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Footings with large eccentricities.
2

Footings with large eccentricities.

Footings with large eccentricities.

(OP)
I have a question about designing a combined footing to support a concentrically braced frame.

Generally, I size the footing to provide a FOS against overturning and sliding > 1.5.  Once I know the general geometry I then check the footing bearing pressures against the allowable bearing pressure in the soils report.  This requires me to calculate e (which is based off the service loads).

Once everything is acceptable I then need to size the footing for strength.  In order to be in compliance with the ACI I need to get my moments in to an "LRFD" format.  This is where I get a little confused.  Am I supposed to recalculate an eu base on the ultimate load combinations.  Or can I calculate the required forces (moments and shears) based off the service load combinations and then factor the loads using a "Psuedo" load factor?

I have run into instances where during the initial design the footing will work (e < L/2) but when I use the factored loads the footing no longer works (eu > L/2).

Sorry if this is a simple question but I just can't find an example of a footing with large eccentricities.
 

RE: Footings with large eccentricities.

This has been discussed before.  I was of the opinion that for the concrete design you need to use the concrete load factors.  Most others felt comfortable using a pseudo load factor on the service bearing pressures.

RE: Footings with large eccentricities.

I agree with StructuralEIT.  And yes, I have encountered the same thing--a footing which works under service loads but not under ultimate loads.

DaveAtkins

RE: Footings with large eccentricities.

How can a footing work under service loads but not under ultimate loads?   

The proper way to perform the calculation is to use service loads to determine soil pressure, shear resistance of soil and resistance to overturning, applying whatever safety factor you wish.

Strength calculations of concrete and reinforcement should be based on factored loads in accordance with the code.   

BA

RE: Footings with large eccentricities.

BA-

This happens if you have a high WL moment.  The WL moment gets factored @ 1.6 and the DL axial load gets factored @ 0.9. There are other scenarios, but this is the most common that I've encountered.  The load factors skew the location of the resultant (compared to the service loads).

RE: Footings with large eccentricities.

This happens a lot to me.  If you are designing foundations under service load with e very close to L/2 there is a good chance that it will be "unstable" (e>L/2) when you factor the loads for strength design.  Like was mentioned above, it is usually the DL/WL cases that this happens to.

I guess the options are 1) increase footer so it isn't an issue, 2) reduce LF on overturning load, or 3) draw shear and bending diagrams based on service loads and apply some LF to that for strength design.

RE: Footings with large eccentricities.

What I typically do when this becomes an issue is start taking advantage of the soil overburden for additional axial load.  That is typically not done for sizing the footing because the geotech typically gives "net" allowables, but you can benefit from the use of it when factoring loads and skewing your resultant location.

RE: Footings with large eccentricities.

BA-
Here is a possible scenario.  Say you have a 4x4 ftg with service loads of Pd=83.33k (including ftg self-weight), and Mw=95k-ft.  The service combination (0.6DL+1.0WL) will come up with e=1.9' (95k-ft/50k), and the footing will be stable - not by a lot, but stable nonetheless.  When you use the concrete combinations (0.9DL + 1.6WL), you get e=2.03', which is outside the footprint of the footing and is, therefore, not stable.

RE: Footings with large eccentricities.

SEIT,

Okay, I see what you mean.  And I would agree with your earlier comment that it is legitimate to consider earth load as part of the dead load.  

But if a high water table is present, I think you would have to deduct buoyancy forces from dead load or, in other words, consider the submerged weight of the footing and soil.

The discrepancy appears to be a result of a roundoff error in a particular code and does not occur in all codes.  If, for example the factor for concrete combinations was taken as (0.9DL + 1.5WL) instead of (0.9DL + 1.6WL), the two methods would agree.  Alternatively, if the factor for service load was taken as (0.6DL + 1.0666WL) instead of (0.6DL + 1.0WL), the two methods would agree.

BA

RE: Footings with large eccentricities.

2
don't use factored loads for foundation design.   

RE: Footings with large eccentricities.

Why not?

BA

RE: Footings with large eccentricities.

archeng-
How do you justify NOT using LRFD combinations for concrete?

RE: Footings with large eccentricities.

Perhaps I misunderstood the questions asked, but it appears to me that the question is regarding the pressure resultant location within the "kern".  The concrete footing is designed using strength design (USD, not LRFD), but the soils portion is not.  When you start sizing the footing width, length and checking soil pressures, use unfactored loads.  After you size the footing for unfactored loads,  use factored loads for moment and shear to determine reinforcing and footing thickness for the width and length calculated using allowable loads.  At least that's how I was taught to design footings.  If I misunderstood the question, my apologies.

RE: Footings with large eccentricities.

archeng59,

I agree with your approach.  But sometimes the resultant location is outside the "kern."  When this occurs, the footing may work under service loads, but when using factored loads, the resultant location may be completely off the footing.  And so the footing would need to be larger for the factored load case.

DaveAtkins

RE: Footings with large eccentricities.

I check the bearing pressure, overturning and sliding using asd loads and a safety factor of 1.5 as applicable.

Then I check the concrete and rebar for factored loads, conservatively this is 1.6 times the allowable bearing pressure actions.

The additional factor is for the concrete design and not for the soil, typical allowable bearing pressures have a factor of safety of 2, or even more if settlement is an issue.

RE: Footings with large eccentricities.

There will always be confusion when engineering checks for service and ultimate limit state needs to be performed. Soil-structure interaction has always been best engineered with an allowable stress approach since there are many uncertainties with the material (the soil) to begin with.

I am having the same problem with highway bridge design at the moment, where you need to consider lane factors, dynamic factors, ultimate limit state factors and service limit state factors which can become all so confusing when knowing combination applies with what and designing for actions on your structure which will never co-exist.

RE: Footings with large eccentricities.

Rechecking (or checking) the soil bearing pressure using factored loads will result in a conservative footing size.  If the pressure resultant is within the kern, or even slightly outside the kern in some cases, when checking the soil pressures using service loads, the footing will be ok.  There is no need to recheck with factored loads.  The allowable soil pressures are not factored values, so why check the resultant location for factored loads?  Not a comparison of apples-to-apples.  In almost every case, you will have to upsize the footing.  IMO, that's never bad, but it is unnecessary.

RE: Footings with large eccentricities.

I disagree with both csd72 and archeng59.

The bearing pressure is checked using service loads.

The concrete design should be done using factored loads, which is not the same as multiplying the bearing pressure (calculated using service loads) by 1.6.  This is because 0.6D + W is not proportional to 0.9D + 1.6W.

DaveAtkins

RE: Footings with large eccentricities.

What part of what I stated do you disagree with?

RE: Footings with large eccentricities.

I think there is a basic miscommunication happening.  No one is saying that you should check soil bearing pressures using factored loads.  The fact remains, however, that in order to do the footing design you need to determine what the soil bearing pressures are using factored loads.  You don't need to compare that value to anything, but an issue does arise if the resultant falls outside of the footprint of the footing.  I don't believe anyone is advocating using factored loads to CHECK soil bearing pressures, but you do need to use factored loads to GET soil bearing pressures to do the footing rebar design and shear checks.

RE: Footings with large eccentricities.

(OP)
The question was asked in reference to a footing that I am designing that supports a 4 story concentrically braced frame with a low amount of dead load to counteract the overturning forces generated by wind (currently, seismic overturning forces are less than wind).

Under some load combinations e=13' (this eccentricity includes the effects of the soil and footing weight).  Under service load combinations, the footing design is acceptable with regards to stability and allowable bearing pressure.  However, the eccentricity of the load is outside of the kern distance (outside the middle 1/3 of the footing).  

When the strength design load combinations are applied (to size the footing in accordance with the ACI) the eccentricity of the load falls off the edge of the footing (eu>L/2).... Making it impossible to size the footing because I end up with negative bearing pressures (which are impossible).

I was told by an older engineer to use generate the moment diagrams based off the allowable bearing pressure and then apply a "pseudo" load factor of 1.6 to size the footing in accordance with ACI.  He justified his answer by saying the code doesn't make sense in this instance.  How can a footing work for service load combinations and not strength design combinations?

My text book seem to only cover ideal cases where this never happens.  However, the general outline of the analysis method above is covered (geometry based off serviceability combinations... strength based off strength equations).

  I was just wondering what other people do when they encounter problems like this?  

I guess you just end up making the footing bigger (although it is pretty big right now).
 

RE: Footings with large eccentricities.

SteelPE,

As I understand it, common engineering practice is to size the footing geometry (i.e., footprint) based on service loads with the addition of the 1.5 additional factor of safety as you have stated.  Allowable soil bearing pressures are typically already factored by 2.0 so the additional factor of 1.5 is reducing the allowable to 0.33 of the ultimate (i.e., 1/2.0/1.5 = 0.33)

I was once told by a former SOM engineer that the design factor for foundations is almost always 1.55 (your guy said 1.6).  The method you stated of factoring the service moments is very reasonable and is easily done by prorating the service loads e.g., DL=50psf, LL=100psf use a factor of 100/150x1.7 + 50/150x1.4 = 1.6

So if you are using 1.6 as a "psuedofactor" then based on ASD you are using a reduction of 0.85/1.6 = 0.53(Ultimate) or a factor of safety = 1.88 and the soil you are using 0.33(Qult) or factor of safety of 3.0.  Clearly the soil design is much more conservative than the concrete design already.

To me LRFD is the same thing as ASD only in reverse, for example in steel design ASD says use 0.66Fy, but, LRFD says Pu < 0.85 Pn, if LL=100psf, DL=50psf, TL=150psf DL=0.33TL and LL=0.67TL therefore the "psuedofactor" = 0.33x1.2+0.67x1.6 = 1.47 this is equal to using (0.85/1.47)Fy = 0.58Fy.  So to me LRFD is just a way of using a variable factor of safety based on some statistical methods (i.e., it is understood that DL is known to a very high level of certainty hence the lower Load Factor than LL)

 

RE: Footings with large eccentricities.

OK--

I will admit that simply bumping up the bearing pressure due to service loads to create a factor of safety when designing the concrete should be OK.

But it does not meet Code--that is my point.  You are not checkingt the concrete for the factored load combination.  You are checking the concrete for the service load combination multiplied by a factor.

DaveAtkins

RE: Footings with large eccentricities.

This is neat.

Philosophically, a structure ought to be sound
(strength/stability) under the application of
factored loads.  By this standard, our friend's
footing is unsafe as it results in a statically inadmissabe
state of stress for the soil.

I think that the LRFD load cases should
replace the 1.5 OT / 2.0 slide fpactors altogether.
Satisfying 0.9D + 1.6W while
remaining stable should suffice.  This seems
more rational to me.  

RE: Footings with large eccentricities.

Does anyone even know where it says that you need a F.S. of 1.5 for footings?  I know where it says it for retaining walls, but I've never seen it for footings.

RE: Footings with large eccentricities.

I think this should resolve the issue,

Section 15.2.2 of ACI 318-02 states:

"Base area of footing or number of and arrangement of piles shall be determined from UNFACTORED forces and moments transmitted by footing to soil or piles and permissible soil pressure or permissible pile capacity determined through principles of soil mechanics."

SEIT,

I believe the 1.5 factor for sliding and overturning appears in NAVFAC DM-02.  It is understood that this factor is applied to Qallow.  And Qallow=Qult/2.0 typically.

Remember we are designing for two different materials, the soil and the concrete.  You can typically design a steel structure using ASD then use LRFD for the foundation the same holds true for the soil.  You should actually be able to design the concrete based on ASD if you are a die hard, it is still a rational engineering method and will probably give very conservative designs.

I think the problem is arising in application of the load factors if you apply them to the forces acting on the footing it will change you eu.  But if you apply them to the soil pressure diagrams (break out each diagram based on DL, LL, W, E, etc.) you should not have any issues.  Someone (that same SOM engineer) once told me just turn the footing upside down and you have a beam now its easy to visualize.

RE: Footings with large eccentricities.

(OP)
StructuralEIT,

I believe that was discussed a long time ago in another forum.  

http://www.eng-tips.com/viewthread.cfm?qid=183966&amp;page=1

To summarize, the FOS is built into the .6D +1.0W load combination.  If you use .6 x (dead load resisting moments) then you only nee to provide Mr/Mo > 1.0
 

RE: Footings with large eccentricities.

DaveAtkins,
 
where does the code say otherwise? If the code specifically addressed this issue then we wouldnt be having this discussion.

Anyway, I cannot see how it makes any difference to the safety of the structure as the soil usually has an ultimate bearing capacity of around twice the safe bearing capacity. This means that at ultimate loading the reaction can be further away from the centre of the footing to resist overturning.

This would seem to create a greater moment, but this moment will not be greater than that applied which is conservatively taken as 1.6 times the service load.

I must note that this method is conservative for bearing pressure but not for uplift, but uplift is rarely critical for design of concrete footings under overturning.  


 

RE: Footings with large eccentricities.

csd-

I think the point Dave is getting at is that you have to use the LRFD combinations to get the factored moments and shears in the footing to do the rebar design/shear checks.
As far as teh 1.6 factor on service bearing pressures - I haven't run numbers on actual examples, but I'm not completely convinced that 1.6*service pressure footing moment (the actual moment that the rebar is designed for) is always equal to (or greater than) the moment you design for when you factor the column loads and determine the bearing pressures using those factored loads.  The actual resultant force (shear) may be higher, but the fact that it's location is closer to the centroid of the footing leads me down the path that it's not always conservative.  
Just to take a very basic example.  A 1.6K soil resultant located 1' away from the critical section gives a Mu=1.6K-ft, but a 1.5K soil resultant located 1.15' from the critical section gives a Mu=1.73K-ft.  Granted, this is only 8% difference, but the idea that it's not using the correct load combinations (and that it's not conservative) is what Dave is driving at.

RE: Footings with large eccentricities.

SteelPE-

I followed along with that thread (and even participated to a small degree).  I don't disagree that the 0.6D is the safety factor, but there is an explicit safety factor (of 1.5) written into the retaining wall portion of IBC.  I've never seen anything similar for spread footings.

RE: Footings with large eccentricities.

I agree that the situation is unclear when it comes to overturning and bearing pressure but fortunately this only needs to be checked once.

But I would be interested to see where the resultant of a load combination 1.6A + 1.2B is greater than 1.6(A+B).  

RE: Footings with large eccentricities.

If A is moment only and B is axial load only, it's certainly possible.  If you change that to 1.6A +0.9B and A is again moment only and B is again axial load only, it becomes even more possible.

RE: Footings with large eccentricities.

0.9B only applies for uplift which, as I said above, is generally not critical for the concrete design.

Thanks for the constructive criticism, I appreciate the debate and would be more than happy to be proved wrong. Learning is a lifelong thing after all.

RE: Footings with large eccentricities.

I appreciate learning as well.  Does it say anywhere that the 0.9 factor is only for uplift?  Why would it not apply to an overturning situation where there is a high wind moment and little axial load?

RE: Footings with large eccentricities.

Yes it applies to overturning as well.

I cannot see this being critical in normal footings for both wind and live loadings as the column will generally be central and the P/A + M/Z will be greatest in compression when both P and M are greatest.

These loads are also generally calculated elastically but a plastic soil pressure distribution is just as valid at ultimate loads and less conservative.

The rest is just playing with numbers and really does not make any difference to overall safety.

RE: Footings with large eccentricities.

In my opinion, the 1.5 safety factor is applicable only for calculations related to overturning and sliding.  Bowles' Foundation Analysis and Design text has a chapter (chapter 8 in the 4th edition) on spread footing design that is decent.  Wang Salmon's Reinforced Concrete Design text has a chapter on footing design (chapter 20 in the fifth edition) that is decent.  Probably other texts exist that are as good or better.

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