+1 --> Place joists over studs in the bearing wall.
> site built beam...
Done that. Works. Takes a little more time. Need to verify the span per load. Pay attention to the width which will need to be supported at the ends. Solidify an exact plan because the odd inch here/there can be a real headache. There are tables for building beams from sawn lumber.
+1 --> Blocking (tightly; full depth or close) between joists at the beam.Help keep joists straight over time.
What _is_ required by code:
International Building Code (IBC), in addition to having to install blocking where joists overlap over a center beam, blocking is also required every 8 feet for 2x10 and taller joists. ... As long as blocking meets this requirement, it does not necessarily have to be centered over the length of the floor joists.
And a more recent code: (IRC modified for CA, 2016)
R502.7.1 Bridging [ie. blocking]
Joists exceeding a nominal 2 inches by 12 inches (51 mm by 305 mm) shall be supported laterally by solid blocking, diagonal bridging (
wood or metal), or a continuous 1 inch by 3 inch (25.4 mm by 76 mm) strip nailed across the bottom of joists perpendicular to joists at intervals not exceeding 8 feet (2438 mm).
Here is the IRC link. It's a good site with relatively easy access to many codes:
https://up.codes/viewer/california/ca-residential-code-2016/chapter/5/floors#5
The page linked above relates to all floors generally. The first half is about wood floors. Language is mostly understandable. Much more data than any particular issue needs, but but the span tables may be helpful. A quick skim gives an idea of what the "authors" felt important to floors and then it's a matter of running down the subsection titles to find your area of interest.
Have a plan for lifting heavy structure like the beam. You want to be able to adjust stuff easily and safely once the piece is (mostly) in place.
Regards,
Rufus