You can always post 2 pics of the spreadsheet one showing its layout and the other one with the formula shown in the cells, means perps have to build the spreadsheet as opposed to just picking it up and running wit it?.
That purlin would be way undersized using todays regs, even with just taking the standard snow load of 0.75kn/m2 and assuming the purlin supports 1m of roof each side of it i.e. 2m2 , so loading per metre run is 1.5kn, taking c24 timber the actual bending moment in the beam would be 40% over...
Forget my comments I thought you were trying to obtain a flush surface for fixing new plasterboards but it appears that you have structural issues hence your sistering of existing rafters , although having sistering rafters that are effectively cut in the middle (where the maximum bending...