I think it is braced.  Once you weld the pans in, and fill the pans with concrete, you kind of have a beam, laid on its side, which can resist the buckling.

But I think others here may disagree.

DaveAtkins

The pans are generally at the center of the stringer, I do not know if the pans can brace the top compression flange.

I would say it is braced at the point of each tread nose.....maybe every 12"....which might be the same as "fully" braced. I dont think I'd consider it unbraced.  

At the separations and details typically provided by the treads it is difficult for the compressed flanges to deform freely in lateral torsional buckling as a free beam would do. If only linking the compressed flanges we might only be thinking in one somewhat risky relative bracing where the unused stiffness against LTB in the other stringer braces the one being considered against its own LTB. For just 2 stringers that's an uncomely proposition, except on overdimension.

In any case the fact is that threads and their support many times (but not always) engage the stringers in such a way (threads joined to the webs, compressed flanges restrained against torsion by their union to the thread and vertical plate of the step) that the outfit becomes reasonably stout against LTB of the compressed flange, say, the upper flange.

Only when unable to restrain torsion by the general weakness of the thread your conservative assumption will be the required one. There's a way out of this and is modeling the stair with all details, even providing initial imperfections, with P-Delta and P-delta, then (segment) member analysis by formulas in the code(s), and you will know if you are safe against this in whatever the case.

You have to select a compact section.  But I think the compression flange is braced.  The maximum un-braced length would be the distance between the treads.  The "Z" shaped treads will provide adequate bracing to prevent buckling and provide torsional restraint.   

http://www.FerrellEngineering.com

I consider it braced. I do 3 or 4 of these a month for a fabricator.  Don't forget that the handrail attachment at 48" provides a compressive stress interruption, similar to bracing.

I agree with everyone else.  Stair stringers are braced in the weak direction by the treads and in the strong direction by handrail posts.

I'll pile on as well: braced at the treads

Metal Stairs Manual (AMP 510-92), The Metal Stairs Manual, 5th Edition (1992). Table 5.26 Load and Deflection Table for Steel Stingers says under general notes: "Stringers are considered to be laterally braced by attached treads and risers."

See manual at:
https://www.naamm.org/amp/amp_technical_literature.aspx
 

Some codes require unsupported flange lengths(Compression & Tension) as well as effective lengths(Unbraced length around weak & Strong Axis) to be specified. My view on your case is as follows:

1. Top(Compression) & Bottom(Tension) flanges is supported.
2. Weak Axis - Braced at the length between treads.
3. Strong Axis - Unbraced. The stringer is free to flex over the full length.  

The stringers and treads form a vierendeel truss against lateral movement as well as being a torsional restraint.

I treat my stringers as fully restrained.

The proof of this is that I have designed many vertical plate stringers on this basis and never had one failing.

csd72...I too, have designed many stair stringers in the same manner as you described; however, I doubt that any of the stringers that either of us has designed has ever or will ever see their full design loads.

The stringers are fully braced.

csd72 and Ron, those flat stringers work well as long as they are connected to a stable platform and base. We used to use them for low stiles, no legs, the stringers were the only support and they worked fine. So then we had some high stiles and the damned things wobbled. We had to backfit some bracing under the steps.

These were with bolted grating treads.

Michael.
Timing has a lot to do with the outcome of a rain dance.