You can use the calculators at the American Wood Council to run numbers for both the floor and the roof. To obtain a proper answer to the question of what's needed to span 16 feet you need to supply more information. With a shed roof the snow load becomes a very important factor. Available lumber grades also matter; select structural may not be available in all areas or may be quite expensive compared to the common grade #2.
When calculating the span remember that the span distance is measured between the supporting members. That is, if the span from outside of one wall to the outside of the other wall is 16 feet, and the walls are built using 2x6 (1.5 x 5.5 actual) then the actual span would be 16'0" - 5.5" - 5.5" = 15'1"
There are two calculators working in slightly different ways.http://www.awc.org/calculators/span/reversecalc/reversecalc.asphttp://www.awc.org/calculators/span/calc/timbercalcstyle.asp
The deflection value and live load varies with use; floor joists, ceiling, roof with or w/o snow load.
Examples of code-prescribed deflection limits and live load values are:
* Living room floors L/360 & 40 psf
* Bedrooms and habitable attic floors L/360 & 30 psf
* Attic floors with limited storage L/240 & 10 psf.
* Rafters L/240
If the span calculator indicates that a certain size, grade, type of wood would span 15'10" under a certain set of conditions I would recommend going up a size in the lumber or spacing them closer. The calculator gives maximums spans, and in my opinion pushing the limits is not a best building practice. Just my conservative opinion.