Approach for designing unbraced (steel) frames. 12

This is a sway structure, I think the k- values for columns should be more than 1.

Yes, if a p-delta analysis was NOT being performed you would need to use K-values greater than 1. But what I am asking here is: does the p-delta analysis compensate for that.

"But what I am asking here is: does the p-delta analysis compensate for that."

hand calculation using code prescribed formulas (k values, etc)is an approximate solution to p-delta effect.

A computer program capable of doing such should be more refined than hand calculation.

Does that mean if you do a P-delta analysis AND use K values that you are being overly conservative?

There are 3 sources of buckling for this type of frame:

1. - largeP large delta effects - due to translation of ends relative to each other.
2. smallp smalldelta effects - due to deformation of member between ends.
3. buckling due to initial out of straightness of member.

In a second order analysis, 1 and 2 are taken care of in the analysis and 3 is allowed for by designing the member with K=1.

As shin25 said, the code K values are an approximation of this process.

csd

Thanks csd, et al.

Check out the latest AISC specification - they have three methods to deal with structural stability and I think two of these deal with using Pdelta analyses and how to treat the k values.

I agree with the above that a proper Pdelta analysis can substitute for k values > 1.

So can someone please confirm my understanding?

If I have a sway structure and I am NOT performing a P-Delta analysis using my analysis/design software, I must use the nomograph of sway frames to find the appropriate K values?

If I have a sway structure and I AM performing a P-Delta analysis using my analysis/design software, I can use the nomograph for non-sway frames despite having a structure that is sway?

I think that based on what was said here you would still have to use K=1.0. If you use nomograph for non-sway frame you will k<1.0.
That being said, I still have to convince myself that you can get away from K values by doing a P-delta analysis.
I am not convinced yet.

alright, thinking about this a little further. I don't think you can use a k=1.0 for a sway frame just because you do a P-delta analysis. To say that P-delta analysis and k values are accomplishing the same thing is IMO not correct. K values have been around for quite a qhile, correct? It is my understanding that second order effects being accounted for in the code is relatively new thing.
Also, I believe what CSD says about the second order effects taking care of two of the three buckling causes, but in Chapter H (pg 16.1-70 of the 13th edition), under design of members for combined forces, it clearly says Pc is teh design axial compreessive strength determined in accordance with Chapter E. In chapter E they make no mention of allowing a k=1.0 if you do a P-delta analysis.
The P-delta analysis is just giving you increased moments to design for. The k value is affecting the axial strength, I don't think they be substituted for each other.

Study the Direct Analysis Method. The whole thing is based on k=1.0 to get away from all this terrible effective length stuff.

Here are the three methods that AISC identifies:

[blue]DIRECT DESIGN METHOD[/blue]
Limitations: none
Analysis: Second order (either computer Pdelta or use
the B factors in chapter C)
EI and EA: For members - used reduced values of EI/EA
Notional Load: to account for initial
out-of-plumbness use 0.002(Yi) at each story where
Yi is the gravity load (D+L) from LRFD combo or 1.6 times the ASD gravity load.
K value: k=1.0

[blue]EFFECTIVE LENGTH METHOD[/blue]
Limitations: [&Delta;]/[&Delta;]_o < 1.5 where
[&Delta;]=Pdelta deflection and [&Delta;]_o=
first order deflection.
Analysis: Second order (either computer Pdelta or use
the B factors in chapter C)
EI and EA: Use actual EA and EI values
Notional Load: to account for initial
out-of-plumbness use 0.002(h) at each story where
h = story height.
K value: k= based on sway frame (i.e. >1.0)

[blue]FIRST ORDER METHOD[/blue]
Limitations: [&Delta;]/[&Delta;]_o < 1.5 where
[&Delta;]=Pdelta deflection and [&Delta;]_o=
first order deflection. AND P/P_y < 0.5 for
all columns contributing to lateral stiffness
Analysis: First order
EI and EA: Use actual EA and EI values
Notional Load: Apply additional lateral loads = 2.1([&Delta;]/L)Yi where Yi is the height of each floor level and [&Delta;]/L is the max. ratio of first order drift to height at each level and Yi is the gravity load (D+L) from LRFD combo or 1.6 times the ASD gravity load.
K value: k= 1.0

star for JAE for that post - very comprehensive. So, for a RAM model, we should be inputting an additional lateral load at each floor level (in each direction) to account for the leaning columns and using a k=1.0. The notional load should be in there no matter what, it appears.
It seems the only difference between the direct design method and the effective length method is that the effective length method uses the initial EI and EA values. You can account for the inelasticity using the tau sub a factor, but then you still get a k not = 1.0.

The notional load can be replaced by putting the imperfection into the model (ie. moving a node over in the model l/500) instead of applying a load.

That seems quite cumbersome. It would need to be moved over H/500 in both directions correct? Additionally, if the building isn't perfectly regular, you need to run it once with it moved in the +x and +y directions and then again with it moved to the -x and -y directions to account for the critical case, crrect?

Yes, it has to be checked both ways if you are modeling the out of plumbness, but you would have to do that with the notional load also.

oops...sorry.
[red]CORRECTION[/red]
The notional load for the Effective Length Method should read:

Notional Load: to account for initial
out-of-plumbness use 0.002(Yi) at each story where
Yi is the gravity load (D+L) from LRFD combo or 1.6 times the ASD gravity load.

Just like the Direct method....sorry for the confusion.

Okay, I am still very much confused about this topic.

I did a fair bit of research on this matter and it seems like there is a major difference between AISC and CISC codes (the latter is which I follow.)

According to my understanding, AISC specifies that you must use K>1 even if you conduct a p-delta/p-sigma analysis. You are only exempted from using the magnification factor U. That is all! You can get away with using K>1 by applying the loads incrementally in your model and meshing your columns.

The CISC, I believe, allows you to use K=1 if you conduct a p-delta analysis. (Which could be why the CISC handbook does not even have a nomograph for K>1)

Though with all that said, I am still not quite clear as to why the K-value is treated independently from P-delta analysis in the AISC code. A few individuals stated that K factor is to estimate P-delta, but from the literature that I have read, this is NOT TRUE, but I don't know why!

Thanks.

I am sort of in agreement with clansman. The k factor goes directly to the design axial strength of the column. Second order analysis is going to affect axial load significantly less than it will moments. I am failing to see the direct correlation between second order analysis and k factors.