I am in the process of building an octagonal gazebo and am trying to figure out the size of the roof framing I will need. 

The span of the structure 16′ 9″ and the roof pitch is 6/12. I plan to have the maximum rafter spacing be 24″.I have calculated the rafters to be 9′ 4 5/16″  with an additional overhang of about 20″. I do live in Minnesota where we can get significant snowfall as well. Thanks in advance for your guidance.