Lateral Torsional Buckling 1

[Rocks1]

Does anybody know a method for determining "rt" in AISC 360-16 Formula F4-8 for Lateral Torsional Buckling for the beam shape below?
The top flange is in compression, The combined shapes are an S24x105, C10x15 and a 7/8x12 plate.

 

[JAE]

F4 technically doesn't apply to your non-symmetrical shape.

But that said, generally rT is based on the weak axis moment of inertia of the compression flange plus 1/3 of the compression web. For your case, if the side channel is in compression along with the top beam flange then you might get some general value of moment of inertia of that.

You could also ignore the channel, and design the beam to resist LTB without it - which I think would be conservative.

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[JoshPlumSE]

You could also ignore the channel, and design the beam to resist LTB without it - which I think would be conservative.

That's got my vote.

 

[Agent666]

This type of general built up section perhaps lends itself more to the use of a rational buckling analysis rather than trying to apply code equations that may have been intended for more standard sections.

It's pretty easy to do in something like MASTAN2, and it's free. Check stability fun module 4 for the basics, I believe there are also YouTube videos for running through the setup for each module. Basically you are able to output a buckling moment for any cross section under any loading regime using this approach which can be used directly in AISC provisions.

 

[JoshPlumSE]

Agent666 -

That seems like a reasonable thing to do if you're writing a paper on the subject or trying to get your PhD. It's not always safe to just grab software and use the output. Not, for something like this, you would need to understand what the program is using for residual stress assumptions, member imperfections and probably a number of other things. I'm sure it can be done, but it would be a lot of work unless you've been using MASTAN for similar projects for awhile.

For regular design of a simple structure, it's probably overkill. The amount of time and energy you spend on that probably isn't worth any cost savings.

 

[Agent666]

Josh, if you work through the stability fun modules for mastan2 it explains all these options and the exercises are built around comparing these options directly against code equations to show the exact same answers in many cases. Mastan2 allows for applying initial imperfections, residual stresses, etc. It's got a pretty clunky interface but if someone was to work through the stability fun modules it'll become second nature.

While I agree it is a higher level of analysis requiring a higher level of understanding, you certainly don't need a PhD to understand or do these types of analysis in your day to day work. For unique analyses I have more faith in the method than fudging code equations meant for singularly or doubly symmetric sections to suit for non symmetric sections. You are then in an area where you have no idea if the answers are correct/conservative or grossly in error.

I certainly agree the alternative of ignoring the channel may be conservative. For this section there is no symmetry, so my thinking is the principle axes do not align with the web. Therefore for any vertical loading there is an out of plane response (bending about both axes). Should this be considered, is it significant?

I don't know just looking at it as never experienced designing this type of non symmetric section. But I'd look at this in a bit more detail than your usual beam, and the buckling analysis would be one method to justify this aspect. Certainly you'd like to think if the top flange is in compression that the channel increases the resistance to LTB. The thing is it may not be conservative if the out of plane deflection due to the rotated principle axes effectively increases the effective initial imperfections. A rational buckling analysis and using the answer in accordance with your code is a good approach in these situations to justify if your code allows it (most do but its rarely used I guess).

 

[JoshPlumSE]

Agent666 -

I've messed around with MASTAN a bit. Not a ton, but enough to suggest that it can do what you are saying. I actually think it was a real good idea to suggest taking a look at it is one legitimate option. It wasn't one that I though about, but it could be a real good solution.

That being said, I wouldn't want to do it for a job like this under a normal design deadline. And, that's even with my being reasonably familiar with the program. Part of it is that I don't know how I would present this in my calculations for plan check review. I'm pretty sure they'd accept the idea that just ignoring the channel would be conservative. However, I'm not sure what it would take to convince them that the MASTAN analysis and all the assumptions behind it are legitimate.

Caveat: I have worked for companies that do structural analysis and design checks for most of the last 17 years (first with RISA now with CSI / SAP / ETABS). While I'm intentionally trying to promote or criticize any particular program, I am not exactly an unbiased observer.

 

[Agent666]

Yeah totally understand that reservation regarding getting it reviewed down the road. The fact that the reviewer doesn't understand this type of analysis however shouldn't really be a reason for not allowing it, if the code allows an analysis like this. Time to get a better reviewer at that point?! At least Mastan2 seems to tick all the boxes with respect to the 2nd order effects (initial imperfections, residual stresses, considering warping stiffness, etc) that need to be allowed for. This is of course provided you implement them in your model, which is another criticism of mastan2 that you start with none of the things you really need to correctly do the analysis being selected as defaults, another is printing anything from it is a chore.

I'd advocate you could simply keep these more detailed results to yourself (piece of mind for you as the designer) and present the simplification for review, and if its questioned present the more rigorous analysis (path of least resistance). This only works if both analyses show it works though, and you are often resorting to these more rigorous analyses because the simplified approach didn't quite work and there might be a significant benefit in consideration of the effect of the channel towards LTB.

I reckon if you knew the most critical member based on initial checks, that setting up the model and running it would take at most about 1-1.5 hours. I guess that needs to be held up against whether the result has some payback in terms of using less material/improved behaviour and can be tolerated with respect to the size of the project and the like. If this was a single isolated member, just ignore than channel and make it larger and move on, if it was used 100 times throughout a building I'd look at it in more detail.