You want the 3.5" x 7" wood beam to span 155"?
Is this a gable roof?
What is the city and state so I can look at snow loading?
What is the rafter length?
That 3.5" x 7" beam is really not even close to the correct size.
What are you calling the max moment. That is not the correct magnitude nor units for the bending moment.
I calculate a maximum moment of 5,250 #-ft
Deflection is not the same at moment.
The deflection under a full design load in the 3.5" x 7" beam is over 1"
100 plf means about 15 psf. That is DL only. That does not account for the required roof minimum live load of 20 psf. It also doesn't account for the creep deflection.
I don't think so. I think you just didn't account for all of the loading and all of the deflection. These are not things you would necessarily know if you don't do this every day.
It does. By a factor of almost 3.
No problem. I'm happy to help. Good luck with your project.