The optimum depth for your joists should be about 28 to 30"... ' your 24" is a little shallow... and might be prone to some vibration. Cutting it to 12" for 1/3 the span will likely cause problems... you might try something else...
Intermediate support of the joist via column, wall, beam - at the point where the joist must be reduced. Re-analyze the joists's shear moment diagram capacity and verify that intermediate web strengthening is OK or needs strengthening.
Suppose at cut we drop a column. For 12 feet we can add a steel beam and remove the joist. For the remaining joist still in service with new support at column, do we need to do any modifications or simply add vertical member (web stiffener) at column top should be fine
Yep - Crown06 - just to repeat - when you design a joist, it has a theoretical shear capacity that varies across the span from the original max. end reaction - to 0 at midspan. However, the SJI requires the joist manufacturers to at least design the joist web members for 25% of the shear at the end (some years ago it was 50% so the older the joist the more hefty the webs).
When you shorten a joist span, you have the potential to create a larger shear at the new end from what it was originally designed for. Simply construct an "original" shear diagram and superimpose it over your new shear diagram to check if you are ok.
