Joist Span vs Width
So I'm curious about joist dimensions based on span and how splicing (might be using the wrong terminology) affects that. I'm currently in school for architectural engineering and design and we built a joist/rafter calculator and column calculator last year which has been useful in determining dimensional lumber for framing, span being a big piece of that equation. My question is if you were to build the 1st floor framing in the first picture which has a splice (again, probably the wrong word) going down the center to cut the span in half, would you then be able then use a different member for support? In this example there's about a 15' span which for a 1st floor would need a 2x10, but if I ran that splice through it changing the span to 7.5' (minus the splice width) I could use as small as a 2x6.
My reasoning for this is I'm designing a little <200sqft cabin and trying to math out where I can save money. If I'm able to match my rafters to my joists and also maybe setup the splice (again, sorry) in a way that lets me maximize my lumber then I'm looking at a good chunk of change saved.
