The main purpose of fastening the steel beam up into the wood framing is to provide lateral torsional bracing for the steel beam. I would rather not design the steel beam as unbraced because it will increase the weight of the beam.
Client wants the shallowest possible beam. New beam will support the existing joists above - so it will be a dropped beam (not a flush beam). Back in 2018 a member (Scratch3r) posted "I recently used a 45-degree washer to screw the top flange of a steel beam to the underside of an existing top...
