P-Delta Analysis

[DCBII]

Hi,

Is it necessary to consider P-Delta effects when designing trusses with significant bending in the chord members, or are P-Delta effects for the main lateral force resisting system only.

If it is necessary, does anyone have any tips on how to approach it. Is it necessary for me to multiply my ASD loads by 1.6 and then divide the results by 1.6 if I'm not using the Direct Analysis Method of Appendix 7? Section C2.2a(b) of the Specification has me a little confused. Are P-Delta analyses ALWAYS carried out under factored loads, no matter what?

 

[JoshPlumSE]

I would say that it is required. Of course, you can avoid it by using the 1st order analysis options in chapter C (which requires that you add notional loads to the structure to produce an effect similar to P-Delta).

If you are using a computer program to do your P-Delta analysis then check to see if the program already includes that 1.6 factor for the 2nd order effects (RISA will do this whenever you use the ASD 13th edition steel code). If not, then you will want to multiply all your loads by a factor of 1.6 and then divide out all your results by a factor of 1.6. Note that this is for member capacity and stability. If you check serviceability issues (deflections, drift et cetera) then you wouldn't have to include this factor.

FWIW, that 1.6 factor is used because 2nd order effects are highly non-linear. If they didn't require a factor like this the LRFD design method would be at a distinct disadvantage when compared to ASD.

 

[ToadJones]

I would say you could run a "little" p-delta analysis.
I would "big" P-delta would apply to the structure/drift/sway.

I know STAAD will also run a big or little p-delta. In a truss, my guess is the little p-delta wont amount to very much if deflections are held to a minimum.

 

[abusementpark]

JoshPlum,

If you assume that the D+.75L+.75W ASD combination will govern, then wouldn't you factor the Dead Load by 1.6 and the Live Load by 1.2 (i.e separate factors for dead and live)? I realize he might not be dealing with Wind for his truss, just want to clarify.

 

[ToadJones]

I havent read over the DAM method in a while and have never used it, but I thought it was 1.6 for all.

 

[ToadJones]

http://communities.bentley.com/admi...o-2007-direct-analysis-method-screencast.aspx

 

[DCBII]

Thanks for all your responses. It sounds like I'm stuck with the 1.6 factor. The problem I'm having is that as far as I can tell STAAD won't multiply forces and divide results by 1.6 unless I tell it to use the Direct Analysis Method. It doesn't seem to be too friendly with ASD used in combination with other P-Delta methods.

 

[JoshPlumSE]

If you were doing the DL + 0.75 LL + 0.75 WL by hand then you factor up the whole thing by 1.6 which turns it into 1.6*DL + 1.2*LL + 1.2*WL.... Of course, then you divide all the results by 1.6 after you have fully accounted for P-Delta.

For a truss, you still have P-Big Delta and P-Little Delta. The panel joint deflections are the "big delta" effect and the chord curvature between panel points would be the "little delta" effect. It's analagous to a braced frame turned on it's side.

I agree with Toad, if your 1st order deflections are relatively small then you will not likely experience much 2nd order amplifications with your truss.... at least not with the KL/r ratios that we would normally use for the truss members.

 

[Lion06]

Hold on a second, guys. I haven't read anything in AISC that would suggest that the DAM would apply to a building component, such as the truss mentioned in the OP. The DAM is geared to building stability.

Why would you apply the DAM to a gravity truss anymore than a gravity beam? Of course, I'm assuming the truss is supporting gravity loads, but I didn't see anything in the OP to suggest otherwise.

As far as the second order analysis goes, it really depends on your software. I know the programs I use only do a P-big Delta analysis, so to capture the P-little delta effects I break the compression members into 4-6 pieces (always an even number so there is a node at the center) and run the P-big Delta.

 

[ToadJones]

Lion-
There are many applications where trusses are in fact an integral part of the building stability. Staggered truss frames, Mill/ Crane buildings come to mind.

I assumed the OP had a situation like this.

 

[Lion06]

I don't disagree, but when the OP says, "........ or are P-Delta effects for the main lateral force resisting system only.", that's suggesting that it's not part of the lateral system. If it's not part of the lateral system, I don't think it's appropriate to apply the DAM to it.

That being said, the second order analysis is always appropriate. The DAM goes far beyond a second order analysis, though.

 

[ToadJones]

Lion, I guess a few days between posts caused me to fall off the train of thought.
In saying that the DAM is far more than a second order analysis, are you referring to it yielding design loads as a result of the second order analysis?

 

[ToadJones]

days = hrs

 

[Lion06]

Yes, I'm talking about the requirements of notional loads and reduced stiffness and having to run everything at factored loads (even if you're using ASD).

 

[RFreund]

Please correct me here as I would like clarification (this is more of a question then statement):

Doesn't the DAM try to capture the P-DELTA effect caused by lateral loads which produce a displacement which produce additional moments (due to the axial force and deflection)in lateral resisting members.

Therefor if a truss is only resisting gravity loads there would most likely only be p-delta effects which is the additional moment/stress from the deflection and axial force.

?

EIT

 

[Lion06]

RFreund-
Close, but not exactly. Any software program can capture the P-Delta effects rather easily. The point of the DAM is to account for additional things. Reduced stiffness factor accounts for material yielding at strength level loading and the associated reduction in E that comes along with it. The notional loads attempt to capture all columns being out of plumb by the maximum tolerance per AISC. These additional load effects really just increase the second order effects on the structure, but it is more than just doing a second order analysis. Even if you're not using the DAM (say you're using the old k-factor method), you still should be doing a second order analysis, it just won't include things like the stiffness reduction factor and notional loads.

 

[JoshPlumSE]

Lion6 -

Have you read anything that suggests that DA Method does NOT apply to components such as a truss? I have not.

In reality, the DA method is about stability and is a very generalized method. It can be applied easily to trusses. In fact, the beauty of the method is that it can apply easily in cases where K values are difficult to caculate.

1) The notional loads (which account for member imperfections and out of straightess), could certainly be adjusted.... better yet, you could model in some assumed imperfections in your truss chords.

2) The inelasticity of the cords as they approach buckling would be the same for columns or chords, so a stiffness reduction would be appropriate. Remember, this is done because our members will tend to fail via inelastic buckling rather than elastic buckling. And, the DA method is really an attempt to get our elastic analysis methods to capture this inelastic buckling effect.

Obviously, you are not required to use the DA Method. But, it should be easily applicable to any structure as long as we're still talking about Hot Rolled steel design.

Now, I believe it has been calibrated to be most accurate with the strong axis buckling of wide flange members. So, when you have a truss, you could argue that the stiffness adjustments may not as accurate as they could be. But, you could say the same thing about the column curve formulas (which use one curve for all members even though more accurate curves are available for other members).

 

[Lion06]

App. 7 i AISC 360-05, 7.1 says "..... All components and connection deformations that contribute to the lateral displacement of the structure shall be considered in the analysis."

I don't think it was ever the intention of AISC that all gravity members (truss or otherwise) be subject to the DAM.

If I'm mistaken, and it says otherwise somewhere, please let me know.

 

[DCBII]

Lion06 has caught the intention of the original question I posted.

I get the impression from reading the provisions that they were intended for vertical systems like moment frames, braced frames, etc.

However, if they are applicable to lateral systems why wouldn't it apply to gravity systems? Steel doesn't know which way is up, down, left, or right. It leads me to believe one of two things:

(1) Either it does apply to gravity systems, or (2) we are intentionally designing lateral systems with some extra precision.

 

[Lion06]

Look at Chapter C. It says that individua member stability is provided by satisfying the provisions of Chapters E, F, G, H, and I.

The DAM is meant to lead us away from the old k-factors. There are many assumptions in the nomographs that are commonly violated (one that comes to mind is that all columns buckle simultaneously).

Even all of the examples that I've seen on the application of the DAM have only included lateral load resisting systems. I've never seen gravity elements incorporated.