"Do not use K-factors if you're running a p-delta/p-sigma analysis" 4

[GalileoG]

Hello all,

This morning my boss came around the table after reviewing my structural model and states that the reason why we use the effective length factors is to account for p-delta effects. So, if we are to run a p-delta analysis in our structural model, then I can take k = 1. Of course, when my boss stated the above, that was earth shattering for me because forever I've been running a p-delta analysis while using k factors greater than 1. I remember reading a discussion about this on this forum a long time ago, but I can't seem to recall what the verdict was, but I do know there were a lot of confused fellows like me.

I follow the CSA-S16 (Canadian)

Thanks

 

[Lion06]

I don't believe it is as simple as running a second order analysis because computers have been doing that for some time and the K=1 just made it into the steel spec. You need to also account for material inelasticity (which is where the reduced EI comes in - if you don't use this in your analysis you will be underestimating your second order effects which makes the K=1 invalid), and you must also account for material imperfections and erection tolerances (notional loads).

 

[frv]

Your boss is wrong.

K factors account for member fixities other than those in the Euler column (pin-pin w/ no lateral translation).

Your boss is probably referring to the Direct Analysis Method. As StrEIT summarized above, carrying out a RIGOROUS 2nd order analysis is only one part of the DAM. You must account for loss of stiffness, member imperfections and so forth.

 

[connect2]

k = 1.0 CSA S16.1-94 and forward of course. See 'New Canadian Provisions for the design of steel Beam-Columns', Kennedy et al, Can. J. Civil Engineering, Vol. 17, 1990. In the abstract the following 'For frames dependant on the frame stiffness for lateral stability, no longer is the traditional method, using effective length factors greater than one, allowed.' You are required to do a second order analysis though. Which is the point.
You might want to read 'Proposed provisions for the design of Steel Beam Columns S16-2001', Can J. Civil Eng. Vol.27, all those recomendations were adopted in CSA S16-01, S16S1-05 and Supplement #1 to it as well.

 

[connect2]

The second paper cited contains this statement 'In other words, the function of the notional load is to allow the use of actual length of the column in computing the compressive resistance in sway frames rather than using effective length factors greater than 1.0'. The purpose of notional loads. Material imperfections, erection tolerances, residual stresses are accounted for elsewhere.

 

[Lion06]

connect-

That is not the way it is for AISC. If you don't take care of the inelasticity, erection tolerances, etc. in addition to the notional loads you can't use k=1.0. That is the basis for the DAM which is the only situation in which you can use k=1.0. If you don't use DAM, then you are, by default, using the effective length method (which by definition uses an effective length, kl).
Again, this if for AISC.

 

[JAE]

StructuralEIT, your quote:

and the K=1 just made it into the steel spec. 

I think is meant in reference to the use of second order methods in AISC and not to the code in general, right? k=1.0 for columns, struts, etc. has been around since Adam bit the apple.

 

[Lion06]

JAE-
Right, I guess I should have said that k=1 in all regardless of lateral system used just made it into the spec meaning you can now use k=1 where you couldn't before (i.e. sway frames where k is greater than 1). Like you said, k=1 for gravity columns (regardless of lateral system), struts, etc. has always been used.

 

[Lion06]

But, in order to qualify for k=1 for columns, regardless of lateral system, as questioned in the OP, you need to meet more criteria than simply doing a second order analysis.

 

[frv]

StrEIT-

I don't have my spec in front of me, but doesn't the amplified second-order method also allow you to use k=1?

That's the method with the B1 and B2 factors.

 

[Lion06]

Well, you can use it, but it is part of the DAM. It is just an acceptable alternative to the rigorous second order analysis, but you still need to comply with the other requirements.

 

[Lion06]

e.g. the B1 and B2 must be based on the reduced stiffness factors and you must still include notional loads

 

[ash060]

You know that AISC has a little online seminar that is free to watch that explains everything

http://www.aisc.org/Content/Navigat...ls/A_New_Approach_to_Design_got_Stability.htm

I watched it is very informative, and has all the information on the DAM

 

[asixth]

Is the k-factor referred a moment amplification factor. I had the situation not so long ago where I was designing a reinforced concrete column for lateral forces by an elastic analysis and required an additional moment amplification because of the slenderness of the column. However, the design code I was using allowed an amplification factor of 1 when using a second-order analysis. This then raised the question, if I am to perform a second order analysis, I should be modelling the vertical loading so I can adequatley account for the p-delta effect which I think the k-factor refers to.

 

[Lion06]

The amplification factor of 1 makes sense if you are doing a second order analysis since the amplication factor is meant to BE the second order analysis.
k factors (or effective length factors) are meant to account for end conditions that are other than pin-pin, NOT to account for second order effects. You can go through the derviation of buckling loads (even using energy methods - or you can use the more time-consuming differential equations) and you will see that the buckling load is dependent largely on the end support conditions and that the difference between those buckling loads is the effective length of the column (which can be considered the distance between inflection points). Since it is the distance between inflection points that is considered the effective length of the column, it is clear that ACTUAL length needs to be replaced by an EFFECTIVE length when calc'ing column buckling loads. Doing a second order analysis does not negate the need to account for end support conditions UNLESS you account for all the other criteria and variable as outlined in Appendix 7 in AISC 360-05 for the DAM.
Just think about the requirement for the effective length method.........You are still supposed to use a second order analysis, but you ALSO have to use effective lengths of columns.
Doing only a second order analysis DOES NOT, in and of itself, automatically allow the use of k=1 (unless you have a braced frame).

 

[Lion06]

I don't know if this is included in ash060's link above, but check out this paper forwarded to me by AISC some time ago in response to a question.
Please note that there are cirumstances in which you can use k=1.0 for moment frames in both the second ordeer analysis using B1 and B2 as well as the first order analysis methods, BUT you need to meet several other criteria IN ADDTITION TO the analysis (e.g. drift ratios, see the paper). It's not accurate to say "a second order analysis automatically means k=1.0" for frame columns.