How did you come up with such a precise figure for the weight of the roof? Usually roof load is computed as a combination of dead load (weight of material), plus live load. Live load includes wind load and snow load (if applicable). Seismic load is used to decide on the type of fasteners to connect the pieces together.
In your case, the roof has a projected area of 216 square feet, and you assigned a load of 3111 lbs, which is about 14 psf projected. This is too low for snow country, but you did not indicate where you are, so hard to say what an appropriate load would be.