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Notional Loads

Okay, this caught me totally off guard: "It [Notional Loads] accounts for partial yielding and the effect of initial imperfections in the columns." "Second, because it [Notional Loads] accounts for the pdelta moments directly, the use of effective length factors greater than one are obviated and its use allows effective lengths equal to actual lengths to be used." Straight from Pg. 219 from CAN/CSAS1601 (Eight Edition) So, if I were to apply a lateral load equal to 0.005 x gravity load which is what the notional load is, I can get away with not performing a pdelta analysis AND using effective length factors of one? Why the hoopla about Direct Analysis Method then? Clansman
"If a builder has built a house for a man and has not made his work sound, and the house which he has built has fallen down and so caused the death of the householder, that builder shall be put to death." Code of Hammurabi, c.2040 B.C. 

271828 (Structural) 
16 Mar 09 22:25 
"So, if I were to apply a lateral load equal to 0.005 x gravity load which is what the notional load is, I can get away with not performing a pdelta analysis AND using effective length factors of one? Why the hoopla about Direct Analysis Method then?"
I don't know the details of the Canadian method, but what you describe isn't right by AISC App. 7. The notional load models the initial destabilizing effect of outofplumbness. That's why you can use the initially OOP geometry corresponding to H/500 OOP instead of using notional loads.
Inelasticity is modeled using EI* = 0.8*taub*EI where taub varies from 1.0 for cases with low axial stresses to 0.0 when there's so much axial stress that the member doesn't have any unyielded parts left to provide some EI stiffness.
The PDelta analysis is a critical step also because that's how you'd detect that the frame is unstable for story buckling.
You have to combine all three of those to get away with K=1.0. 

Lion06 (Structural) 
17 Mar 09 5:19 
271828 is correct, the Pdelta analysis is a critical component. I would be extremely cautious of any code telling you that Pdelta analysis isn't necessary. 

Thanks for the responses. I have scanned the page and attached it to this post. I am curious to hear your interpretations. Clansman
"If a builder has built a house for a man and has not made his work sound, and the house which he has built has fallen down and so caused the death of the householder, that builder shall be put to death." Code of Hammurabi, c.2040 B.C. 

kslee1000 (Civil/Environmental) 
17 Mar 09 10:44 
I think other than "0.005 x gravity load", which should be preferably writen as "0.005 x sum of factored loads contributed by that story", you read it correctly. 

271828 (Structural) 
17 Mar 09 10:57 
First off, they use 0.005*Sum(P) for the notional load whereas AISC uses 0.002. Perhaps they've fudged the factor up somewhat to help account for anticipated inelasticity (even though the axial forces are unknown initially) and initial imperfections other than initial OOP. In other words, they might not require EI* to be used in the analyses. It seems very unlikely that their OOP tolerance is 0.005*H, so I think these other effects are lumped in there. If they are lumping the effect of inelasticity into the 0.005 rather than computing it directly for each member, then their method would seem more crude and less accurate than the AISC DAM.
I agree that notional loads transform a symmetric gravityonly load combo from a bifurcation problem to a bending problem when it comes to story buckling. (There would be a trivial solution without the notional load, so an eigenvalue buckling analysis would be required to really figure out the story buckling load.) However, the resulting bending problem will only give info on story buckling if the analysis is nonlinear and robust. By adding the notional loads, the analysis is the story buckling equivalent to the column buckling analysis that StrlEIT was trying to do in a previous threadbump the structure into its anticipated mode shape and then apply vertical loads. If we have small secondorder amplifications, then story buckling is OK.
When they say in the last paragraph "...it accounts for the PDelta moments directly,..." I don't interpret that to mean that one can now get away with a firstorder analysis. I think that might be slightly misworded and should be more like "...story buckling is accounted for directly."
I think people look over taub when they think of the DAM. To me, that's more the essence of the DAM than is the notional load. It has the power to simply (automated within a program) capture the effect of EI softening due to yielding in compressive residual stress areas. Nobody would've EVER thought to try and include that the analysis preDAM. It's also included *where* it needs to bein the analysis, not in the design strength equations. Now we have the equivalent of an inelastic story buckling check in our analysis! (Similar to Fcr=Fy*0.658^(Fy/Fe) for column buckling. Previously, we could only reasonably get the *elastic* buckling load from the analysis.) The more I learn about the DAM, the more I like it.
[Steps onto soapbox]Looking back, the ELM is heinously abstract and difficult to accurately apply to most real situations. I'd speculate that 90% of people who use the ELM don't use it correctly considering leaner columns, different boundary conditions than those assumed in the alignment charts, girder axial loads, column inelasticity, etc. Good riddance to the ELM as far as I'm concerned. Viva load DAM!!![/steps or falls off the soapbox] 

Clansman, Clause 8.7.1 on page 122 indicates a preference for a second order analysis, but offers the amplification factor as an alternative. The magnitude of "notional load" of 0.005 times the gravity load applied horizontally at each storey was established on the basis of a flagpole column and is conservative for columns with double curvature. If a closer analysis is required, it is better to use a second order analysis. Best regards,
BA 

Thank you all for the great responses. I was able to find a wonderful journal titled "Effective Length Factor K, A Travel From AISCASD to AISC Unified Code" by Parkhi. There's a paragraph on the Canadian notional load and pretty much confirms 271828 thoughts on the matter. The Canadian notional load is 0.5% as opposed to the American 0.2% because it accounts for material inelasticity. The journal also says that k = 1 can be used only when a pdelta analysis is performed (OR accounted for in the strength equations) AND when notional loads are used. Clansman
"If a builder has built a house for a man and has not made his work sound, and the house which he has built has fallen down and so caused the death of the householder, that builder shall be put to death." Code of Hammurabi, c.2040 B.C. 

Lion06 (Structural) 
17 Mar 09 18:39 
I don't think Pbig delta can be accounted for in the strength equations. Only Plittle delta. That's because Pbig delta is a structure issue where the strength equation is for a member. You can, however, use the B2 multiplier. 

StructuralEIT, I have no idea what you are talking about...PBigDelta or PLittleDelta? And what is the B2 multiplier? Keep in mind you are talking to people who do not necessarily relate to your particular jargon. Best regards,
BA 

In the AISC code, the distinction between global structure Pdelta and local column Pdelta is made by using capital and lower case deltas, respectively. B2 is a factor used to capture Plittle delta effects when doing a first order analysis, thereby simplifying the calculation. If you "heard" it on the internet, it's guilty until proven innocent.  DCS
http://www.engtips.com/supportus.cfm


Lion06 (Structural) 
18 Mar 09 7:08 
BA What steel code do you use and where did you go to school? Pbig delta and Plittle delta are common terms  certainly not specific to my school or geographic location. In fact, that is the way it is referred to in any steel text that I've read.
As swearingen notes, Pbig delta are the second order effects from the member ends displacing relative to one another (global structure) and Plittle delta are the second order effects from local member displacements between the member ends (local member effects).
The one correction I would make with swearingen's post is that the B2 multiplier is to account for global second order effects (pbig delta).
B1 is a modification factor to account for member second order effects if a first order analysis is done. B2 is a modification factor to account for global second order effects if a first order analysis is done. 

StructuralEIT, To answer your first question, I don't use any steel code now. Before I retired last June, I used CAN/CSA S1601. My school was the University of Alberta where I received a BSc in Civil Engineering in 1955 and MSc in Structural Engineering in 1964. I know about the Pdelta effect (capital delta), but until now I was not aware of big and little delta or B1 and B2. I may be wrong, but I don't believe they are mentioned in the Canadian code. Maybe Clansman can comment on that. In any case, I won't comment further as I don't have a feel for the subject. Best regards,
BA 

A few years ago, I wrote a program for frame analysis. It worked correctly but it did not take into account the PDelta effect. I modified the program in a fairly simple way. At the end of each run, the node geometry was modified by the calculated deflection of the previous run. This was done repeatedly until the change in geometry became small enough to ignore. Best regards,
BA 

BARetired, The B1 and B2 factors that StructuralEIT is referring to are known as the U1 and U2 factors on S16. Clansman
"If a builder has built a house for a man and has not made his work sound, and the house which he has built has fallen down and so caused the death of the householder, that builder shall be put to death." Code of Hammurabi, c.2040 B.C. 

Oh, and I got laid off today! Needed to share with someone. Damn the slump Calgary is in. Clansman
"If a builder has built a house for a man and has not made his work sound, and the house which he has built has fallen down and so caused the death of the householder, that builder shall be put to death." Code of Hammurabi, c.2040 B.C. 

Clansman, My condolences about the layoff. Some of the larger firms in Alberta are hiring engineering staff on a contract basis. Possibly you could let the word out that you are available. Over the long haul, perhaps you might consider hanging out your own shingle. I did that in 1969 and have enjoyed every minute of it...well, nearly every minute. Best of luck to you. Best regards,
BA 

You're deadon with the description of B1 and B2, StructuralEIT. My mistake... If you "heard" it on the internet, it's guilty until proven innocent.  DCS
http://www.engtips.com/supportus.cfm




