K Factor for Lateral Column

[lutein]

Greetings
Could someone please shed some lights on this question?
I am analyzing a braced frame (cross bracing). By AISC Graph to determine K value for column, should I use Sidesway Inhibited or Uninhibited graph? As we know, the K value for a lateral frame depends on the inflection point of the buckling mode shape. For a frame that is braced by a 'yieldable' material, i.e. steel, I think it is unsafe to use a K value of 1.0 or less than that. However, there is no other approached suggested by AISC other than the Nomograph in Commentary for Chapter C. I was wondering is there anyway that I could determine the EXACT K value for lateral columns, so that I would know my assumption is good?

Please help.

Thank you

 

[JAE]

I would use k = 1.0. You have no sidesway in the frame due to the X brace - and once you have no sidesway - the chart gets you a max. 1.0.

Sidesway Inhibited is defined (by me...and, I think, consistent with AISC) as a condition in a frame where the lateral stability of that frame does not depend upon the column bending but rather some other "external" device such as a shearwall or brace. Thus, even if the column does sway to some extent, the frame does not depend on the column stiffness to prevent the sway.

Read the Commentary in Section C2 of the latest (Third Edition) of the AISC Manual.

 

[lutein]

JAE,
Thanks for your good advice. I agree with you that a braced frame does not really depend on column stiffness to prevent the sway (of course, colummn stiffness does matter, but not major).

Is there anyway that we could determine the "exact" K value for these braced columns? I tried to use Elastic Critical Buckling Analysis to determine the critical buckling load for column, and by that, I can determine the K value,
K = (pi/L)*SQRT(EI/Pcr). Do you think this would give us the exact value of K?

I would like to perform such analysis to the critical frames just to be sure, for 'sleeping' purpose,

Please advise

 

[JAE]

If you are checking an existing design and need to get the "exact" K value due to a tight load capacity condition, I'm not cognizant of any other K method such as you discuss above...perhaps some others out there have more savvy in that arena.

For a braced frame....K=1.0 is the correct, and maximum, K value to use. You would not be unsafe using 1.0.

If you have a seriously flexible structure, where you do have X braces, but maybe have a very flexible, long diaphragm, then the "braced" columns would sway with the diaphragm and, in their laterally altered state, still behave as a pin-pin braced column. You would just have to be sure to include the second order effects in the design of your diaphragm and braces.

Sorry I can't help you further with your concept.

 

[lutein]

JAE, I really appreciate your helpful input. Thank you.

 

[idly123]

Hi,
I belive this answer should be OK..

The decision on wether a frame is braced or unbraced depends on the "DEGREE OF FIXITY" of a joint...this decides wether there is a lateral displacemnt or not..and this depends not only on the column stifness but also on the stifnesses of all members that are coming in to the joint.
I belive american code does have some provision for deciding wether the frame in a particular storey is braced or not ,this is based on the "STABILITY INDEX Q"..this is a function of the storey height, total laterla loads, individual axial loads in compression members and the flexural rigidity of all the members in that storey.....for a more detailed expression and various methos of evaluation please refer the Book on "Reinfoced concrete design by Unnikrishnan Pillai and Devadas menon"........Conceptually the best book i have come across till now.
Hope it helps
regds Raj

 

[JAE]

Well, yes, Q (stability index) does relate to determining whether a building is sway or non-sway (in terms of a moment frame). Here we have a braced frame where the columns are NOT participating in keeping the frame upright.

ACI uses this (see chapter 10). But the original post above was concerned with a steel braced frame. The interior columns (not being a part of the X brace) do not behave as a FRAME COLUMN. They are simply pinned columns "going along for the ride" with the drift of the building. Their lateral drift adds to the overall frame second order effects, but they do not "feel" those effects.

 

[lutein]

I agree with both of you guys:
JAE - I agree with you that the columns in braced frame do not play amjor role in resisting the sway.
DRRaj - I agree with you that the sway properties of the frame has to do with the column-girder-lateral sway-lateral shear.

Here is what brought this up - I was working on a building more than 6 stories high. The sway was like 2", which is fine over this story height. But with sway of 2", I don't feel good to treat the frame as braced frame. So, I ran an anlaysis, and determined that one of the columns has a K of 1.5. Reason? Possibly because of the sway. In this case, I tend to agree with the Q formula. However, as mentioned by JAE, AISC recommends sidesway inhibited graph for braced frame......

Here is another exmaple that I ran through : A pined-pined column, the critical buckling load = pi^2 * E * I / (KL)^2
A critical load buckling analysis gives me K=1.0. When I applied a lateral movement to the column, K>1.0. Because the inflection point of the column moves up.

However, I am still working on running a finite element anlaysis on a braced frame to study the effect. I will post the result when I am done.

But, thank you very much guys for your time and help!

 

[trainguy]

This business of running FEA analyses on braced frames to determine k_factors / buckling loads is has usually been performed by regulatory authorities in preparing their design codes. I suggest you carefully apply the procedures from your design code, including reading the commentary, and you will be able to design accordingly.

For example, selecting K=1.0 works for braced frames IF you have included 2nd order effects in your analyses. If it's for seismic loads, the 2nd order effects need to be amplified for inelastic deformations. All this stuff is usually documented such that you DON'T NEED to run critical buckling analyses. Some codes (like the Canadian S16.1) even provide amplification factors that can be used directly on linear frame analyses. As long as you are in conformance with the code's strength, stability, and deflection requirements, you should be OK.

 

[idly123]

Hi,
I have another point to make..a well judgement of bracing again depends on degree of fixity of joint. This is better understood by joint characterstics and M-phi relation ship for the joint, only then can u decide wether its going to be a moment frame or a sway frame.
hope it helps
regds
raj Raj

 

[JAE]

trainguy - you said what I was trying to say...only better.

 

[longisland]

Hi,
I'm inclined to agree with DrRaj that the k value is dependant on the joint detailing. As you have demonstrated in your 2 models that the column inflection point shifts as you change your boundary condition at the column end.

 

[JAE]

Whoooo...you all are making this way more difficult than it is. The original post indicated that this is a steel X-BRACED structure. Therefore, it is BRACED....therefore you use k = 1.0 for your columns. The frame does not depend upon the lateral moment-stiffness of your column. The column is just going along with the frame laterally for the ride....not participating in the bracing.

If there is an inflection point beyond the column ends, then you are assuming that the column is rigidly attached to the frame with some kind of moment connection. This is not typically done...you don't go to the trouble of X-bracing a frame and then design moment connection at all the gravity columns.

Thus, you have a pin-pin connection on your column and you have k = 1.0.