Column K Factor - Different per floor, self-check 3

[AggieYank]

Column K factors:

You have a column continuous from the foundation to the 3rd floor. Each floor is a diaphragm.

Column is fixed at the foundation.
Column is tied to 1st floor girders with pinned connections.
Column is tied to 2nd floor girders with pinned connections.
Column is tied to 3rd floor girders with pinned connections.

There is x bracing from the foundation to the first floor.
There is no bracing from the 1st to the 2nd floor, the idea is that the columns will resist lateral movement through their own bending.
There is a moment frame from the 2nd floor to the 3rd floor.


My answers. K factors are according to the latest AISC manual.
Foundation to 1st floor - K=0.8 (Fixed - pinned).
1st floor to 2nd floor - K=2.1 (Continuous up = fixed - free at top)
2nd floor to 3rd floor - K = 1.0 (pinned - pinned).

Is everyone in agreement with me, or do I have something wrong. Thanks. I was recently questioned on this, and wanted to be sure.

 

[AggieYank]

Thanks UcfSE.

jmiec, the second level doesn't brace the column against lateral translation. The column(s) brace the second floor against lateral translation. I might not have followed you. If you meant third floor braces column from translation, or you meant rotation / buckling at the second floor then ok.

But if you design the column as pinned from the 1st to the 3rd floor, what is stopping the second floor from moving laterally? Do you design the column as 1) pinned from 1st to 3rd floor, then 2) cantilever from 1st to 2nd floor supporting laterally the second floor? And if so, what k factor would you use for the analysis of 2).?

 

[AggieYank]

Ok I follow you jmiec. The moment frame is a portal frame, where the columns are separate from building columns, and so you wouldn't analyze the portal frame as a two story frame, and the frame wouldn't brace both the second and the third story. The portal frame only braces the 3rd floor.

 

[miecz]

AggieYank,

Yes (to your last post), the portal frame has no intermediate level, except to pick up load, and it's columns extend from the first to the third level. With this length and K=2.1, KL will be, like, 40 feet(!) for the portal column.

With this model, the only thing holding the second floor from translation is the bending stiffness of the portal column. Doesn't seem like this would calculate.

 

[AggieYank]

jmiec, I posted this before, but you may have missed it / skimmed it.

The moment frame is a portal frame from the 2nd to 3rd floor, where the columns are separate from building columns, and so you wouldn't analyze the portal frame as a two story frame, and the frame wouldn't brace both the second and the third story. The portal frame only braces the 3rd floor.

 

[JAE]

AggieYank - wow - I'm gone for a few hours and look at the discussion! Nice to know you have great people such as haynewp, jmiec, and UcfSE to get input from.

I would suggest one other thing...I've been touching on the P[Δ] aspect and I just finished doing a quick study of RISA after attending the new AISC seminar on the 13th Edition Manual. Chapter C in the new manual has three different methods of designing for frame stability - one of which suggests a full second order analysis. But they were careful to point out that you have to consider BOTH P[Δ] and P[δ] effects - the first dealing with the end nodes of the column (sway effect) and the [δ] effect due to curvature along the length of the column.

They mentioned that most programs only deal with P[Δ] and not the other. I checked RISA and this is true of the program...only [Δ] considered. But I found that by adding lots of joints along the length of the columns, you can take into account the curvature effect as well - works great wtih RISA's P[Δ] turned on. Use a physical member in RISA and nodes about 1 or 2 feet apart and see what sort of curvature....or stability....you truly have.

 

[miecz]

AggieYank,

But this is my point. Because the second floor is essentially hanging in the breeze, you can't analyze the portal as though it is pinned (or fixed) at the second level. The portal is pinned at the top of the braced level, and extends for two levels.

JAE,

Thanks for the RISA tip. I'll have to try it. Great to know that RISA's physical model will consider the small delta effect.

 

[AggieYank]

jmiec. The portal doesn't extend down to the second floor. It will in no way take 1st-2nd floor lateral load. If the columns were truly pinned at the 1st floor, the building would fold over like a deck of cards. But the columns aren't pinned, they're continuous up through the first floor, and these columns are what stop the 2nd floor from laterally translating (too much).

 

[pba]

Just some thoughts from having skimmed through this discussion:

How is the column restrained about its minor axis. All this discussion relates to major axis only...

I tend to think very simply about such problems. If you are reliant on the stiffness of a column passing through the first level then that stiffness needs to be fully realised in the frame that is built. This means that there has to be force transfer into the beams or column below. If this cannot be proved using a better approach than 'gut feeling' it is probably unwise to rely on it.

Likewise what is the difference in connection at second level that makes this beam/column interface behave differently? Again if you can't explicitly demonstate that restraint exists how can you justify using it in the design?

It genuinely goes against the grain to say this - If you can't justify this by hand then a 3D computer model may be of help in determining the effects of the various combinations of fixed or pinned joints.

Always remember we have a duty to be conservative in our assumptions. When you have to do design in the 'grey areas' then conservatism is even more important.

 

[miecz]

AggieYank,

I think I see your point. With a diaphragm at the first floor, every (continuous) column in the building helps to restrain lateral force from the 1st to 2nd floor level.

I wouldn't know how to analyze it that way, so I would be stuck using the conservative assumptions stated above. Sorry I can't be more help.

 

[AggieYank]

pba, minor axis is taken care of. No need to make this more complicated than it already is. I also tend to think of things as simply as possible. The joints are pinned at the 1st, 2nd, and 3rd level but the columns are continuous through these joints. I'm always conservative in the "grey area". Also known as, "when in doubt, make it stout".

As far as "If you are reliant on the stiffness of a column passing through the first level then that stiffness needs to be fully realised in the frame that is built. This means that there has to be force transfer into the beams or column below. If this cannot be proved using a better approach than 'gut feeling' it is probably unwise to rely on it.": There is lateral force transfer into the girders at the first floor diaphragm, but no transferred moment. When you put it down on paper, it's relatively simple, and isn't a gut feeling.

The column / beam connection at the second level is the same as at the first level. The difference in the column from 1st to 2nd level and the column from 2nd to 3rd level in the analysis is that there is a portal moment frame which provides lateral resistance at the 2nd-3rd level, meaning the columns are sway inhibited. The columns from the 1st to 2nd level are sway UNinhibited as they rely on their own stiffness / strength to provide lateral resistance.