By code in most jurisdictions, a deck stairway must be at least 36 inches wide. This is also the maximum width of a stair built with closed stringers. Note also that new design values for visually graded southern pine have changed as of June 1, 2013, resulting in changes to maximum span for both cut and solid stair stringers (see Stair Stringer Requirements).
Best practice is to attach the stringer with full bearing against the deck header, and use a metal connector. At the bottom, the stringer should rest on a footing designed to resist a 40 psf live load and a 10 psf dead load. The new design values also increase the minimum size for southern pine treads in solid stringers from 2x6 to 2x8 (...
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