Overturning checks, buoyant force load factors 1

[quasiblu]

Dear All,
using American standards here. For overturning checks, one gets quite different results if he does 1) or 2):

1) Dead*lever / (Moment,wind + Buoy*lever) > SF,min
2) (Dead - Buoy)*lever / Moment,wind > SF,min
In my opinion, 1) is the formally correct approach (note that it brings to bigger foundations).

The difference are bigger when FS,min is > 1.0

Then the possible different results are even more, depending on the load factors applied (0 or 0.6 or 1.0 or 1.6 to buoyant force).
ASCE 7 has this load H in Section 3, but reading the commentary I see H factors are set after horizontal pressures of bulk material dynamic effects when loading/unloading is made. Water table is a whole different phenomenon, and one should consider a variation of the water table elevation, not in general factors to the pressure given in the geo report as unique number, sometimes after a probe made just once on site.
Also, buoyant force normally cannot grow any bigger than the characteristic value it would bring when geo dictate it is at finished grade level, which is common in the projects we deal with.

So, does anybody know of authoritative literature giving specific instructions?
To go for either 1) or 2)?
Or giving more specific guidance for the load factors for buoyant force?

In some standards from other countries they would generically write that the load factors can be adjusted (reduced) when the engineer can prove there is no possibility for the loads to go beyond a certain value. This also might be a nice thing to find in American standards as well.

I thank you.

 

[la belle vie]

Why not do the calculations with unfactored loads and determine a single factor of safety. That’s how we do it in the dam world with requirements for safety factors based on the extremeness of the loading. Also, for example, Con-Edison specifies a single 1.2 safety factor for their manholes for buoyancy case.

 

[phamENG]

The correct approach is the one that satisfies statics. If your moment arm is the same, both equations will give you the same answer. Two is just a transformed version of 1 that is only valid if there is only one lever variable.

If lever = x:

Dx = M.w + Bx (Equation 1)
Dx - Bx = M.w
(D-B)x = M.w (Equation 2)

If they have different moment arms, then obviously you have to manipulate the equations differently. But it's simple algebra.

As for factors and combinations - the safety factors are built in. You don't do the load factors and combinations and then compare it to a different safety factor. In your case where the buoyant force is destabilizing (contributing to the primary variable load effect), you would use 0.6D+0.6W+1.0H for load combination 7 of the ASD load combinations in ASCE 7. You would compare it to a factor of safety equal to 1.

(This assumes we're talking about a building's footing.)

 

[quasiblu]

Agree, it would be acceptable for me whichever methods between FS,min=1 with factored loads, or FS,min>1 with unfactored loads, but sometimes project specs asks for a mix of them.
My fav is FS,min=1 with factored loads, which allows to address uncertainties where they are and how it is needed by using the load factors.
For numerical differences between eq 1) and 2) I will follow up with examples as soon as I can.

 

[cvg]

agree with la belle vie. USACE has a good guideline on the FS based on normal vs unusual vs extreme loadings.

EM 1110-2-2100 Stability Analysis of Concrete Structures

https://www.publications.usace.army..._1110-2-2100.pdf?ver=3faDbW17ExfkdYjikk7LKw==

 

[quasiblu]

An example of numerical difference between 1) and 2), considering unfactored loads and FS,min = 1.5

Foundation 3x3 m, thk 2 m.
Water table at top of foundation.
Lever for bouy and SW = 3/2 = 1.5 m
Moment from SW = 675 kNm
Moment from Buoy = 270 kNm
External moment from wind assumed as 255 kNm.

Overturning safety factor as Stabilizing/overturning ratio:
1) 675 / (270+255) = 1.29 < 1.50
2) (675-270) / 255 = 1.59 > 1.50

Thanks for the references, I will have a look.
EM 1110-2-2100 for factor of safety for flotation uses uplift force in the denominator, together with destabilizing effects, so in a fashion similar to equation 1).

 

[quasiblu]

Replying to phamENG:
with unfactored loads, eq. 1) and 2) would bring to same results only when FS ~ 1, and this is what you show transforming 1) into 2), i.e. assuming they are not inequalities.
But they bring different results-design when FS <> 1.

 

[phamENG]

Right, but you said you're using American codes. In American codes for building design, you don't use an additional factor of safety. The factor of safety is already in the load combinations.

But since equation 2 is simply an algebraic transformation of equation 1, it doesn't matter. Just use equation 1 all the time so whatever method you're using it works out.

 

[quasiblu]

Thanks phamENG, I agree.
Unfortunately we are to use standards + client specs + our specs, and FS,min > 1 has remained very popular in specs.
In my opinion it is the set of ASD combs that include 0.6*Dead that has spread confusion. One sees "ASD", thinks he's unfactored, and wants to use FS,min > 1, but that's a mistake with big impact.

 

[phamENG]

It is. Though unless the spec clearly states to use ASCE 7-16 ASD Load Combinations and apply an additional factor of safety of 1.5, you should be okay. You can demonstrate quite easily that 0.6D+0.6W has a factor of safety of 1.5 already built in.

0.6W gets you down to roughly the ASD wind load from ultimate load calculations, so (0.6W)/0.6D=(0.6W)/D*1.66667, where 1.66667 is your factor of safety.

 

[rb1957]

you guys are talking about things I barely understand, but why would the deadweight moment arm be the same as the buoyancy moment arm ? They sound like different things.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[phamENG]

rb - if you have a square footing below the water table, you'll have a uniform buoyant force pushing up on it. So it can be simplified to a single point load in the center of the footing. If you also have a pier with all dead load coming down concentrically on the footing, the vectors will be coincident but with opposite signs. Taking the moments about any point (typically an edge when checking for over turning), the distance from the vector to that point will be the same for both.

In an non-concentric footing (footing that's 6ftx3ft with the pier and dead load located 1ft from the short edge), the moment arms would be different.

 

[rb1957]

ok, I thought height would have something to do with it ... that the buoyancy force depends on part of the total but dead weight reflects all of the total.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[ProgrammingPE]

Equation 2 is incorrect because it effectively reduces the buoyancy force, which should not be done since it is destabilizing.

Equation 1:
D / (W + H) > 1.67
D/1.67 > W + H
0.6D > W + H (OK)

Equation 2:
(D - H) / W > 1.67
D/1.67 - H/1.67 > W
0.6D > W + 0.6H (NOT OK)

D = Moment from Dead Load
W = Moment from ASD Wind Load (0.6*LRFD Wind Load)
H = Moment from Buoyancy Force
Safety Factor = 1.67

Structural Engineering Software:

http://www.structuralcentral.com

Structural Engineering Videos:

http://www.youtube.com/structuralcentral

 

[OK-2903]

I agree that the equation 1 is correct.
Nevertheless I disagree to use load factor 0.6 for dead load in one combination with buoyant force with load coefficient 1.0.
It leads to overdesigned footings if the UG water level is high (even if required overturning SF 1.0 only).
There is probably an unhandled exception for buoyant force with dead load factor 0.6 combination in ASCE 7-2022, cl.2.4.1.
I would very appreciate your opinions.

 

[quasiblu]

My opinion is that dead load factor 0.6 tries to embed 1.5 safety factor to a combination that has a dead load factor 0.9, using an approach that has generated confusion, e.g. it has been put in the ASD group instead of LRFD group, and most important thing, standards should calibrate factors to the variance of the load they are applied! If not so, unwanted consequences are triggered everywhere.

Furthermore, depending on the geometry and the range of possible elevation of water table, which should be given by geologists, the engineer would be able to identify a reasonable range of design values for ASD and for LRFD for the effect of water table, and the standard should allow for that -- but ASCE 7 does not.
In other words, it is the range of unfactored values of the effect of the water table that should be determined by geologists and engineers, and it is to those values that the standard's load factors should apply.

ASCE 7 may much underestimate buoyant force when water table is below foundations -- here the engineer can and must use greater forces than standard's.
But ASCE 7 can also much overestimate it when water table is by finished grade level, because ASCE says to use 0.6 load factor to dead load, by which it somehow wants to embeds 1.5 safety factor to a buoyant force that physically cannot grow so much -- and here the engineer will have a very difficult life if he tries to waive a standard requirement.

 

[human909]

My opinion is that dead load factor 0.6 tries to embed 1.5 safety factor to a combination that has a dead load factor 0.9, using an approach that has generated confusion, e.g. it has been put in the ASD group instead of LRFD group,

As somebody who works in a country that has pretty much fully adopted LRFR for structural design, I whole heartedly agree with this. Factoring down dead loads by 0.6 makes no sense whatsoever in the context of LRFD. Something is very wrong if your structure has 40% less deadload than calculated. 0.9 aligns with what other codes have chose as the suitable combination factor for dead loads. (Eg Eurocode, AS code.)

and most important thing, standards should calibrate factors to the variance of the load they are applied! If not so, unwanted consequences are triggered everywhere.

Exactly. If this isn't the case then then everything becomes even more opaque on what criteria one is designing to and what the likelihood of exceeding that criteria is.