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P-Delta Analysis

P-Delta Analysis

P-Delta Analysis

(OP)
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?

RE: P-Delta Analysis

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.   

RE: P-Delta Analysis

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.  

RE: P-Delta Analysis

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.

RE: P-Delta Analysis

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

RE: P-Delta Analysis

(OP)
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.

RE: P-Delta Analysis

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.   

RE: P-Delta Analysis

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.

RE: P-Delta Analysis

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.
 

RE: P-Delta Analysis

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.

RE: P-Delta Analysis

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?

RE: P-Delta Analysis

days = hrs

RE: P-Delta Analysis

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).

RE: P-Delta Analysis

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

RE: P-Delta Analysis

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.

RE: P-Delta Analysis

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).   

RE: P-Delta Analysis

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.

 

RE: P-Delta Analysis

(OP)
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.

 

RE: P-Delta Analysis

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.   

RE: P-Delta Analysis

Sometimes I really wonder about all these types of analysis....no computers and no one would dream of trying it.

 

RE: P-Delta Analysis

Toad-
I agree 100%!

RE: P-Delta Analysis

I guess it gets frustrating. I spent half my days and sometimes all evening doing research to learn how to do things THAT I HAVE DONE A 100 TIMES!!!!!!!!!!!!!

RE: P-Delta Analysis


By the code, I don't know that you are "required" to use the DA Method for trusses.  My last post probably implies that it's required.  But, really meant to say only that the DAM method is a very general procedure that can be used for any analysis where you want to account for stability effects.

FWIW: I just took a look and the 2010 version of the code removes the term "lateral" from that quote... "all components that contribute to the displacements of the structure." So, the applicability is more generalized that was implied by the language from 2005.  

 

RE: P-Delta Analysis

Has a gravity steel truss ever failed because it wasn't designed for second-order effects?

These codes are getting a little out of hand.

RE: P-Delta Analysis

The codes have officially made it impossible to analyze a structure without a computer.
This scary.
I have worked with lots of folks who could hardly model a single column properly in a FEM program.
I have found it more difficult over the years to grasp the finer points of properly modeling a structure with software than actually grasping the design philosophy.
At times I get genuinely PO'd when checking another's work that turns out to be a botched FEM model.

I'd hate like hell to think that there are guys coming out of school having learned some FEM in school thinking they are design engineers surprise

RE: P-Delta Analysis

Removing "lateral" from that sentence seems to include every single piece of the building, right down to the bent plates at the slab edge.

I still don't think it's the intent to include gravity members in the reduced stiffness requirements.  It just doesn't make logical sense to me.  I guess I'll see how it reads, but it's worded now to be for stability of the structure.  To me, that means if it doesn't contribute to the stability of the structure that it's not intended to be required to meet the requirements of the DAM.  That makes sense to me , including gravity members doesn't.  

I could be way off, though.   

RE: P-Delta Analysis

Thanks for the correction. I should have put more thought into that because as soon as I read your post, it was one of those "oh, thats right" moments.

How about this statement:

So really the second order analysis (or B1, B2 amplified 1st order analysis, I usually use this as or projects don't normally get to out of hand) is to account for the p-delta and P-DELTA effects.  The DAM method is really to account for: 1. Notional loads due to initial imperfections and 2.Inelastic effect of column buckling (I believe this was previously stated.  

I think part of my confusion was/is coming from the fact that the results of the DAM effect my second order analysis (amplified 1st order). In that by increasing the horizontal load and decreasing stiffness (or increasing deflection) gives a higher B2 value.  So I guess I was just looking at it as an extension of the second order analysis, which I guess it sort of is?

As far as FEM goes, I like learning about it but not sure I'll get to put it to use.  Currently our office is more about making some safe assumptions and going back to some sort of strength of materials equations.

  

EIT

RE: P-Delta Analysis

AbusementPark

To some extent, we have been designing for 2nd order effects since the early sixties.  That's why we always used the Cm / (1-fa/Fe) multipler on our bending stresses.

Look at it in terms of that old equation.  Is it possible for the compression chord to fail if you considered only fa/Fa + fb/Fb <1.0 without any consideration of momen amplification?  Of course it is....  

The new codes are a bit more "genearal" than they used to be.  They tell us to account for 2nd order effects, they just don't tell us how.  We could certainly use the old type of Cm/(1-fa/Fe) amplifier, or we can include the effect directly using a P-Delta analysis. to me that is a rational change reflecting the fact that so many engineers are using analysis programs these days.  

My point is only that the 2nd order analysis requirements in the code are not a whole heck of a lot different from old codes..... Rather, it's all the other portions of the new analysis requirements (stiffnesss reductions, and notional loads) that represent changes to the code philosophy.   

RE: P-Delta Analysis

I use the DM to design trusses all the time when doing erection engineering.  Lets say for instance you are setting a truss that has a bolted splice in the middle of it and you want to know the out of plane moment that splice needs to take under construction dead + wind loading prior to the truss being locked in to any diaphragm.  The DM method can accurately capture the increase in out of plane moment due to the dead load in the top chord plus the out of plane wind loading as well as let you know if the truss is even stable without additional bracing or guying (the P-delta analysis will not merger).  As JoshPlum was alluding to this is actually one of the major benefits of the DM method - using it for stability problems and to determine bracing loads in lieu of Appendix 6.   

RE: P-Delta Analysis

BTW the notional loads concept is definitely not calibrated to the design of trusses etc, for that I use direct out of plane modeled initial geometry (sine wave with L/500 out of plane sweep).

RE: P-Delta Analysis

(OP)
WillisV,

Instead of using a factor for on the actual gravity loads to get notional loads, couldn't you use a factor on the chord forces caused by gravity loads instead?

I'm just not sure how to model the initial geometry.  How would you model a curved beam in a finite element program?  It seems like a lot of effort.

RE: P-Delta Analysis

You model it as piecewise linear using the panel points.  It is not too difficult.  Again DO NOT use notional loads to do this, as they were calibrated for building column design, and the distance that the notional load pushes the column over will in all likelihood not equal the L/1000 (where L is the entire length of the truss) value for maximum initial curvature that you are shooting for in this type of design.  Plus, out of plane notional loads will add fake out of plane moments to push it over into the deformed shape that are not really there.   

RE: P-Delta Analysis

(OP)
I guess that's not too bad.  It's just a matter of knowing which buckling mode to shape the initial geometry to.

RE: P-Delta Analysis

DCBII - true, that is indeed the hard part.  You can look at Eigen buckling modes to get a feel for it, but if it is braced in multiple locations etc. you might have to brute force through several different modes to get the controlling forces.   

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