Interesting Case of LTB of non-prismatic beam with long unbraced length

Interesting case study for those here to consider.

Task involved reinforcement of existing PEMB main frame girders. A similar approach could be used on crane rails with hat channels.

Several of the girder's bottom flange lateral braces were removed starting at the haunch and moving in towards the ridge.
Removal of these braces compromised the bending moment capacity of the section and requires retrofit.

Repair strategy involves placing a continuous channel on the bottom flange of the girder over the entire newly unbraced length.
Calculation procedure for this condition was adapted from AISC DG 25 for non-symmetrical sections. Each calculation was run using actual combined section properties, but assuming the section is a plate girder.

Section properties for the combined section are calculated at each end, and the middle of the unbraced length.
LTB strength calculated using Cb and Section 5.4.3 of DG 25.

Findings were:
-Additional Channel increases bending moment strength over the existing condition by around 20%.
-Additional Channel does not preclude LTB, the bending moment strength is still controlled by LTB.
-Not sure what the conventional wisdom on Hat channels for crane rails is, but for this particular section the hat channel does not provide bracing equivalent to continuous bracing.

Hope someone finds this interesting, feel free to chime in with any questions or comments.

dL said:

Hope someone finds this interesting, feel free to chime in with any questions or comments.

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I certainly find it interesting.

dL said:

Additional Channel does not preclude LTB, the bending moment strength is still controlled by LTB.

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I would have to think that this is just a matter of whether or not the right channel has been selected. By way of the purlins, I would anticipate top flange lateral restraint approaching continuous. And, with a stiff enough channel, the bottom flange would also have continuous lateral restraint. Obviously, with both flanges laterally restrained, LTB is moot. In summary:

1) It doesn't surprise me that just any old channel is not sufficient to "brace" the compression flange and;

2) I believe that a channel of some proportions would indeed effectively brace the compression flange.

dL said:

Not sure what the conventional wisdom on Hat channels for crane rails is.

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I'm not an expert on crane beam design by any means but my understanding of the commonly used process is this:

3) Design the wide flange for the vertical load independently of the channel, assuming that the channel deals with LTB.

4) Design the channel for the lateral load, including pretty tight deflection control, assuming that the wide flange does not assist.

This is, obviously, a non-rigorous way to deal with LTB of the wide flange. That said, it doesn't usually take a ton of stiffness to get a bracing job done so, for most practical situations, I suspect that the act of having designed the channel for deflection under first order, applied loads winds up being sufficient.

With a stiff enough channel in play, LTB of the wide flange effectively becomes constrained axis torsional buckling with that axis of constraint being located at the top flange. That, combined with the loads often being supported below the shear center, probably produces a fairly healthy LTB situation for the wide flange.