Footings with large eccentricities. 2

[SteelPE]

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.

 

[SteelPE]

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).

 

[MaddEngineer]

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)

 

[DaveAtkins]

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

 

[KootK]

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.

 

[Lion06]

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.

 

[MaddEngineer]

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.

 

[SteelPE]

StructuralEIT,

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

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

 

[csd72]

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.

 

[Lion06]

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.

 

[Lion06]

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.

 

[csd72]

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).

 

[Lion06]

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.

 

[csd72]

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.

 

[Lion06]

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?

 

[csd72]

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.

 

[archeng59]

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.