Material FOS vs Factored Loads

[KlunkerSolar]

So, this has probably been talked to death over the years but I can't find a thread that discusses this question fully. Should an engineer combine material factor of safety's (Ω in AISI, AISC, etc) with Building Code environmental load factors (ASCE 7-16, Section 2.4 ASD)?

Say I'm designing a steel column using ASD. AISC says my compression capacity is Pn/Ω (generally). I now go to my handy ASCE 7-16 load combinations to determine the ASD loads on the column.
Say I'm using the following load combination;

4DL + SL)
70.6DL + 0.6WL)

Now I'll set the equations;

EQ1)Pn/1.67 ≥ DL + SL

EQ2)Pn/1.67 ≥ 0.6DL + 0.6WL

In EQ1 it seems like we only applying a FOS to the left side of the equation. I'm dividing the Nominal Strength of the steel by 1.67 for a reduced capacity, but I'm not modifying the design loads in any. I've heard that the factor of safety on the right side is "the unlikely chance that both the full DL and SL will occur at the same time" but that isn't quantified in anyway or noted in the Code anyplace that I can find. Is that correct?

In EQ2 I'm still using a FOS of 1.67 for the material but I'm now also reducing the amount of DL resisting the WL by 40% (ignoring the 0.6 on the WL as the reduction from strength design to asd). This seems like a double-dip for the factor of safety although I can see the reasoning to apply a FOS to both. It leads to the question of "what is the total factor of safety I'm using here" and "is it higher than the FOS in EQ1"? Does it make sense to just use unfactored loads and rely on the material factor of safety (Ω) as adequate?

This made a lot of sense to me in my previous life designing building structures. I now live in the solar world where everything is designed to 99% stress levels and factor of safety for loads and materials are hot topics for debate. I keep getting questions around...."I know the weight (DL) of my structure very precisely so why can't I use 1.0DL in load combo 7." or "This is a low risk site (structure unoccupied, set low to the ground and fenced in) so I want to use an Ω = 1.5 for my material design".

Am I correct in my opinion that the left side and right side of EQ's 1 and 2 are independent of each other? In other words, the left side of the equation is based on the likelihood that the material properties are accurate, and the right side is based on the likelihood that the loads are accurate? I believe this is how LRFD is viewed, is it the same for ASD?

I appreciate any clarity I can get on the above. If possible, let's not get into a debate between LRFD and ASD and why one is better than the other, or some mathematical derivation on how they similar. Thanks in advance for any help!

 

[phamENG]

What you're showing is exactly how it's meant to be done. Since you bring up steel and AISC, take a look at Chapter B, Design Requirements.

Ra<=Rn/Omega

where
Ra= required strength using ASD load combinations
Rn= nominal strength
Omega = Safety factor.

You don't get to pick which side of the equation you want to satisfy - the whole thing works together.

The 0.6DL is a Factor of Safety, but not for the material. It's for global stability. Once upon a time, structures were designed to have a global factor of safety (independent of material strength) to resist uplift and overturning of 1.5. The need for that hasn't gone away, so it's been baked into the load combinations. You can use a global stability factor of safety for uplift and overturning of 1.0 so long as you use 0.6D.

ASD assumes a relatively predictable design load level but lower confidence in the material strengths. LRFD attempts to more accurately define the level of confidence for each type of load and for each material strength. So no, not really the same approach (even though AISC has done their best to draw ASD and LRFD in the Steel Manual as close together as they can).

 

[chris3eb]

The 0.6D (or 0.9D in LRFD) load combos also bother me. In my mind, there are two types of dead loads: estimated dead loads (e.g. adding 5 psf for MEP/misc) and known dead loads (e.g. concrete weight or manufactured items). I think these combos make sense for the estimated dead loads, but they really don't make sense for the known dead loads. I wish the code or commentary included a statement similar to below (made up by me) which I believe is the intent:

"Load combinations 7 and 10 may control when the effects of gravity help to counteract the effects of wind or seismic. These load combinations should be considered when dead loads have been conservatively estimated. In the case of very well-defined dead loading, such as when dead loads are primarily due to manufactured items, the dead load factor may be taken as 1.0"

 

[phamENG]

chris3eb - I disagree, unless you choose to apply an additional stability FoS of 1.5 to your structure which is no longer common. It's something of a step back in terms of code development.

 

[chris3eb]

The idea of a stability factor makes sense for something where gravity is your only resistance to overturning. For a piece of equipment anchored to a structure, it seems strange that you would have an extra 1.5 factor on the anchor's uplift due to overturning, but not on the shear on the anchors. Or similarly, is overturning of a piece of equipment so critical that it needs an extra 1.5 factor when a giant beam doesn't have any extra safety factor (other than on the material side)?

 

[chris3eb]

The commentary does talk about the 0.6 coming from stability concerns, so I suppose that's what they are going for - thanks for pointing that out, Pham. It does still feel weird to be talking about stability when things are positively attached though...

 

[phamENG]

No problem. But to your point - if that positive attachment is a/the source of stability from overturning, doesn't that attachment need to designed for that 1.5 FoS? Purely lateral would translate to a sliding FoS. While often at least 1.5 for retaining walls, it's common to use 1.0 for building foundations.

 

[chris3eb]

Well one big difference is that if you are entirely relying on a resisting moment due to gravity, your only factor of safety comes from the reduction in your gravity loads. If you are relying on a steel anchor, then you would have a 1.5 FOS from reducing your gravity loads plus an additional 1.67 FOS on the strength of the material itself. If you didn't reduce your gravity loads, you would still have the 1.67 FOS on the material which is greater than the 1.5 overturning factor. Of course these two safety factors can't quite be compared 1 to 1 because the overturning factor can take your anchor from compression to tension while the material factor can't do that

 

[phamENG]

In essentially every structure with shallow foundations, you're relying on both.

The ASD factor of safety is intended to limit the amount of expected capacity to a certain percentage at expected service load levels. This provides a margin for both material/workmanship defects and overload scenarios. This is important for the steel anchor as it's subject to both.

The stability factor of safety (1.5) for overturning or uplift is really about a margin against overload conditions. After all, when designing with ASD we effectively reduce the wind speed we're designing for by about 22.5%. But that doesn't mean we want a building designed using LRFD to survive a storm that causes a building designed at the same time to ASD to fail. The shallow concrete footing or slab into which your anchor is set is relying on this. The steel anchor itself is, too - or more accurately the global load path in which that anchor plays its part is relying on this.

So while both do account for overload conditions, it's not really possible to separate them from each other since the ASD FoS is doing double duty.

For comparison, look at LRFD. 0.9D+W rather than 0.6D+0.6W. Where ASD reduced the dead load from 1.0 to 0.6 (1.6667, 1.5 if you assume it was 0.9 to 0.6 which is likely as some reduction in dead load is generally a good idea), the LRFD load combination really doesn't reduce it. But it does increase the wind load. That's because LRFD breaks out the two parts of the ASD factor of safety into the load factor and resistance factor. You end up with a comparable global factor of safety for stability, but your material strength factor of safety becomes much more consistent. Not saying one is "better" than the other, but understanding both can help with perspective.

Hope that made sense...

 

[chris3eb]

Pham - after looking further into it, I'm definitely on board with not changing the 0.6D. Here's a few other things that struck me:

Looking at the LRFD combos I think helps to explain my original thought a little better. The load factors were developed with the idea of consistent reliabilities in mind. You need to use 1.2D because of uncertainties in calculating the true dead load - not just at the time of construction put potentially accounting for the marble floor and other things that may be added in the future. Likewise, you need to use 0.9D because your D may be a little overestimated. If your loads were very tightly controlled, I don't think there would be any reason to not use 1.0D everywhere. This may sound strange because then LRFD would give you such better answers than ASD, but that's exactly the point. ASD has one safety factor that accounts for uncertainty in both demand and capacity, while LRFD separates the safety factors. So if have a case with less uncertainty, you could reduce the safety factor. For buildings, I wouldn't ever see this coming up because you can't control what happens in that building, so there is always that uncertainty. But for some smaller equipment where you really do know the weight, I think you can use engineering judgement to tweak the safety factors when there isn't that kind of uncertainty.

For ASD combos 7 or 10, I wouldn't change the 0.6D to 1.0D. The main reason I wouldn't change it is because wind and seismic forces were developed with LRFD in mind and simply applied to the ASD load combos in a way that would produce similar results between LRFD and ASD. Changing the 0.6D to 1.0D would make ASD give much "better" results than the 0.9D + 1.0E/W LRFD cases.

But there is an interesting thing that this brings up - I think that rather than applying a 0.6 factor to D, they should have applied a larger factor to W and E in the ASD cases. The reason for this is that the ASD cases are supposed to use the "real" loads. Commentary section C2.4.1 says, "No safety factors have been applied to these loads because such safety factors depend on the design philosophy adopted by the particular material specification." Well what is the 0.6 factor on D if not a safety factor in this situation? Rather, they could have upped the wind and seismic to something like 0.8W and 0.85E to achieve the same effect. This would actually be consistent with their stated philosophy about not having safety factors on the ASD loads. You may thinking that increasing wind from 0.6W to 0.8W is also a safety factor, but I would disagree. The factors on wind and seismic are more like "conversion factors" because there is no "real" wind or seismic load you can point to - those loads are statistical derivations. That would stop an overeager engineer such as myself from saying that I'm not going to use 0.6D because I know the dead load exactly. I wouldn't have the hubris to decide that for my situation I can use 0.6W rather than 0.8W.

Lastly, regarding the "overturning" safety factor of 1.5, I don't believe that has anything to do with it. The most obvious reason for this is that 0.6D only applies to load combos with wind and seismic. The overturning effect can easily be cause from soil or fluid loads, but those aren't specified anywhere - in fact ASCE 7-16 says "where fluid loads F are present, they shall be included in combinations 1 through 6 with the same factor as that used for dead load D". Another reason is that the commentary section I quoted above says that the ASD load combos don't include any safety factors. I know that people like to point to the old ASD load combo with 0.9D and say 0.9D/0.6D = 1.5 and that's the safety factor. But they didn't change the 0.9D ASD load combo because they decided to overtly add the safety factor, they changed it because they realized that the old ASD equation severely underestimated overturning. From the commentary:

They are saying they added the 0.6 factor to the ASD combo to align its reliability with the LRFD one. You would be hard-pressed to point out where an extra 1.5 safety factor is baked into the LRFD one. A normal LRFD dead load has a "safety factor" of 20% and a destabilizing LRFD dead load only has a safety factor of 10% (ie 1-0.9). So I think the takeaway is that if you have something that needs an extra overturning safety factor because it has no positive connection, you need to add it in yourself. This concept isn't really too dissimilar to when happens the rest of the time in ASD - there is generally a baked in material safety factor of 1.5-2. In the case of something overturning with only gravity resisting, there is no material strength to apply a safety factor to, so it has to be applied to a load.

 

[Guest090822]

KlunkerSolar: You may want to do a bit of research on the philosophical differences between ASD and LRFD. I can offer a brief summary. For ASD, the factor of safety is on the capacity side of the equation and it's a blanket "global" factor of safety. It's nice because you know exactly what factor of safety you are dealing with. In LRFD the factor of safety is on the load side of the equation. The higher the certainty or accuracy of the load, the lower the load factor; the code was developed based on statistics. In fact, when doing your research if you don't see intersecting bell curves you are in the wrong place ! You can determine your overall factor of safety at the end by simply going back and checking your unfactored loads against your capacity you determined using the load factors. The overall "global" factor of safety basically varies in LRFD.

 

[phamENG]

On a positive note, we agree on what to do in practice. 0.6D is inviolable.

Though I don't think we agree on how we get there. You're thoughts on keeping 1.0D and modifying the wind to achieve a FoS for stability is interesting. I'll have to think on it a bit. I disagree on your assertion that the combination doesn't include an overturning FoS. The sentence before your highlight specifically says that it "eliminates inconsistency in the treatment of counteracting loads in allowable stress design and strength design and emphasizes the importance of checking stability." (Emphasis mine.)

As for it missing in LRFD, I disagree. Don't look at it as the ratio of expected dead load to the strength design level wind load - look at the relative increase. If we assume that there is a 1.5 FoS for stability (coming from the change from 0.9D+ASD Wind Load to 0.6D+ASD Wind Load, 0.9/0.6=1.5), then we should be looking at the increase in load from that level. Dead load goes up 0.9/0.6=1.5 and wind goes up 1.0/0.6=1.6667. They both go up by about 1.5, so the factor of safety for stability is roughly maintained, and you get consistent reliability for two structures each designed by a different method but subjected to the same wind event. So if anything, the LRFD load combination was written to include this FoS, and the ASD load combination was updated to include it, too.

Regarding the fluid and soil loads, you're right about soil loads but (in the general case) not fluid loads. ASCE 7 and the IBC look at fluid loads in terms of storing fluids like a tank. So if you have a tank overhanging the side of the building, yes - it's going to be a unique situation where your fluid causes overturning. But, generally, it isn't going to cause overturning of a 'normal' structure. If you have a unique case, it's your responsibility to apply unique design considerations. Soil loads are applied differently, and have load factors from 0.6 to 1.0 for ASD and 0.9 to 1.6 for LRFD, thus providing the requisite factor of safety against overturning. Flood loads are handled differently from standard fluids, and can have destabilizing effects. Link

For one last thing - take a look at 1605.1.1 Stability in the 2018 IBC. It says that "where overall structure stability (such as stability against overturning, sliding, or buoyancy) is being verified, use of load combinations specified in Section 1605.2 or 1605.3 shall be permitted." So if we agree that 1.5 remains an important factor of safety to maintain for global stability (formally codified in the old UBCs, currently codified for retaining walls, and generally considered sound practice), it implies that it is 'baked in' to the load combinations.

 

[KlunkerSolar]

@chris3eb @TheRick109 @PhamENG

Thanks for the feedback.

@Chris3eb - I had never read or heard what you highlighted regarding the 0.6D being similar to 0.6W in that the 0.6 was used to bring it in line with strength design. I'm not sure that it changes the argument for the increase to 0.6 if you know the weight precisely. Couldn't I argue that if I'm using LRFD where the combo is 0.9D and, saying I know the weight precisely, I'm going to decrease this to 1.0 is the same, in concept, as increasing 0.6D to 1.0D for ASD?

@therick - I see the capacity side factor of safety using the Ω, but isn't there some factor of safety on the loads when you reduce load combinations like; D+0.75L+0.75(0.6)W? Aren't you introducing a safety factor by saying it's a low probability that the max L and W occur at the same time?

 

[dauwerda]

chris3eb, there are a few past threads on this topic as well, nutte gives a nice summary of the history in this one (excerpt below)
thread507-352021

Some history on the topic:

ASCE 7-95 does not have the 0.6D+W (or 0.6D+0.7E) load combination. For the traditional 1.5 factor of safety against overturning and sliding, they say a couple paragraphs after the load combinations that the overturning moment or sliding force must not be more than two thirds of the stabilizing effects form the dead load. 1/1.5 = 2/3, so this is the traditional way of doing things we’re all familiar with.

ASCE 7-98 does have the 0.6D+W (and 0.6D+0.7E) load combination. Also, the paragraph about overturning and sliding was removed. The Commentary states that these two load combinations were added to remove the inconsistency between ASD and LRFD, and to increase the emphasis on stability checks.

And, here are a few more shorter ones where this is discussed:
thread507-374976
thread507-471243
thread507-450974

 

[KlunkerSolar]

Interestingly I see this note in the link that PhamEng just posted.

If we are limiting something to 2/3 it's actual value then, I would argue, this is a FOS.

 

[phamENG]

KlunkerSolar - you might be able to justify it...as long as you go back and add the old 1.5 FoS for overturning at the end. I think you'll find that it's an extra step that provides no added benefit.

 

[phamENG]

Yep. It is. That's precisely what I've been saying. BUT...it's important to not conflate it with material factors of safety. Two different things.

 

[Guest090822]

KlunkerSolar - you are confusing the "material" factors of safety with the percentage of the loading used for each group. For ASD you generally have no more than 75% of any transient load acting simultaneously since the probably of occurrence is low. There is a difference between the factor of safety relating to the member design versus the loading applied.

 

[KlunkerSolar]

So now I have two ways to look at the right side of the equation from my first post;

EQ2) Pn/1.67 ≥ 0.6DL + 0.6WL

1) ASCE 7 Commentary - No factor of safety added. 0.6 added to bring ASD in line with LRFD.
2) IBC - 0.6 factor added to ensure a only 2/3 DL used to resist overturning (they call it a "factor" but not a "factor of safety"...not sure I see the difference here.

Which explanation is correct? I'm leaning toward the ASCE explanation since that would also address why there are no load increases to DL or SL in EQ1 below.

EQ1)Pn/1.67 ≥ DL + SL

Anyway, I think I have the answer to my overall question. Material FOS have nothing to do with load FOS (if they are used in some way) and must be treated separately.

thanks all

 

[phamENG]

KlunkerSolar - where you do you see it stated in the ASCE 7 commentary that there's no factor of safety? I don't see it at all, and I think trying to read that between the lines is not appropriate, especially when doing so creates an otherwise non-existent conflict between ASCE 7 and the IBC.