Eccentically Loaded Pad Footing Design
Eccentically Loaded Pad Footing Design
(OP)
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.






RE: Eccentically Loaded Pad Footing Design
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.
RE: Eccentically Loaded Pad Footing Design
DaveAtkins
RE: Eccentically Loaded Pad Footing Design
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.
RE: Eccentically Loaded Pad Footing Design
RE: Eccentically Loaded Pad Footing Design
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: Eccentically Loaded Pad Footing Design
RE: Eccentically Loaded Pad Footing Design
RE: Eccentically Loaded Pad Footing Design
RE: Eccentically Loaded Pad Footing Design
DaveAtkins
RE: Eccentically Loaded Pad Footing Design
In order to design the footing itself, you can increase that profile proportionally for dead, live, and lateral loads, no?
RE: Eccentically Loaded Pad Footing Design
DaveAtkins
RE: Eccentically Loaded Pad Footing Design
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?
RE: Eccentically Loaded Pad Footing Design
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.
RE: Eccentically Loaded Pad Footing Design
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.