P-DELTA effect and K value
P-DELTA effect and K value
(OP)
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?
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?






RE: P-DELTA effect and K value
RE: P-DELTA effect and K value
Other aspects that should be considered before you can consider using a K= 1.0:
RE: P-DELTA effect and K value
DaveAtkins
RE: P-DELTA effect and K value
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.
RE: P-DELTA effect and K value
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
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.
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.
RE: P-DELTA effect and K value
What we are discussing in this thread is an ordinary moment frame.
DaveAtkins
RE: P-DELTA effect and K value