Can you confirm that this is indeed a floating stair jdengos? It makes a big difference to the advice that we're giving you.
jdengos said:
The slab will help only the top flange, not the bottom flange.
Not necessarily. With the addition of some angle braces up to the slab/beam intersections behind the stringer connection, the slab can be made to effectively restrain the bottom flange as well.
jdengos said:
Plus the lateral moment is huge (144 k*feet on one stringer, total 288 k*feet).
Regardless of what detailing you go with, I'd recommend modelling the connection at the bottom of the stringers (point A in my sketch) as a flexural hinge. Three reasons for this:
1) As you're finding out, dealing with all that torsion (lateral moments) is tough and;
2) Even if you successfully deal with the torsion, the supporting beam will be very flexible with regard to twist and, therefore, likely not behave as you've modeled it.
3) The dominant behavior for these kinds of stairs tends to be axial load in the stringers being resisted by the axially stiff floor slabs. Modelling and designing your system to suit this mechanism will likely be the path of least resistance and best performance.
Without knowing anything about your particular string/slab detailing, I've sketched a possible detail that I think would work well here. There would be no appreciable torsion in the W21x50. All of the reactions would really be springs of sorts of course as there is flexibility in all things, particularly the beams.
Often times, demolishing some of the slab is the only way to keep the transition detail clean.
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.