 

[ishvaaag]

Your footing once the proper solicitations are portraited needs to meet from the soil side as well the requirements of equilibrium, i.e., nor allowable compression nor overturning or slippage required safety factors can be exceeded. This means of course that for eccentrical situations the acting pressure on the soil is NOT given dividing the load in the column by the whole footing area. Whatever ACI may say, you need to have a rational assumption of the response of the soil, that for vertical loads means having some compressed area within the footing, meeting equilibrium with the load applied where the eccentricities put it, what means that the center of gravity of the reaction pressures will be also at such point.

One usual assumption as long as we are not tight in compression capacity under the footing is to assume a plastic distribution of the pressure on the soil in the compressed area. To this effect you place service load P at corresponding ex and ey, and draw an A1 subset of the area of the footing centered on that position; P/A1 must be less than allowed working stress for the soil.

(If you are on a bad soil and tight respect allowed working stresses on the soil many would elect to chose a elastic response of the pressure, but the concept is the same).

From this moment on, the niceties of closed form formulations are lost for this eccentrically loaded footing; seen upside down you have a plate sustained in a column and loaded at some surface near a side or corner.

You need to dimension your footing for the forces occurring in such a model, ensuring a proper load path. If you want economy you may elect to dimension for such actual model (if there was only an hypothesis, but there are a number of them, and you may design it for minimum rebar weight following the envelope). If you want a regular pattern of longitudinal reinforcement, simply determine the maximum pressure in any of such areas with pressure in the loadcases, and proceed as if the total acting load was such max pressure multiplied by the total area of the footing; this will give a notional load that may be far bigger than service level axial load P.

For checking against punching shear you will need to follow the procedures adscribed to two-way slabs in punching shear, or design the case with a program that gives the shear reinforcement automatically.

 

[DaveAtkins]

I have run into this same problem in the past. When the footing size is sufficient for working loads, but not for ultimate loads (because the resultant load is on the footing for working loads, but off the footing for ultimate loads), then I make the footing bigger.

DaveAtkins

 

[JoshPlumSE]

I have done two things in the past when I have encountered this issue.

1) Like DaveAtkins suggest, just make the footing larger.

2) I assume that my soil reaction occurs at the calculated eccentricity point. Then my required footing shear capacity is constant from the edge of footing to the face of my pier. My moment at any point in the footing is equal to that reaction times the distance to my eccentricy point.

There is not a whole lot of "physical" significance in the design methodology of point 2. So, I prefer method 1. But, I cannot see any code requirements that would prevent us from using method 2 when we are in a pinch.

 

[gobsmacked]

Can't remember who said it, but worth repeating that the structures we design are always unaware of the many assumptions we make about their behaviour.

 

[paddingtongreen]

I have an admission to make. Having designed successfully for many years before the various versions of ultimate design were forced on us, I drew the line at making the footings bigger. I multiplied the effects of the loads by the factor. I designed for and found equilibrium for service loads, keeping the loads separate. Say the bending moment on a footing, at the service load equilibrium, was made up of Mll+Mdl+-Mwl, I then multiplied these by the appropriate factors to check against the ultimate.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[miecz]

Daring admission paddingtongreen, as it apparently violates the letter of the code. Now that you've taken the lead, I'll admit to doing the same thing, as I've not seen a real world example of the code solution published in any of the literature.

 

[LTTANG]

My sentiment (common sense) is that the footing will see no more than the moments or shear imposed on it by the column. If the code wants to bump up the values for strength design, then I'll have to design them separately without trying to follow any design standards. One can go looney trying to follow the codes. I thank you all for your thoughts.

 

[ron9876]

I am with paddingtongreen. If you check soil pressure and stability and the footing works it doesn't make sense to me to change size of the footing. The only question after that is what factor to apply to the service stresses. I usually go conservative and use 1.6 since most of what I do is governed by wind.

 

[DaveAtkins]

While I don't think a footing will be unsafe if you design it using factored STRESSES, this is technically incorrect. You are supposed to factor the LOADS, not the stresses.

DaveAtkins

 

[ToadJones]

I might be off base here....but say you developed a soil pressure profile using service loads. If the there is some moment on the footing that can be resolved into a load 'P' at distance 'e', you'll just have a linearly varying soil pressure profile at service loads.
In order to design the footing itself, you can increase that profile proportionally for dead, live, and lateral loads, no?

 

[DaveAtkins]

No, because with 0.6D + W the resultant may be on the footing, while with 0.9D + 1.6W the resultant is off the footing.

DaveAtkins

 

[JoshPlumSE]

ToadJones -

The problem with just factoring up the soil pressures is that the eccentricity itself may have changed. Therefore, the centroid of the soil reaction has to change to match the new eccentricity.

Let's say that dead load is a pure axial force, and that Wind is a pure moment.

e_service = M/P

But, then you add in load factors for concrete design and you get:

e_factored = 1.6M / 0.9P.

Now, the shape of the soil pressure has to change to accomodate the change in the eccentricity. If you're really unlucky then you have to deal with Litang's original question. What do you do with the eccentricity for the factored load is off the footing?

 

[paddingtongreen]

In fairness to myself, I wouldn't do this to a single pole or even a two column portal or braced frame. Structures with multiple columns have other redundancies. If someone magically applied the factors to the loads for one of the columns, it would lose moment capacity, but only partially. The moment would re-distribute through the rest of the structure as moments or force couples.

I really don't believe that all of the loads on a structure will be multiplied simultaneously in real life, nor do I think every piece of concrete and every piece of steel will be minimum strength, all at the same time.

I do believe that the "perfect storm" for the service loads could combine with some items of minimum strength material, but not the multiplied loads and all material being the weakest permitted, certainly not understrength.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[ToadJones]

I guess I wasn't totally following the OP.
I see what you are saying and I have run into it where I was forced to use a spread footings that had very little axial load and large moments and a caisson or drilled shaft was not possible.
In this case I would make the footing large enough to accommodate.

for transient loadings I'd be less concerned.