Torsion Sketch

[jreit]

Hello.

I have a case where we need to attach some cables to the bottom flange of an existing composite section that spans ~20'.
The section is also braced by stringers.
I am trying to decide the best way to analyze the torsion imparted into the section.

My initial thought was to neglect the slab at the top, treat the section as non-composite and calculate the torsional moment as acting around mid-depth as the shear center. Then I'd use the simplified AISC DG09 procedure to calculate the normal warping stresses in the flanges.
The top flange is braced by the stringers and by inspection would not be a concern. The bottom flange should be analyzed with the additional normal warping stress.

However, a colleague pointed out that neglecting the concrete slab would be non-conservative as the slab would push the shear center of the composite section upwards beyond mid-depth and would increase the torsion moment demand on the section. If I did that, I'd have to use the more rigorous method laid out in AISC DG09 as the stresses would be too high using the simplified method.
My concern with that rigorous method is how to best analyze the end restraints. The end restraints at the bottom are pinned but at the top are fixed. Would pinned-pinned be too conservative when used in conjunction with the larger torsion moment demand? But would fixed-fixed be non-conservative as the bottom flange is not really restrained against warping?

Another idea is to treat the beam as a non-composite section but with a depth of 78-24 = 54" with pinned-pinned end supports.

 

[KootK]

Can you install kickers or fly braces inline with the cables, either:

1) Connecting the bottom flange to the slab or;

2) Connecting the bottom flange to the stringer?

Or is your mandate to do this without adding any new structure?

My concern with considering the beam alone, without the participation of the slab, is that that approach doesn't do a great job of respecting stiffness within the system. By the time that you fully mobilize the beam in warping, you may well have already damaged the stud connection between the beam top flange and the slab. That connection is what is likely to absorb the the torsion first, until it fails.

How long are the stringers and what does their connection to the girder look like? That may present additional opportunities.

How thick is this concrete slab? If it's very thin relative to the beam depth, that may invalidate some of my comments.

 

[jreit]

Cannot add any new structure unfortunately.
The slab is ~8" thick and the stringers span 25' and are bolted on with a simple shear angle connection.
If I can resolve the lateral force as lateral bending in the bottom flange and consider the combined effects on that bottom flange, would that be a conservative enough simplification?
If that load path works, I wouldn't need to analyze the top flange or slab,

 

[jayrod12]

So what we're hearing is the owner essentially just wants you to sign off on their proposed plan, but they refuse to do any upgrades if necessary? That's not a client I would want to work with.

 

[WARose]

Seems to me like if it worked just considering the I-beam (non-composite).....the steel would likely be ok. (Unless it tried to transfer something through the studs that the studs and/or the slab couldn't take.)

I wouldn't bank too much on the end constraints giving me favorable torsional stresses. That's kind of a grey area that I would check both ways.

Speaking of that....if your bottom constraint is pinned....I'd take a hard look at that. A "pinned" restraint doesn't transfer torsion to the support without creating problems with stresses in the web.

 

[KootK]

If I can resolve the lateral force as lateral bending in the bottom flange and consider the combined effects on that bottom flange, would that be a conservative enough simplification? If that load path works, I wouldn't need to analyze the top flange or slab,

That's exactly what I'd do given that the the beam top flange has immense lateral restraint. It's basically a simplified version of the bi-moment, torsion checking method. The one, additional check that I would make would be to:

1) check the lateral deflection of the bottom flange.

2) work out how much beam rotation at the top flange is implied by #1,

3) make sure that I felt good about the rotation from #2 with respect to it's tendency to damage the slab / top flange connection.

Obviously, you need a support condition that can deal with the lateral reactions that you will be assuming to be delivered by the bottom flange in this model.