Lateral Torsional Buckling of Hollow Steel Sections 1

Warping constant is zero for closed hollow sections.

I don't have my code in front of me, but if I remember correctly they don't explicitly require LTB checks for closed hollow squares. I believe in 13.6 (laterally unsupported) it says for closed square and circular sections you just check it as per 13.5 (laterally supported)

For a square HSS beam? I don't think LTB is possible. You'd have to have something like a really tall rectangular HSS with a short width to cause any LTB in an HSS. Even then, I'm not sure.

The key is that you need the weak axis buckling and torsional stiffness of the beam to be significantly lower compared to strong axis in order to have LTB. It just doesn't happen with HSS.

According to the AISC Manual, a square HSS will experience unacceptable deflection long before it experiences LTB.

DaveAtkins

Hi,

In my view you check regular bending/deflection/shear. A hollow section won’t buckle LTB style - unless you’re into some totally obscure slender plate girder that’s massively disproportionate of course which I assume you’re not.

We had some fun investigating the likelihood of LTB in tubes here: Link. The sketch below is some of my hyperbolic handiwork from that one exploring the possibility of LTB in a section bending about its weak axis. In summary:

1) Theoretically, you can LTB anything.

2) Practically, it's very difficult to LTB an HSS until the [Ix:Iy] ratio starts to get high.

OP said:

I have not found much information on the warping constant for hollow sections. Logically, it would make sense for it to be negligible or zero

Click to expand...

This raises another interesting point of pedantry. While the the warping constant for closed sections is often taken as zero:

1) It is, in fact, not zero.

2) It's actually more than a comparable wide flange.

3) I believe that it is truly zero only for circular cross sections.

3) We take it as zero simply because, for a closed section with a modest [Ix:Iy] ratio, the St.Venant torsional stiffness skyrockets and dominates the expression for torsional stiffness. It's just a convenient way to zero out the term that accounts for warping torsional stiffness.

An SHS can’t avoid work by buckling, thus it won’t buckle.

It’s an interesting question as to what the slenderness cut off is for hollow sections. How narrow do they have to get for it to be easier for them to buckle than to keep on bending...

The latest AISC spec has LTB buckling capacity formulations for both SHS and RHS. So one need no longer resort to H:W rules of thumb which I've encountered in the rang of 2.0 to 4.0.