I just wanted to clarify that we were talking about the same thing, since the topic was “hurricaine straps”, and I would just call the wood at the bottom flange a plate or blocking. In some areas 1x3 or 1x4 lumber is attached to the bottom of ceiling joists to stiffen the framing and provide space for wiring (instead of drilling joists) … that is just called joist “strapping”
The preferred method for attaching joists to a steel beam is to use a packed beam or wood top plate, with simpson connectors, so that the joist loads are transferred directly to the vertical web of the steel beam. But for typical light residential loads joists can be supported by the flange of the steel beam, as long as the flange is thick/stiff enough to prevent it from bending down. And Simpson makes a special joist-flange hanger that is welded to and supported by the beam flange.
I dont see a significant issue as long as the joists are connected/nailed to the plate
Also the the plate should be bolted to the beam, or the joists on either side of the beam connected together (subflooring continuous across the beam or steel straps from joist to joist) to hold the joist in place against the beam. Also I would sight along the bottom of the steel beam flange to make sure it isn’t bending.
JMO & 2-Nickels …