Factor of Safety Questioned 11

[jheidt2543]

I found the following statement in one of the responses to a forum question. I would like to hear some opinions/discussion regarding FS relating to this following statement:

“I would calculate the bending moment based on the real load, not the safety factor. AISC has its own safety factor built in the allowable stresses. If you use a SF of 2 in your loads, and compound those SF built in AISC allowable, then you are over sizing the beam!”

For a steel beam, using A36 steel and the allowable stress in bending is 24 ksi (yes, depending on compact section provisions it could be 22 ksi), the reduction is (1-24/36) or 33%. I have always viewed this reduction as the result of some “uncertainty” in the average allowable stress of A36 steel, call it a factor of safety for material properties.

The IBC 2000 code requires that dead loads be increased by 40% and live loads by 70%, factors of safety due to the “uncertainty” of the loading conditions. Now if we combined these two (assuming for this example that DL=LL) then we have introduced a FS of 33% + [(40%+70%)/2] = 88%.

For the same beam in concrete, with a phi of .85, the material factor of safety would be 15% and the code required factored loads would still be 55% for a total of 70%. I would think that there is less variation in the material properties of steel than concrete, but this little analysis doesn’t show it.

Does this seem right??? Is the above thread response correct? It seems to me that the writer's comment leaves out the code required load factors. (Names and dates are left out to protect the innocent <g>)

 

[Qshake]

Why, I remember way back when...we had to hike uphill in 3' of snow (both ways too!) just to get to school in order to contemplate these sorts of things.

With allowable stress design or working stress design, it was the practice to use the service loads, unfactored, and determine a required shape based on the code allowable stress, 20 ksi for grade 36 ksi steel for example.

That, of course, has changed and with load factor and LRFD brings...well, load factors and resistance factors.

 

[CanyonRat]

>I found the following statement in one of the responses to >a forum question. I would like to hear some >opinions/discussion regarding FS relating to this following >statement:
>
>“I would calculate the bending moment based on the real >load, not the safety factor. AISC has its own safety factor >built in the allowable stresses. If you use a SF of 2 in >your loads, and compound those SF built in AISC allowable, >then you are over sizing the beam!”

This is true assuming you are designing by ASD (allowable stress design). The factor of safety (FS) is in the allowable stresses. Do not arbitrarily increase your loads unless you are unsure of the load itself. However, the loads are usually defined by the code so why increase?

>For a steel beam, using A36 steel and the allowable stress >in bending is 24 ksi (yes, depending on compact section >provisions it could be 22 ksi), the reduction is (1-24/36) >or 33%. I have always viewed this reduction as the result >of some “uncertainty” in the average allowable stress of >A36 steel, call it a factor of safety for material >properties.

The allowable stresses are usually a fraction of the yield point of the steel. ASD is based on &quot;elastic design&quot;. The &quot;uncertainties&quot; are based on several factors which are stated in just about every design text I've seen. ASD is based on service loads so you don't apply your own factors.

>The IBC 2000 code requires that dead loads be increased by >40% and live loads by 70%, factors of safety due to the >“uncertainty” of the loading conditions. Now if we >combined these two (assuming for this example that DL=LL) >then we have introduced a FS of 33% + [(40%+70%)/2] = 88%.
>
You are talking LRFD or LFD which is different than ASD. Load factors are applied to the loads but ultimate values with an appropriate resistance factor are used. As far as I know the IBC still allows ASD but I may be incorrect. I've got one around somewhere but I'm not going to look it up. Again, the differences between ASD, LFD, and LRFD can be found in your steel design text, or your concrete text, or your timbers text, or your masonry text.
>
>For the same beam in concrete, with a phi of .85, the >material factor of safety would be 15% and the code >required factored loads would still be 55% for a total of >70%. I would think that there is less variation in the >material properties of steel than concrete, but this little >analysis doesn’t show it.
>
>Does this seem right??? Is the above thread response >correct? It seems to me that the writer's comment leaves >out the code required load factors. (Names and dates are >left out to protect the innocent <g>)

You need to look up the differences between ASD, LFD, and LRFD. These are very very basic design principles and it sounds like you need to figure out the difference before you do any design. Bottom line... you cannot mix and match the different methods.

MikeD

 

[JAE]

jheidt2543,

You are mixing design methods as canyonrat stated. You basically have two methods to CHOOSE from - (yes - even in the IBC you can use either): ASD or LRFD

With ASD Steel, you have

Load Factors = 1.0 (or, in other words, no load factors)
Allowable stress reduction factor = 0.6 (yes it varies but let's use 0.6 for our conversation). This is applied to the yield stress - let's use 36 ksi as you used above.

This would mean that, under the actual loads (1.0 x load) you would design your member to not be stressed higher than 0.6 x 36 = 22ksi. Your safety factor then is 36/22 = 1.64.

With LRFD Steel, you have (per the IBC)

Load Factors for Dead = 1.2
Load Factors for Live = 1.6
Strength reduction factor = 0.9 for flexure

For a case where DL = LL your Load factor averages to 1.4.
So your safety factor is 1.4/0.9 = 1.56. In this case I've just used the single load combination of DL + LL (there are others of course) and looked at flexure only (shear has a different SRF).

Both are similar in their load factors but these comparisons vary if you have a structure with higher Live Load where the LRFD penalizes you (because in actuality the live load is much more uncertain; requiring a higher safety factor).

In concrete, the load factors are the same (Load factors are independant of the material) and the Strength reduction factor for flexure is a bit different too. But the overal safety factors are quite similar.

The key points to remember are:

1. Do NOT mix &quot;allowable&quot; stresses with load factors, or
2. Do NOT add the safety from an allowable stress with that of the safety from load factors (as you did in your fourth paragraph)
3. ASD allowable stresses include both the safety factor for the variability in loads and the variability in material properties.
4. It is incorrect to state, as you did above, that the 36 ksi yield stress is an &quot;allowable&quot;. It is actually your limit state. The allowable is the reduced value of 22 ksi
5. Our talk here of &quot;safety factor&quot; is really a mis-use of these load factors and strength reduction factors. The combination of load and strength factors in LRFD simply try to develop a statistical confidence against the probability of failure. LRFD does this better than ASD due to its separate factors for dead, live, wind, etc. and the development of different strength reduction factors for different modes of failure (moment, shear, axial).

 

[jheidt2543]

Qshake,

I'll bet it was a one-room school too! I'll bet they had 18 year old bars with 25 cent tap beers, those were the &quot;good old days&quot;.

Thanks for all the comments guys!

 

[CanyonRat]

JAE:
Good explanation; much better than mine. One addition to number 5. I was going to mention the statistical side but was tired of typing I guess.

LRFD has been statistally 'calibrated' pretty much across the board at least for bridge design. ASD is not really as far as I know. Maybe pieces are. More of a hodge-podge.

MikeD

 

[JAE]

I don't believe there is any statistical basis for ASD's factors but I could be wrong. I know that the 0.6 and 0.66 factors for steel are based on long-time experience and are probably not numerical in their source.

 

[BigH]

Can I extend the discussion? The discussions to date have been for concrete and steel - really pretty uniform materials &quot;from place to place&quot; - behaviour relatively well understood. What about soils on which the structures sit? Should we use ASD or LRFD in analysing bearing pressures/loads? I'd be interested in views on this extended query to this thread. Thanks . . . and [cheers}

 

[JAE]

In the U.S. you will usually find geotechs using an &quot;allowable&quot; bearing stress with factors of safety ranging from 2 to 4. These are usually factors applied to a limit state based on a maximum amount of settlement, or in some cases, a maximum failure capacity, although this is more rare.

 

[Ron]

Good discussion...

As you will note in reading over the entire group, there is confirmation that as the predictability of load and materials increases, the need for a &quot;Safety Factor&quot; decreases. This is why the FS for bearing capacity and other Geotech parameters is much higher than for steel design. Similarly, concrete (though very predictable in properties) carries a greater need for &quot;factoring&quot; than steel, just to compensate for the field variables and the natural variations of materials.

Controlled, manufactured products (steel, aluminum, some wood, etc.)offer greater predictability thus greater confidence in the design parameters.

I agree with JAE that many of the accepted parameters are based on experience and observation (not a bad &quot;proof test&quot; as long as you have lots of data!), not statistical proof. The steel industry had an early sales motivation for consistency and, in my opinion, have turned that sales motivation into a viable, predictable engineering parameter that we all use, respect, and rely on.

 

[jheidt2543]

BigH, I just recieved the May 2003 issue of &quot;Structual Engineer&quot; magazine and there is an article titled &quot;Foundation Engineering - Judicious Use of LRFD and ASD in Foundation Design&quot; on pages 18-22. It discusses the advantages and disadvantages of both design methods as they pertain to foundations. There is also an example retaining wall design.

Thanks to all for all the good discussion in the above posts.

 

[BigH]

jheidt2543 - can you scan it for me and send to bohica@rediffmail.com? I can't get that mag over here in India.

The one point I was making - most steel and concrete design work (I presume) is based on strengths of materials - not on deflections, movements, etc. So it makes sense to use factored loads in determining sizes. For soils, as we have discussed in the geotechnical forums, bearing capacity of spread footings seldom governs the design of the footing - it is usually the permitted settlements, differential movements, rotations that govern. These, many times are dependend on sustained loading (like consolidation settlements). Such loading is not practically covered by the LRFD, in my opinion - based on my understanding of it. Geotechs need real loads for real situations to determine the movements associated with them. Tomlinson has revised his great foundation book to meet with LRFD of the Euro-Code - much to my consternation. When he dealt with the real world, it was much better book. I am afraid that geotechs are being &quot;forced&quot; into the LRFD situation by &quot;designers&quot; who probably are the dominant force in code revisions, etc. since they are the ones mostly using them.

I'll look forward to the paper - thanks.

 

[Focht3]

BigH covered this topic well from a geotechnical standpoint. Let me add a minor point that structural engineers should keep in mind when dealing with geotechnical parameters. Geotechnical engineers often use terms such as &quot;allowable bearing pressure&quot; or &quot;allowable skin friction&quot; in our reports to permit the structural engineers to complete their designs. Unfortunately, the form of these geotechnical terms - and others - implies that these geotechnical parameters are equivalent to &quot;allowable stress&quot; in steel. They are not equivalent.

The term &quot;allowable bearing pressure&quot; would more properly be &quot;the pressure at which an 'acceptable' amount of settlement will occur.&quot; That's a real mouthful; so the term &quot;allowable bearing pressure&quot; persists. It's an unfortunate historical term which does not have a suitable substitute.

The structure of LRFD does not seem - to me - to be structured in a way that effectively deals with geotechnical parameters. How do you use LRFD to deal with design parameters that are essentially deflection limits?

 

[JAE]

Focht3,
I haven't read any of the LRFD Geotechnical literature lately, but the basic format of LRFD can certainly apply to geotechnical, even with the use of maximum settlements as the criteria for the design.

ASD - and traditional geotechnical procedures, as is mentioned above, use a maximum acceptable settlement as the basis for the so called &quot;allowable bearing stress&quot;.

In this case, the maximum acceptable settlement is, essentially, a limit state. In ASD, the geotechnical engineer will apply some safety factor to that settlement to get the &quot;allowable&quot; value:

pressure at max. acceptable settlement/SF = allowable pressure

...and the equation for loads is:

allow. pressure < pressure from actual loads

This is no different than in steel where:

max. yield stress/SF = allowable stress

...and

allowable stress < stress from actual loads

In LRFD, you take a more statistical approach and split the safety factor into two factors - one to provide a degree of safety based on the resistance and its level of variation. The other based on the various loads and their individual levels of variation. So in steel it is:

phi x resistance > (Load 1 x SF1)+(Load 2 x SF2)+...

For soils, I would bet that it is really the same:

phi x (press. from max. acceptable settlement) >

(Load 1 x SF1) + (Load 2 x SF2) + ... etc.

The use of LRFD here with soils would do exactly what it does for steel - provide different levels of safety factor for different loads based on their variability.

To some extent, I would think that you geotechs do this already in the ASD format by using your intuition when applying a safety factor.....&quot;should I use 2, 2.5, or 3?&quot;

In ASD, you are always faced with the problem that you NEVER provide a uniform degree of safety against failure. This is because ASD does not directly take into account the type of loads applied to the foundation. A structure with lots of dead load and little live load will have a different probability of failure than a similar structure with small dead load and lots of live load.

 

[BigH]

JAE - one, too, has to remember that soil is much more &quot;statistically&quot; scattered than steel and concrete. Look at any of the formulations for obtaining, say, the phi value from SPT test results. Scatter is more than 30% off the &quot;trend line&quot; - so, you want us to factor a safety at the pressure giving the maximum settlement - 'ell, most of the time, soil engineers cannot give the estimate of settlement within 30% - see discussions Focht3 and I had in earlier soils forums. And, so what if we NEVER provide a uniform factor of safety against failure - because failure as you wish to describe it is shear failure - and &quot;at&quot; failure, the actual shear stresses are &quot;post&quot; peak for some areas of the failure and just at peak for others - in other words, stresses in the soil mass vary from point to point and these have implicatons on the mobilized shear strength at that particular point. We are not interested, as structural types might be, to use a uniform factor of safety in all situations - in piles I might use 2.5 but in foundations of soft clays, I might want 3.0 (based on normal geo computations - and, to be honest, since the soil engineer has to estimate the strength of the soil from some pretty archaic tests (SPT) and even more &quot;accurate&quot; tests (piezo-cone), it is an estimate - the strength we are, in the art, happy to use for our best estimate of the soil behaviour in shear. But, as said, it is usually the settlements - and 20% variance in estimates is &quot;good&quot; - would that be good for steel? I shant think so but it is good for us. So, we have the two schools - those that work with uniform materials and those that don't. What is good for the goose is NOT necessarily good for the gander. Structural types can be the goose - I don't care; we'll take the gander. You want accuracy - okay, but the geotechnical field does not lend itself well to the accuracy of which you wish to achieve. Leave us to our system that has served all very very well for so many years. You want to change - go ahead, but our guests. Most of us in the geo field DON&quot;T want to change. Why, in your codes, etc. do you want to force us in a direction that doesn't make logical sense (at least to me and I am sure to many others).

Many thanks - I look forward to continued dialogue on both sides of the coin.

- by the way, I ran into a quote (now don't go and say this is inappropriate!!) but, something along the line from Ben Franklin: &quot;Beer is God's way of showing us he loves us!&quot;

 

[JAE]

BigH
Good comments. In fact, I was surprised that right after I posted the above, I came across an article in Structural Engineer magazine titled, &quot;Foundation Engineering - Judicious Use of LRFD and ASD in foundation design&quot;, by Walter E. Hanson, PE, SE, and Donald D. Oglesby, PE, SE.

It covers the use of both systems for geotechnical design. Their website is

http://www.gostructural.com

Don't know if the article is on the site or not -

I don't disagree with you on your points. Just want to clarify that the term &quot;safety factor&quot; and &quot;probability of failure&quot; are not the same thing. You mentioned that you might use a higher safety factor for a case with less assurance. This is exactly what LRFD does - only it does it by varying the safety factors to make uniform the statistical probability of failure of ANYTHING.

Whatever your material, design, etc., there are statistical data that can be measured in terms of variability. You said above - &quot;what if we NEVER provide a uniform factor of safety against failure &quot;....that's exactly the point. The safety factors are not (and shouldn't be) uniform. They vary with your ability to predict. For soils - I believe you are exactly right...the variability is very high...so using a more statistically accurate approach to setting your safety factors would give you a better handle on the true degree of safety that you are getting.

I know that even in Structural Engineering there are many who simply despise the LRFD approach. I don't disagree....you must use more effort to get to a higher precision answer without necessarily getting paid for it. A real bummer. So ASD can work and LRFD can work....

I would say that LRFD is &quot;better&quot; in that it is more accurate in getting a proper degree of safety, but ASD is &quot;better&quot; in that it has been successful for many years and takes less time.

 

[Focht3]

JAE:

Thanks for the link; unfortunately the article doesn't appear to be available online. But I did find en editorial on ASD vs LRFD, which I will read this weekend. It's about 858k and in PDF format.


A major problem with LRFD lies with the selection of the risk of failure due to a particular kind of load. Unlike concrete or steel, we cannot really use lab or field tests to provide us with the kinds of information that is known about the failure modes for concrete or steel. As a result, our &quot;tests&quot; involving rates of failure are typically full scale structures - the completed projects. Many of the failure modes are not amenable to model tests, or result from minor variations in soil properties that the meager geotechnical studies we are forced to perform do not allow us the ability to rationally evaluate statistically. And even when we have enough tests, it's damn near impossible to know the implications of minor variations in soil properties on the design methods.

We have theories to account for all of the major ones, but there are often three or more methods that could be used to evaluate each failure mode. And statistical data on failures is often nonexistent, so we have no way to rationally evaluate most of them. Axial capacity of piles is a notable exception, thanks in large part to the offshore oil industry.

Can we do a better job of providing some statistical evaluation of the soils at a given site - which would permit us to provide a rational basis for providing the structural engineer with geotechnical parameters for LRFD design? We can. But it will take significantly larger budgets for geotechnical investigations, and inclusion of the geotechnical engineer as an active and valued member of the design team. And I mean much larger budgets - by a factor of 3 or more. Remember that there is a pretty steep learning curve involved, and you simply cannot expect geotechnical engineers to take a great deal of perceived risk - real or not - without sound engineering to back it up. And that sound engineering will require significant investments in field exploration and lab testing - as well as engineering effort to get a grip on the site and project requirements.

I am highly critical of most of the efforts by academicians to inject probability theory in geotechnical engineering design. Most involve a dizzying array of probability parameters that are completely foreign to the practicing engineer, with no way to leverage existing knowledge into the proposed design methods. Predictably, these methods have been largely ignored by all but a few geotechnical engineers. However, J. Michael (Mike) Duncan authored a paper titled, Factors of Safety and Reliability in Geotechnical Engineering that was published in the April 2000 issue of the Journal of Geotechnical and Geoenvironmental Engineering Vol. 126, No. 4. Discussions of the paper appear in JGGE Vol. 127 No. 8. This paper deals with the variability in soil properties; it does not deal with failure modes or mechanisms. But it is an excellent start. You need to read both the paper and the discussions to get a full appreciation of the issues involved - from a geotechnical perspective.

If you treat us like mushrooms (by keeping us in the dark and feeding us bovine excrement), all you'll get are toadstools...

 

[JAE]

Focht3 - appreciate your comments on the extreme variability of soils - even from site to site where the variability of fat clay at one site could be different from the variability at another.

But whether you are doing ASD or LRFD, you are still dealing with that same variability. So the selection of the which method to use should be independent of how scattered your minimal data is.

With ASD, you are still assigning a safety factor to get to some perceived level of safety (probability of failure)...with ASD you are just using a &quot;shoot from the hip&quot; and &quot;its worked well in the past&quot; method to get to that level of limited risk.

With LRFD, you are doing the same thing, just separating the variability of loads (which we have a better handle on than soils) from the variability of the soils.

Both systems deal with the variability, both deal with limiting the probablility of failure....they just assign safety factors differently.

Setting a resistance factor (phi) is difficult with soils ...that's not an argument. Just how to get a good phi in LRFD and how to get a good safety factor in ASD are the difficult questions....

 

[Focht3]

I think I understand the disconnect, JAE. First I should say that I can see using LRFD now for some foundation types - principally piles/piers/caissons that derive 90% or more of their capacity from skin friction. Most geotechnical engineers will calculate ultimate skin friction values, then apply a factor of safety to arrive at allowable skin friction values. This is the same basic process as you have described. In addition, small variations in skin friction from location to location (and along the pile) are less important because the pile capacity is cumulative. Minor overstressing of these foundation types won't cause any significant problems in most soils - at least with &quot;reasonable&quot; factors of safety, er, resistance factors...

Spread footings, mat foundations and piles/piers/caissons which rely on &quot;significant&quot; tip bearing/bearing pressure are a different story. When using ASD for the foundation types, I seldom calculate an ultimate bearing capacity and apply a factor of safety to arrive at an allowable bearing pressure. I usually look at the expected movements and reduce/increase the bearing pressure accordingly. Why don't I calculate the ultimate bearing capacity? Simply because my experience tells me that it doesn't control the design, and that simply relying on p[sub]ultimate[/sub] divided by F.S. = 3 will get me into trouble - the foundations may experience too much settlement.

I guess that one way to handle this would be to calculate p[sub]ultimate[/sub] and choose reduction factors that limit the allowable bearing pressure to the value of p[sub]allowable[/sub] to something no greater than my other calculations tell me will result in acceptable performance. My concern is twofold: 1) that the LRFD procedure won't necessarily use the reduction factors in the manner I have envisioned, and 2) I will end up in endless arguments with structural engineers telling me I'm too damn conservative. (I'm not - but I use more sophisticated approaches than most of my competitors, and end up with more reasoned and consistent answers.)

Unfortunately, AISC has used the same brute force method to &quot;educate&quot; geotechnical engineers (&quot;cram it down their throats&quot that they did with USD. (I wonder how many structural engineers realize that LRFD is really repackaged USD - another design method that has failed to achieve widespread acceptance?) A brute force method that, frankly, I resent. AISC still hasn't addressed the concerns of the majority of the geotechnical engineering community. We haven't been engaged at all in the LRFD development process. And then they wonder why we continue to resist USD/LRFD!

Anyway, enough ranting. None of this was directed at you, or any other structural engineer, in particular. But you've gotten a small taste of how many in the geotechnical engineering community feel about LRFD. And AISC.

 

[ARH]

I think the question of using load factors and bearing capacity is a lot simpler than discussed above. Bearing capacity is governed by deflections. You do not apply load factors when calculating deflections whether you are working with steel, concrete, or soil.