Eccentricity - Actual e vs. Calculated e

[pob11646]

I have an exterior concrete spread footing, say 10' x 10'. The thickness is 3', say. My column is 2' from the edge of the footing. Therefore, my actual eccentricity, e is 10'/2 - 2' = 3. Now, I have been told that my eccentricity - the calculated eccentricity, that is - can be less than the actual one if I take the weight of the footing into account. The formula for the calculated e, is
M/(Summation of P), i.e. Pe/(P + Weight of footing). Is this formula correct? Most of time, we see e as being just M/P. Does anyone know where this formula is from? lease provide references.

If you look at it, if the weight of footing is not considered, i.e. if Weight of footing is zero, that e is M/P. However, if the weight of the footing is considered, then the calculated value of e becomes smaller the more the weight of the footing is.

Hope someone can verify the accuracy of the formual, and provide some further insight into this. Thanks so much.

 

[kslee1000]

Include the weight of the pad into your cal, since you are checking the stresses at the soil-footing interface.

 

[csd72]

pob11646,

This is correct from first principles - Newtons third law to be precise.

"For every action there is an equal and opposite reaction"

Think of the stages that load is applied.
1. dig a hole - removes load of soil from hole.
2. Fill hole with concrete - applies a uniform load to soil.
3. apply eccentric column load - applies eccentric pressures on soil giving a triangular load.

The final bearing pressure is the combination of all three but generally 1. is ignored.

 

[BAretired]

I'm not sure about further insight into it. The resultant force is W + P where W is weight of footing. The applied moment is P*e. The effective eccentricity on the soil is the location of the resultant force, namely:

e' = e*P/(W+P)

If the footing is submerged below the water table, W would be the submerged weight of footing.

BA