## Notional Loads

## Notional Loads

"It [Notional Loads] accounts for partial yielding and the effect of initial imperfections in the columns." "Second, because it [Notional Loads] accounts for the p-delta 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. 2-19 from CAN/CSA-S16-01 (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 p-delta analysis AND using effective length factors of one? Why the hoopla about Direct Analysis Method then?

## RE: Notional Loads

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 out-of-plumbness. 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 P-Delta 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.

## RE: Notional Loads

## RE: Notional Loads

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.## RE: Notional Loads

## RE: Notional Loads

I agree that notional loads transform a symmetric gravity-only 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 thread--bump the structure into its anticipated mode shape and then apply vertical loads. If we have small second-order 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 first-order analysis. I think that might be slightly mis-worded 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 pre-DAM. It's also included *where* it needs to be--in 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]

## RE: Notional Loads

Clause 8.7.1 on page 1-22 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

## RE: Notional Loads

I was able to find a wonderful journal titled "Effective Length Factor K, A Travel From AISC-ASD 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 p-delta 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.## RE: Notional Loads

You can, however, use the B2 multiplier.

## RE: Notional Loads

I have no idea what you are talking about...P-BigDelta or P-LittleDelta? 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

## RE: Notional Loads

B2 is a factor used to capture P-little 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

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## RE: Notional Loads

What steel code do you use and where did you go to school? P-big delta and P-little 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, P-big delta are the second order effects from the member ends displacing relative to one another (global structure) and P-little 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 (p-big 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.

## RE: Notional Loads

To answer your first question, I don't use any steel code now. Before I retired last June, I used CAN/CSA S16-01. 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 P-delta 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

## RE: Notional Loads

This was done repeatedly until the change in geometry became small enough to ignore.

Best regards,

BA

## RE: Notional Loads

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.## RE: Notional Loads

Needed to share with someone.

Damn the slump Calgary is in.

## RE: Notional Loads

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

## RE: Notional Loads

If you "heard" it on the internet, it's guilty until proven innocent. - DCS

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