Deck Joist Bending Calculations

Hello. I not an ME (I'm EE) but tried my hand at calculating some loads for a 4-season room on a deck I'm building. Just wanted to run it by some peers to see if it looks sound. I'm going to a structural guy in a couple weeks to have formal plans done but wanted to understand this for myself first.

Pretty simple setup. The deck comes out 14' from the house. It's 12' to the beam with a 2' overhang. The 4-season room will be 14x16 (16' along the house). The roof would be a simple slant type (attached to house, then sitting on a wall at 14' out). I know this puts considerable load on the overhang, and wanted to compute the bending force on the joist it's sitting on (there are 12 joists this room would sit on). The Fb for the 2x10's I'm using is 1050 psi. I used 50 psf for load in the room, and also 50 psf on the roof. In the end, I got that each joist would see a bending force of 598 psi, well within limits.

Thanks for the help. Picture attached.

Your efforts to calculate the forces and deflection are commendable however, your should look into any local codes to see if they have a 'span table' that they use for structures that are not stamped. You can probably find one for both floor joist and rafters.

Yes, span tables are common. But having a wall over a cantilever is the part that is not in the codes, this would have to be calculated to make sure the joists can handle it (which the structural eng will do), this is the part I was asking about.

With respect, I don't want to get into the weeds about codes and so forth, I really just want to understand the math behind this. Can you, or someone, comment on what I have done mathematically?

I attach a segment from "Building Construction Illustrated" by Francis D. K. Ching (A favorite of mine on the subject) which suggests that cantilevers of 24" or less might not need engineering analysis.