P-DELTA effect and K value

[Shindey]

We are having some disagreement over whether or not to use a K=2.0 for a cantilever column.
My view is that we should use BOTH PD as well as K value.
The structure is thick slab resting on four columns. The slab is about a meter thick, the columns are 500mm dia 20mm thk.The height of column is 8.5m.
The columns are pinned at base.

My argument is that the PD is the analytical aspect, whereas K addresses design aspect. As a counter exmaple, if the only load on column is purely axial, then including PD
in analysis will not have any effect on the moment, and then we would design the column K=1.00 which would go against design philosophy of buckling load.Buckling load caters to
manufacturing and construction defects(in some ways).

Am I right in my argument?

 

[jdgengineer]

Are the columns a part of the lateral force resisting system? If they are not, I would personally consider them to be pinned at the top as they are braced by the lateral force resisting system. The P-Delta effect would introduce a little moment into these columns as the axial force would no longer be concentric.

 

[JoshPlumSE]

I would say that it depends on your design code. Codes which allow you to use K = 1.0 for cantilevers would generally required that you apply some "initial imperfection" to your model or apply a minimum lateral load (maybe referred to as a notional load). That way, the P-Delta effect would cause buckling even for cases where there is no other defined lateral load.

Other aspects that should be considered before you can consider using a K= 1.0:
[ul]
[li]Make sure your analysis accounts for P-little delta (i.e. member curvature) as well as P-big delta.[/li]
[li]P-Delta analysis is good at accounting for elastic buckling. But, are there inelastic effects that may need to be accounted for as well.[/li]
[/ul]

 

[DaveAtkins]

I don't understand how the columns can be cantilevers AND be pinned at the base.

DaveAtkins

 

[JoshPlumSE]

Yeah, I didn't quite follow at first either.

However, I believe it may be more like an inverted cantilever. Rigidly restrained for rotation at the top, but allowed to drift. In that case, the traditional K factor calculation is virtually identical to a cantilever.

 

[KootK]

I'm going to assume that your assumptions are as follow for the sake of discussion here.

1) Pin based columns.

2) Tops of columns assumed to be 100% fixed rotationally by the relatively thick slab.

3) The tops of the columns are permitted to sway laterally.

4) You are taking the old school effective length, K-factor approach.

5) No other vertical load is being stabilized by the columns other than that supported vertically by the columns

Am I right in my argument?

I believe that you are wrong. P-Delta is fundamentally about the destabilizing effect of the relative sway displacement occurring between the ends of a member. The K=2, cantilevered column approach has that trasnslational sway effect already built into it. Just look at the diagram that always accompanies this case: it shows the free end of the member laterally translated relative to the fixed end. I you try add P-Delta to the K=2, cantilever design you will be, to some degree, double counting the P-Delta effect.

If you choose to, you could employ the more modern direct design method (DDM) to design the column. In that case, you would use K=1 and you would model P-Delta effects as well as a bunch of other sources of non-linearity as previously mentioned. Prosecuted correctly, you would also come to about the same answer as you would get using the effective length, K-Factor method.

My argument is that the PD is the analytical aspect, whereas K addresses design aspect.

I also disagree with this assertion. The stability demands for strength and stiffness come from the analysis side. The provision for that strength and stiffness constitute the member design side. And K definitely represents the stability demand side of things as it represents assumptions made about the instability deformation of the structure, just like a P-Delta analysis does. It's easy to get confused about this because, with the effective length method, K shows up in our design equation. One could easily, and correctly, rewrite the Euler buckling equation like this if one wished to separate analysis from design:

Pf < PI^2 x EI / (KL)^2 <-- [ORIGINAL]

Pf x (KL)^2 / PI^2 < EI <-- [KootK REWRITE]

[ANALYSIS BASED DEMAND FOR STIFFNESS] < [DESIGN SUPPLIED MEMBER STIFFNESS] <-- [MORE KootK REWRITE]

For it is true that Pf, K, L, and PI are all, rightly, analysis parameters.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[DaveAtkins]

Then I would not use the term "cantilever column." That term is specifically used in seismic design for a type of lateral resisting system for which you are severely penalized.

What we are discussing in this thread is an ordinary moment frame.

DaveAtkins

 

[WillisV]

You are essentially asking if second order effects are required to be investigated when using the effective length approach, and the answer is yes they are, the requirements to implement p-delta did not appear in conjunction with the DM method and were actually required in the beloved green ASD manual which used effective lengths exclusively, so I would say that you are indeed correct in that the K=2 is a design column curve modification and separate from the also required inclusion of second order effects.