Actually reviewing my working through "sizing rough sawn joists and beams" by ed levin, I notice that it is at bending that I get lost.

I can calculate the extreme fiber stress, 3897psi, but what do I check that against? The example has 1500psi for red oak but I don't know where that value came from. I'm guessing that it comes from a table which means that at a guess that a 8x10 beam is not going to be big enough even in box. The E of green yellow box (11mpa) is 28% greater than green american white oak (8.6mpa I don't have a figure for red oak). Therefore if I add 28% to 1500psi gives me a figure of 1918psi. Is this reasonable?

That would then mean i'd need a box beam 12"x12" (f=1804psi). Yes?

Or in softwood (f<1343) 12" x 14".