Eccentricity

[NM34]

Hi All,

I’ve searched through the eccentricity topics on this forum and can’t find my queries; any help would be much appreciated. Apologies if these answers are trivial, I haven’t been designing foundations long (normally I’m site based):

a) I have a pad foundation with a moment (M_a), and a vertical (V_a) and horizontal (H_a) load applied at an offset (x) from the centreline and a height (h) above the founding depth. The foundation is rectangular; the self weight (V_sw) acts at the centreline.

To calculate the effective foundation width (B’) for a bearing failure ULS verification, I need to know the eccentricity (e).

Using the general form:
e = M/V

Is my eccentricity 1:
e = (M_a + H_a*h + V_a*x) / V_sw

Or 2:
e = [(M_a + H_a*h) / V_sw] + x

For a small V_a, I have conservatively (gives a greater e) in the past used the latter (2), but I think that’s wrong.

b) When calculating the eccentricity, should I use unfactored actions and self-weight? I’m in the UK and design according to Eurocode 7. My initial thoughts have been that for an eccentricity calculation, V_sw is a ‘favourable action’ and should be factored accordingly (γ_G,fav = 1.0). However the ‘Communities and local government’ guide to BS EN 1997, in Example 4.2 uses an unfavourable factor (γ_G,unfav = 1.35) for all terms and I can’t find any other examples to refute this.

Thanks.

 

[DCBII]

Neither equation is correct:

M = Sum of moments acting about the center of the footing/soil interface:
= M_a + H_a*h + V_a*x

V = Sum of ALL vertical forces acting on the footing
= V_a + V_sw

e = M/V
= (M_a + H_a*h + V_a*x)/(V_a + V_sw)

Are you comparing these values to "net" allowable soil pressure or "gross" allowable soil pressure? If your comparing to net V_sw will drop out of the equation since it's already been accounted for by reducing the gross allowable soil pressure. If e is greater than 1/6 of the length of the footing then gross allowable soil pressure must be used or the footing must be lengthened to prevent uplift. This is because net pressures are based on the assumption that superposition applies, which assumption breaks down when uplift occurs.

Larger values of e may be conservative for one load combination, but unconservative for another. Usually multiple load combinations must be checked, which requires finding e and the soil pressure distribution multiple times.

In the U.S. (where I practice) a common practice is as follows:

(1) Stability (overturnig, sliding, and bearing pressure) is checked against unfactored loads. A factor of safety of 1.5 is required for overturning and sliding. Alternatively a value of 0.6 can be applied to the dead load for overturning and sliding checks. This essentially gives you a factor of safety against overturning and sliding, plus an allowance in case you overestimated your dead load.

(2) Strength (concrete & steel design) is checked against factored loads.

I hope this was helpful.