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Eccentrically Loaded Spread Footing Design Question
4

Eccentrically Loaded Spread Footing Design Question

Eccentrically Loaded Spread Footing Design Question

(OP)
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.

RE: Eccentrically Loaded Spread Footing Design Question

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.

RE: Eccentrically Loaded Spread Footing Design Question

(OP)
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.

RE: Eccentrically Loaded Spread Footing Design Question

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.

RE: Eccentrically Loaded Spread Footing Design Question

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.

RE: Eccentrically Loaded Spread Footing Design Question

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.

RE: Eccentrically Loaded Spread Footing Design Question

I would use the service e for both.   

RE: Eccentrically Loaded Spread Footing Design Question

ucfse-
what is the rationale for that?

RE: Eccentrically Loaded Spread Footing Design Question

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)

RE: Eccentrically Loaded Spread Footing Design Question

I would use different e values also.  

RE: Eccentrically Loaded Spread Footing Design Question

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.

RE: Eccentrically Loaded Spread Footing Design Question

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.

RE: Eccentrically Loaded Spread Footing Design Question

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

RE: Eccentrically Loaded Spread Footing Design Question

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.

RE: Eccentrically Loaded Spread Footing Design Question

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.

RE: Eccentrically Loaded Spread Footing Design Question

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.

RE: Eccentrically Loaded Spread Footing Design Question

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.

 

RE: Eccentrically Loaded Spread Footing Design Question

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.

RE: Eccentrically Loaded Spread Footing Design Question

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.

RE: Eccentrically Loaded Spread Footing Design Question

(OP)
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.

RE: Eccentrically Loaded Spread Footing Design Question

I understand the points made and have debated with myself before.  Either way, ask yourself, is it any more reasonable or accurate to use a factored e and factored loads in an equation that probably was not meant for ultimate load conditions?  Do you violate any assumptions by doing so?

RE: Eccentrically Loaded Spread Footing Design Question

I have always struggled with this also. In my opinion you have to use service loads to check service allowable soil stresses. But if you use ultimate loads to design the footing you probably will get a different soil pressure distribution which isn't correct. I use service loads, calc soil stresses and apply a psuedo load factor to the soil stresses to design footing. This also isn't strictly correct but you can use a multiplier that you know is at or above the LRFD stresses.

RE: Eccentrically Loaded Spread Footing Design Question

I never said anything about using factored loads to check bearing capacity.  But to design the footing, you have to.  If the factored loads change the e, well so be it.  I don't think it would make that big a difference in the reinforcing of the footing to worry about it.  We have all wasted more money (in man hours) talking about it, then it would have cost to add an extra piece of rebar or two.  

My point is, there are many things we need to worry about.  But a little extra reinforcing in a footing is not one of them.  Many engineers analyze things to death which are relatively inconsequential to the overall performance of a structure.

RE: Eccentrically Loaded Spread Footing Design Question

One old practical method to design the footing with moment (assume concrete footing rest on soil):

1. Obtain service level soil stresses.
2. Multiply the service load stresses by a factor of 1.6, or 1.65 if LL>>DL, (since at the old time the DL factor was 1.4 & LL factor was 1.7)
3. Design the concrete footing use the factored stresses.

This method is acceptable for eccentricity/moment caused mainly by the transient loads (wind/earthquake). For permenent eccentrical loadings, you will need to find other solutions, best is to eliminate the eccentricity at the first place (using piles, ties, offset footing pad...).  

RE: Eccentrically Loaded Spread Footing Design Question

kslee1000 this is what I mean. If you use factored moments to calculate loads on piles in pilecaps for instance you may or may not get a tension load in end piles which will require tension reinforcing in the pile and top reinforcing in the pilecap. You very well may not get acceptable results when you use factored loads to determine pressure distribution under footings. This is especially true with moments from lateral loads such as shearwall pilecaps.

RE: Eccentrically Loaded Spread Footing Design Question

Add'l thinking on the method I described previously:

By doing so, you are not necessarily design the concrete footing to withstand the whole factored loads (which is at the limit state), but you are sure that your footing will not fail before noticeable cracks suddenly developed on the walls/floors due to excessive progressive/permenent settlement, since the footing was sized against the allowable (elasticsteady state) soil pressure.

The unit load factor also ensure the footing has adequate strength to resist pressure above the presumptive static soil pressure at the split second of peak reversible loadings.  

RE: Eccentrically Loaded Spread Footing Design Question

ilikeconcrete-
I would make a very large bet that if your e for service loads is 2.5' from centerline of a 6' square footing (the resultant is acting 6" from the edge of the footing) that your allowable soil stresses will rarely work.
This is not a hard discussion and I'm not seeing a case for using anything other than the factored loads.  the factored loads are what they are.  The e just comes along for the ride.

RE: Eccentrically Loaded Spread Footing Design Question

(OP)
StructuralEIT-

Trust me, it happens.  Design a spread footing for a shear wall.

RE: Eccentrically Loaded Spread Footing Design Question

I have designed footings for shearwalls, but the OP was stated as a spread footing for a lateral column.  
 

RE: Eccentrically Loaded Spread Footing Design Question

Hmmm, very interesting.  I read all of the above and ran a handful of scenarios with varying DL/LL and Moment/Axial ratios through my 'Footing with Moment' spreadsheet.  

The two methods:
1)  Determine soil bearing pressure with Service loads and pseudo-factor those pressures up to determine Factored level internal forces in the footing.
2)  Determine the internal footing forces by using Factored level column forces, and the associated Factored level soil pressures.

None of the cases I ran showed more than a 10% difference in the critical internal footing forces.  What was interesting was that the Overturning Safety Factor was up to 20% less when using method 2 (for higher Moment/Axial ratios).  Of course there is some small error because my spreadsheet does not use any factoring for calculating footing self-weight.

I most agree with something kslee1000 touched on.  The 10% discrepancy tends to indicate that the method selection does not substantially impact footing internal forces.  I would focus my efforts on forcing the failure mode to behavior that warns the inhabitants of impending failure.  Its scary to think that an overload situation would either break the footing or overstress the soil - because if that happens and the 'toe' moves... overturning stability disappears quicker than an Architect after receiving an invoice.

RE: Eccentrically Loaded Spread Footing Design Question

Use service level loads and design the footing with ASD from ACI 350.  It's conservative and you only have to analyze the footing once.

RE: Eccentrically Loaded Spread Footing Design Question

If you are designing a shearwall footing for mostly overturning moment and limited applied dead load where the footing weight has to be sized to provide the needed dead load to resist overturning(0.6D+W)and limit soil stresses you will find a substantial difference if you do the same calc with factored loads.
I don't think that designing this condition with applied factored loads is acceptable. It frustrates me that the building codes don't address things like this.

RE: Eccentrically Loaded Spread Footing Design Question

2
I may be bringing this post back from the dead but generally I design the bearing capacity of the footing for service loads, making sure the allowable bearing capacity of the soil is not exceeded.

When designing the base for flexural steel, I then assume that the full allowable bearing pressure is developed over then entire base, convert to ultimate loads (i.e. multiply by 1.35) then design the flexural steel based on this loading.

RE: Eccentrically Loaded Spread Footing Design Question

i've been thinking about this on weekend and its not quite as simple as people are suggesting for some cases. Imagine the loading puts servicability outside middle third, you have a base area in tension. then if you factor your loads for RC design the e increases further, therby theoretically increaseing the area of base in tension and reducing your bearing area. You then have a possible condition where you may be able to design less or more steel depending on which e you use. i.e. tension steel in top or bottom over different zones.  

RE: Eccentrically Loaded Spread Footing Design Question

I agree with Gumpmaster and/or asixth.  Why make this so complicated?

RE: Eccentrically Loaded Spread Footing Design Question

If you are finding that factoring your loads gives you opposing effects than your service loads, than I would investigate the load combinations with one or more loads not acting as stated in ASCE-7.

RE: Eccentrically Loaded Spread Footing Design Question

It seems to me that I've had cases where using factored loads to calculate the moments resulted in dramatically higher moments than calculating service load moments, and then factoring those moments.  It's been a long time, but I think using factored loads changed the bearing profile dramatically.  It may have had to do with the  eccentricity being within the middle third for service loads, but not for factored loads.  In any case, I concluded that the intent of the code was to provide a factored strength derived from service loads.  So, for the concrete design, I calculate moments and shears for service loads and then factor those results by 1.6.  

RE: Eccentrically Loaded Spread Footing Design Question

The concrete is designed on factored Loads. The Footing is sized based on allowable loads. "e" does change for factored vs. unfactored loads. Footing stabilty and bearing capacity are still more akin to allowable stress. For step by step see Bowles "Foundation Analysis and Design"

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