Direct Design Method - AISC

[JAE]

In Appendix 7 of AISC 13th Edition the Direct Design Method is described. I understand it OK - have gone to seminars, etc. and written an in-house procedure to use it along with our RISA 3D program.

The only thing that has come up that has us questioning the use of it is that it doesn't seem to take into consideration the possibility of a long, flexible diaphragm in the building being designed.

Notional Loads are applied laterally to the structure being analyzed which represent an initial out-of-plumbness of the frame of L/500 (0.002 x dead load).

If you take a large warehouse - say 200 ft x 200 ft - and have a flexible metal deck vs. a theoretically rigid diaphragm, it seems that the notional load doesn't get affected by it.

The AISC procedure doesn't seem to directly include any provision for the [blue]rigid vs. flexible[/blue] deck behavior.

With a flexible diaphragm, the [Δ] of the braces on either end of the diaphragm will induce leaning in the interior gravity-only columns. Also, the distortion of the metal deck under lateral loads will also add to that leaning of gravity columns. This combined leaning will create additional P[Δ] lateral thrust forces that will further distort the deck AND the braces. This further distortion will cause additional P[Δ] forces etc. until the building converges or collapses.

Again - the Direct Design Method doesn't explicitly address this other than in the commentary it mentions that Notional Loads are for the purpose of accounting for "...any other effects that could induce sway that is not explicitly considered in the analysis".

So my question is - If we first design the diaprhagm, and determine some lateral deflection - and use an INCREASED Notional load (i.e. higher than 0.002Yi) would we be OK? If so how much higher is appropriate?

Are there any papers or articles out there that address this issue? I've posted a question to AISC Technical staff and awaiting a reply but I thought I'd ask here.

 

[structuresguy]

Hmm, interesting question. I am just starting to get into the DDM from the new manual. (I confess that I still use the green book most of the time). Will be interesting to see how other people feel about this.

Like you, I am working on an in-house procedure and presentation on the topic. Unfortunately, I have not been to any seminars on the topic. Have you found any good resources on the web regarding DDM?

Thanks

 

[JAE]

I found this quote at gostructural.com:

"This difference highlights the fact that low-rise structures with high gravity-to-lateral load ratios are often more stability sensitive than multi-story structures and warrant careful assessment of second-order effects."

This sort of confirms my worry/question about this issue.

 

[haynewp]

Since deck distortion is part of the nonlinear contribution, I think that they expect this flexibility to be input into the model so that it will be included in the P-DELTA/delta analysis. I know that doesn't help much, but that is what I anticipate the intention is (3D model analysis seems to be required).

I have not seen any papers on using an increased initial notional load to account for diaphragm flexibility.

 

[JAE]

haynewp - I'd agree with you - it's just that including CORRECT diaphragm stiffness characteristics is tough to do in 3d models.

And for large warehouse buildings, a 3D model isn't always that necessary - although with Revit, BIM, etc. we probably will in the future anyway.

 

[haynewp]

Before you say it, I know that making a 3D model is really not practical for most single story box buildings. I am not really sure what I would do about including the diaphragm flexibility effects.

 

[haynewp]

You posted that one right as I was typing (again). LOL

 

[JAE]

Woo... this ESP thing has got me scared...

 

[ash060]

But you use the larger of the lateral loads whether applied or notional.

So in your example about the warehouse the applied lateral loads would control the design of the lateral force resisting columns not the notional loads.

In the seminar I went to they said use one or the other, and that notional load was just considered a minimum unless you had very large second order displacements compared to the first-order displacements, in which case you add them together.

 

[haynewp]

I think you apply the notional loads always. This is to estimate initial structure out-of-plumbness.

 

[haynewp]

I know what you are confusing, you can either put in the notional loads OR model in the initial out-of-plumbess directly.

 

[Lion06]

No, actually if the ratio of your second order drift to your first order drift is less than 1.5 (The B2 factor), then you need to include the notional loads in ONLY the gravity combinations, not in the lateral combinations. You could be conservative and apply it in all cases, but the spec doesn't call for that.

 

[Lion06]

I know this may be way off base, but let me throw this out there and get some opinions. First for a flexible diaphragm, the only torsional lateral cases to consider are the ones where it is explicitly stated in the load case (e.g. the torsional wind case) because a flexible diaphragm distributes the lateral loads based on trib width and not relative stiffness. Now, assuming the flexible diaphragm distribution, the relevant frames will drift accordingly and see the appropriate second order effects. The only issue I can see is the displacement of the diaphragm between frames causing additional displacements of the gravity only columns inducing a greater leaning column effect - is this what you're talking about?
OK, I just reread the OP and found out that is exactly what you're talking about.

Here is my opinion, If you design the diaphragm first and know the max deflection (say 1/4" between frames) on an 11'-4" high frame then the max additional displacement is H/500. Try adding an additional 0.002Yi (which is probably conservative).

 

[WillisV]

How were you dealing with this effect prior to direct analysis being introduced?

 

[JAE]

Ah..WillisV - you had to go and expose me!

Prior to the DAM (I love that abbreviation) I did this:

1. Calculate/Design the diaphragm - determine the lateral distortion of the diapragm and average it over the full width of the diaphragm...this is the average "lean" of the gravity-only columns.
2. Calculate the additional lateral thrust from this lean (equal to total roof dead load times the deflection and divided by the average height of the roof.).
3. Apply that lateral thrust to the endwall braces.
4. Design the braces with P[Δ] effects applied.

What this doesn't do....and what the DAM doesn't appear to do...is include further second order effects from second order distortions of the diaphragm.

If the braces themselves deflect, this causes ALL the interior gravity-only column to deflect more, which then induces further lateral force on the diaphragm, which causes the diaphragm to deflect more, which causes more gravity-column leaning, which adds to the P[Δ] forces....etc. until convergance.

[red]This is the root of my question[/red] - there are definitely second order diaphragm effects that the DAM doesn't seem to address...it addresses second order brace effects but there is no "input" that would tell the calculations the level of stiffness within the diaphragm.

I believe it is correct that the Notional Loads are applied to gravity load combinations when second order/first order effects are less than 1.5. When they are more than 1.5 you MUST include Notional Loads as additional to wind/seismic loads also.

 

[haynewp]

My notes on DM have the following:

"Included WHERE IMPORTANT by modeling the corresponding component flexibilities in the analysis...examples:

-Member or panel zone shear deformations
-Connection deformations
-Diaphragm deformations
-Column or brace axial extension and shortening"

I would have thought column or brace axial lengthening/shortening would be a standard inclusion anyway.

 

[UcfSE]

On page 16.1-435, the text in the second paragraph suggests the notional load does account for the diaphragm stiffness in a round-about way with the phrase "...from all effects...", meaning accounting for everything adds up to 0.002. I believe you're right that diaphragm stiffness will affect whether the 0.002 is adequate. Unfortunately, they don't appear to have included anything to evaluate how much of the 0.002 comes from the diaphragm. Perhaps this will be addressed in the future(?).

 

[JAE]

UcfSE - yep - I saw that...and the paragraph on page 16.1-433 where it again refers to "any other effects that could induce sway that is not explicitly considered in the analysis".

I can see figuring out the, perhaps, larger notional load to account for the diaphragm distortion. What I keep struggling with is how you include the variability of the diaphragm stiffness - a more flexible diaphragm would mean a higher notional load for sure - but does the "initial" deflection of the diaphragm, resulting in some initial notional load, take care of the second order effects on the diaphragm itself?

I keep seeing that the notional load only reflects the INITIAL distortion of the diaphragm and the subsequent second order distortions are included in the analysis by using a static number for the notional load.

 

[swearingen]

I'm very curious what AISC has to say about this, but before I hear their answer I'll put my 2 cents out there.

Whatever the paragraph says about "any other effects", I don't believe that this particular case was intended. To get around this problem, you really must accurately model the flexibility of the diaphragm. How could you even come up with an appropriate nodal load without knowing the diaphragm's flexibility? It is completely dependent on that stiffness.

From a practical standpoint, I'd try and get an envelope of what the diaphragm stiffness would be and then lean toward the conservative end of that envelope.


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

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[JAE]

OK - here is AISC's response...basically we must include the second order diaphragm distortion effects in our analysis....

[blue]Please note that Appendix 7 addresses the stability portion of the check and assumes that second order effects have already been considered in analysis. Therefore one would have to model the building and carryout iterative procedures to calculate the second order effects. Alternately one could use the amplified first order procedure in Chapter C of the 2005 AISC specification [B1 and B2] to approximate the second order loads. Please note that all leaning columns have to be considered when carrying out second order effects as per chapter C.[/blue]