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re: wind on stair tower

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Joe,
We have done a few somewhat similar projects, such as a belltower for a church that had open portions but was mainly enclosed, free standing and not supported by the building.
 
This is my gut feeling without studying ASCE or your dwgs... You said it will be supported partially by the parking garage on one side, and then I assume at the outside by two vertical HSS sections that will make up part of a braced or moment frame? I would treat it as part of the building as far as any importance factor or anything is concerned, and your building department will probably like that also as it is a means of egress. But not for wind.
 
For wind loading you said it will be enclosed by parking structure on two sides, but you also say there will be a screening material? I am not sure I fully understand what this is all looking like, but I think the lateral pressures I would compare are that of a free standing wall and then that of a tower. As it will not likely make any appreciable cost difference on something this size, I would go with the worse case of the two. The stairs themselves will also have a vertical projection surface, probably more so than the rest of the structure.
 
If you wanted to get creative you could use the stair stringers and landings as a series of diagonal braces, but since these are probably supplied by the steel fabricator and engineered by them I think I would design this with X braces on the outside frame (if the arch OKs it). But sleep well knowing that your stairs will act as additional bracing (especially if these are steel stringers with steel pans filled with concrete)...
 
HTH,
Andrew