The required spindle length is based on the crank and has nothing to do with the bike frame. You'll need a new BB with a 110mm square taper spindle to use the All City Cranks. The SRAM/Truvative BB has a somewhat uncommon interface.

Call your LBS this is the kind of thing they might have in a box somewhere and could be a cheap purchase for you--and if you don't have the right tools, you'll need their help anyway.