Lateral torsional buckling of channel sections

[Eagleee]

Hi,

I have a question regarding the general methodology of designing channel sections subject to bending (from transverse loads). I have to state from the start that I am unfamiliar with American design codes, although this may not be relevant as I am interested in how the problem is thought of, not necessarily into design equations. Of course, in many cases the two are linked. I'm trying to keep it short, so here goes:
1. For cases in which the transverse load acts through the shear center, do you think that design formulas used for the calculation of the elastic critical moment of bi-symmetric sections can also apply to channels? As a side note here, while the Eurocode does not give guidance on the critical moment, formulas can be found in NCCI's (Non-contradictory Complimentary Information), but they are specifically stated that they should be used only for bi-symmetric sections (I have read in multiple places that despite this, they can also be applied to mono-symmetric sections about the major axis).
2. When the load acts in the center of gravity, the member will twist. This is the most common case in practice. I have been able to find very little information about this. As I see it, this would have an impact on the elastic critical moment itself (since the load is destabilizing), in addition to needing to check a stability interaction between major axis bending, minor axis bending (arising from 2nd order effects) and torsion. Do you generally account for load eccentricity for this type of profile in bending and if yes, how so?

As I said, I am curious about the general opinion of the great engineers browsing this forum. I hope this question has not been asked here before (if so, I couldn't find it). I am very interested also in any suggestion regarding literature which tackles this phenomenon of LTB with a twist (pun intended).

 

[ahypek]

1. Channels are considered doubly symmetric and lateral torsional buckling is a limit state if the unbraced length criteria is met. Also, we use plastic analysis for flexure not elastic.

2. Torsion is a subject that most engineers generally don't touch. We tend to avoid it as much as possible but it exists and as long as it is within reasonable ranges (relative to the torsional rigidity/shear strength of the member) we disregard it. So yes, you can account for load eccentricity and check for shear capacity & rotation but try to avoid putting massive eccentric loads on your members.

 

[KootK]

Also, we use plastic analysis for flexure not elastic.

Yes and no. LTB capacity is generally calculated assuming elastic member properties. For intermediate values of slenderness, we usually interpolate between plastic moment and elastic LTB.

Do you generally account for load eccentricity for this type of profile in bending and if yes, how so?

The most common case is that the framing that causes the torsional load is also a source or rotational, torsion bracing. As such, the torsion is often eliminated or reduce to effectively inconsequential values. As you've no doubt discovered, dealing with flexural buckling and torsion simultaneously is pretty onerous from a calculation standpoint.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Eagleee]

Thanks for the replies. I agree, everyone tries to avoid torsion wherever possible.

Channels are considered doubly symmetric

This is basically the main design info, is it from American standards?

Yes and no. LTB capacity is generally calculated assuming elastic member properties. For intermediate values of slenderness, we usually interpolate between plastic moment and elastic LTB.

I fully agree, as imperfections reduce member capacity most around the slenderness you mention. I was mentioning the elastic critical moment in my original post due to the fact that it is used as a starting point.

As you've no doubt discovered, dealing with flexural buckling and torsion simultaneously is pretty onerous from a calculation standpoint

Indeed, torsion complicates things very much, very fast, but from a theoretical point of view, it is beautiful in its own way.

 

[JeanLucPicard]

Some use softwares to calculate precise LTB.

If you use NCCI, you accually use the extra torsion due to distance between load applied(centroid) and shear center with factors: k[sub]z[/sub]. As you probably know M[sub]cr[/sub] = Eulers critical force × distance. The distance is increased by k[sub]z[/sub] & C[sub]3[/sub].

I've calculated M[sub]cr[/sub] with few different methods for an quasi-angle section. As i remember, methods inculded two NCCI's methods and Thimoshenko method for angle sections. I've got, basically, simmilar results. I should mention that the angle between principal and central axis was small.

Live long and prosper!

 

[WARose]

Do you generally account for load eccentricity for this type of profile in bending and if yes, how so?

Sometimes.....just depends on the situation. Most of the time I'm using channels it's for stair stringers. I don't consider torsion in them because the tread (and it's connections) normally restrains that. In situations where I have to consider torsion in them, I have some spreadsheets i use.