Beam Spam Question

[seadog61]

I have tried my best to figure out what beams I will need for a project.

I am building a Pavilion with 6 x 12 pitch roof. The span I would like to get to center of post to center of post is 15 ft on 6 x 6 post.

The roofing products will weight about 1100 lbs, and I live in Aurora CO which is requiring a 30 lb sq ft snow load.

The front and back spans are +/- 10 ft , not sure this matters though.

I was hoping to use Douglas Fir, seems like I need 4 ea 2 x 12's to make this work, seems like a lot but I'm new to this game.

I just want to make sure I can't go 3 ply or lighter, seems like I may need to go LVL or Glulam, thanks

[seadog61]

I should have given roof sq footage, including the  pitch 288 sq ft

[Don P]

Post a dimensioned sketch please.