Unbraced length/analysis of bent/kinked columns

[bookowski]

Is this correct: I have kinked columns, for example the column extends 2m and then kinks at 10 degrees and continues another 2m. This is intentional, not the result of a failure. To analyze the columns I am breaking it down into smaller segments (say 0.25m) and running a p-delta analysis. Using this approach I should be able to consider the unbraced length to be my segment length (0.25m) when checking capacity. Is that right?

 

[msquared48]

Not that I know of.

I would not even rely on the kink for any lateral support at the 10 degree figure. You still have the orthoginal direction to consider. Depending on the external lateral support, I would look to the full length of the column as the lateral unsupported length.

Mike McCann
MMC Engineering

 

[bookowski]

I don't think this matters but just to add a better description - the kink is in the strong direction, in the weak direction there is fairly frequent bracing.

I believe that using the full length for Lb and using AISC equations is giving me a reduction based on secondary effects. By running a p-delta, and with an initial deformation (which is provided by my kink), I should already be accomplishing the same thing. Does that not make sense?

 

[SAIL3]

KL of .25m is definitely out.
If the col is modeled with the kink, then the program will account for the resulting induced moment.
I would use the ASD 89...no P-DELTA in the program and get the resulting axial and moment forces...then use the fomulas in that code that account for incidental P-delta affects.
What KL to use is an engineering judgement call based on col fixity and controling unsupported length of the col.

 

[MJB315]

Bookowski,

As a "to keep in mind" comment: Don't forget to follow the horizontal loads that are caused by the kinked / diagonal columns through the structure (e.g. horizontal shear at the base plate, horizontal shear at the top-of-column connection, following that horizontal force through the structure). It's just something that can be overlooked at times.

Unless material costs are a major concern, I'd certainly consider a K = 1.0 and the full length of the column as your unbraced length (unless there are braces intersecting the column). P-Delta analysis or not, I wouldn't consider the kink as a restraint in-of-itself.

MJB

"We shape our buildings, thereafter they shape us." -WSC

 

[WillisV]

bookowki - I happen to agree with you if done properly. You also need to reduce the stiffness of the column for residual stresses etc. The unbraced length for LTB of moments would still be the full unbraced column length between brace points, but the unbraced length for flexural buckling of the column under axial loads could be taken as the analysis segment length (node to node). You won't find this explicitly in the code, but its the basic idea behind the Direct Analysis method.

 

[bookowski]

Willis - Yes! I am glad that I have someone in agreement, I was starting to doubt my logic. It's a rolled shape so I do have to account for residual stresses and the LTB length is still defined as the length between true brace points (not the segment length). This makes sense, I just wanted to find some reference that verified my thinking. Haven't seen anything yet though. Thanks for your input. These are very long members and are really designed to their max, I need to take advantage of everything that I can to make this work.

 

[ishvaaag]

I also agree in that length between nodes -I use to call it segment length- with K=1 may be used when all the specs for direct analysis are applied. I also agree with WillisV that the safe approach is using the actual conditions of bracing to determine the length between braces to determine flexural capacity.

However I find suspicious AISC does not state explicitly use actual length between braces for flexural strength determination with the same clarity that use K=1 (even for this, you can use segment length should be clarified) in direct analysis context.

It is surmised that the inclusion of P-Deltas, initial imperfections, and material stiffness adjustment reveal the augmented solicitations that stability requirements may ask for.

This means that the structure at the stable final status at the factored level is showing all the augmented values of both XYZ displacements and rotations about such axes, upon which no further displacement or rotation may be attained under the set of standing factored loads, stability requirements included.

This SHOULD mean that in the same way that we can use K=1 and segment length for the checks since the nodes are linearly fixed at the final status and showing the stability enlarged moments at ends of segments, the nodes are to be also rotationally fixed and showing the enlarged moments and rotations at such ends, and we SHOULD be able to resource to in-segment behaviour, i.e., again, segment length, to ascertain the expected flexural capacity of some member that will have such (final, stable) solicitations at ends of segments.

Since however what WillisV says may very well be the current understanding of the issue for flexural strength in direct analysis context -in spite of the faible clarity about the matter in the code, simply letting the design fall in the ordinary statement of Lb, without any further precision- I will try to find document or tutorial or whatever preferably within AISC docs to clear the actual standing.

 

[JoshPlumSE]

Agree v much with WillisV. Only difference is that I would still prefer to take the length between brace points as the flexural unbraced length. His argument is valid, it's just less conservative.

If I were desperate to get the column to work, then I would consider using segment length for flexural buckling length (as WillisV suggests). But, I'd want to be very diligent in reviewing my design calcs and my analysis results. I might even consider adding a slight lateral load (similar to notional load) at those segment joints just to introduce some extra out-of-straightness for the P-Delta analysis.

 

[bookowski]

I am sticking with the brace points for the flexural unbraced length. I would need to introduce some initial deformation or nodal load if I didn't and I'm not ready to be that aggressive anyway.

I've been looking for references for this and it is laid out fairly clearly in Eurocode 3 in case anyone ever comes up with this problem in the future. Thanks for the inputs.

 

[ishvaaag]

Respect the question of if segment length can be taken as unbraced length for LTB prevention, in the scarce time I have been able to examine the question looking for precise info, it seems AISC is (reasonably) unwilling to go for that. When dealing with this matter we are doing with both the member and structural system behaviour, and whereas just dealing with effects from initial imperfections it seems reasonable notional forces may provide a substitute for the initial imperfections; but when dealing with LTB, the initial imperfection of concern itself is a rotation of the section on own axis itself, and the literature on what one has read (unfortunately for complete understanding, always too little) has never been looking LTB that way. So, in the absence of code and literature support, and of a practical way to establish initial rotational imperfections for 1d elements, I need to conclude that when dealing with LTB actual length between (code compliant) braces needs be considering when stating the flexural strength, what brings me entirely in agreement with what WillisV says.