Eccentrically Loaded Spread Footing Design Question 4

[ilikeconcrete]

I am designing a spread footing for a column that is part of a moment frame and am assuming that the column/footing joint is rigidly connected to reduce the deflections of my frame.

Say my service-level gravity force is 300kips and the associated moment is 150 ft-kips.

When checking bearing capacity, I can calculate my eccentricity to be e = M/P = 150/300 = 0.5ft and determine my bearing stress distribution.

However, I can't find a reference that comments on whether my factored bearing pressure distribution used to design for shear and flexure should be calculated using e = 0.5ft (from service-level forces) or if I calculate a different eccentricity associated with my factored loads such that e = Mu/Pu.

Can anyone point me to a published reference that I can include with a submitted calculation book?

Thanks.

 

[Lion06]

I don't know that there is a reference other than to think about it. The service level e is based on un-factored loads and will obviously be different than your strength level e based on factored loads (since the load cases get different factors).
I would always use the actual e for the condition you are checking. Using the e=0.5' is valid for bearing stresses because that is a service load check, but when doing your strength design you need to use the appropriate e.

 

[ilikeconcrete]

But you can make the argument that the service-level 'e' is the appropriate eccentricity because that is the eccentricity that the footing is supposedly seeing, we've just increased the magnitude of the load on it to provide a factor of safety.

If I was designing this before the LRFD method became the professional standard I would be using the same eccentricity for the concrete design and the geotechnical design and would account for my factor of safety by reducing the allowable stress in the concrete. Therefore I would always be using the 'real' eccentricity rather than some artificial creation that has increased various loads based on statistical factors.

 

[Lion06]

But if you use the factored axial load with the non-factored e, you are getting something smaller than the factored moment that you are supposed to be designing for. The loads are factored for a reason (based on statistical factors as you mentioned), and you can't just ignore it.

 

[Lion06]

Actually, now that I'm thinking about it, for a single spread footing the e won't change, just the magnitude of the loads. Both M and P are being factored by the same amounts so those factors will drop out in the M/P=e calc.

 

[Lion06]

I guess you could have a case where they weren't equal. If there is Pdead, but no Mdead, and some Plive and Mlive. Then the factored and non-factored e wouldn't be the same. Either way, when figuring out the factored soil bearing pressures to be used with the footing design (which is reinforced concrete), you need to factor the loads and change all parameter as required.

 

[UcfSE]

I would use the service e for both.

 

[Lion06]

ucfse-
what is the rationale for that?

 

[Lion06]

I guess I am just looking at this and saying that e is nothing more than a function of M and P. If you are factoring your loads to design your footing, then e is what it is. How do you arbitrarily say, "ah, I don't feel like using that e". That means you are not using the right moment (or axial load)

 

[haynewp]

I would use different e values also.

 

[WillisV]

I think analysis should be performed seperately for service loads to calculate bearing pressures vs. allowable and for ultimate loads to calculate ultimate bearing pressures for concrete design (so I would use different e's). Soil distribution under moment is a nonlinear problem.

Using the same "e" under service and ultimate load is like saying you are going to perform a frame P-delta analysis with service level forces and then factor the results to get your ultimate level forces including P-delta.

 

[structuresguy]

Wow, this is a lot of time worrying about factored/unfactored for a footing design. Just use factored and have a conservative design. Another few square feet of concrete just doesn't cost that much.

 

[oneintheeye]

in a restricted area it could matter though. I would factor. Check overturning at ultimate though.

 

[Lion06]

structuresguy-
I don't think this is a matter of being conservative. No one said to use factored loads to check the soil bearing capacity. It was only questioned that when factoring the loads to design the rebar and thickness of the footing which e to use. If you don't use the e from the factored loads then you are simply not factoring them correctly (because e is nothing more than M/P - if you use something other than the factored M/P then the loads aren't factored as required by the ACI/IBC strength load combinations).
I would never use factored loads and attempt to keep that soil bearing pressure below the allowable - THAT is extremely conservative.

 

[KBVT]

StructuralEIT is spot on, unfactored load effects for bearing pressure calculations and factored load effects for reinforcement and concrete design. It seems pretty straight forward to me.

 

[graybeach]

I agree with StructuralEIT and KBVT. If you factor the loads and then calculate e, you could end up with e out of the middle third which would raise unnecessary, overconservative complications. Checking factor of safety against overturning is another matter. In my view, it should be done apart from the bearing pressure and design calculations. One should not multiply the lateral loads by the required FSO and then calculate e, etc.

 

[csd72]

ilikeconcrete,

Great question! I have never really thought of this before as I dont generally design fixed bases for portal frames. It would make some difference though.

 

[dougantholz]

You should re-calculate your load distribution on your footing. The reason is the load factors going into the moment are likely different than those effecting the column.
Say in the service LC: D + 0.75 x (L + W)
And compare that to the similar strength LC: 1.2 D + 1.6 W + 1.0 L.
Your dead load contributions went up 60%, while your live went up 33% and your wind went up 213 %. Since D & L contributed to your axial, and the moment is likely due mostly to W, the ratio will change.

 

[JStephen]

I had always assumed that you should apply the load factors to the applied loads and then calculate internal forces. If internal forces are proportional to applied loads, there's no difference. If not, as in the p-delta, then I assumed that factors were applied first.

However, in ACI-318, it defines W as "wind load, or related internal moments and forces", and similarly for the other terms. This seems to allow either approach. I think this came up in a previous post about calculating moments in a footing with partial uplift.

 

[ilikeconcrete]

I realize the ratios will change, that's not the issue. Think of it like this: I size my footing based on service-level loads and (for example) it is 6' x 6' and the eccentricity is 2.5' from the center of the footing (i.e. outside the kern due to high moment due to wind and relatively low gravity force...but the footing is stable). Then I go to calculate my factored bearing pressure and increase my wind load by a factor of 1.6 and increase my gravity loads by something less than 1.6. Now my 'equivalent' eccentricity is greater than 3' and my stand-by equations for factored bearing pressure are undefined.

Do I need to increase the size of my footing? I shouldn't have to because it is sized based on service loads. But I can't calculated a factored bearing pressure because as far as the calculations are concerned, a load can't be applied from outside the area of the footing.

So I really don't think it is as straight forward as some of these responses make it out to be.