Nails. If they cannot be placed on top of a wall or beam a joist hanger is required as well.
The purpose of a floor joist support beam in a building's structural framework is to provide support and distribute the weight of the floors and walls above it to the foundation of the building. It helps to ensure the stability and strength of the structure.
A joist, either floor or ceiling are the boards that go across the building and tie the walls together. A timber joist would be a rough sawn beam. Basically a tree that has been squared up.
In construction, a joist is a horizontal piece that runs from wall to wall, wall to beam or beam to beam. A joist is essentially considered to be one of the most supporting pieces towards the structural aspect. It focuses in on supporting beams and other pieces in the floor, ceiling and roof.
A joist is a beam, a supporting structure in a building. The roof joist was riddled with dry rot and had to be replaced.
Trimmer
joist
joist
joist
beam transfer loads from the joist to the wall or column where it supports..
The duct work does not need to be different from the rest just because of the I beam. Just be sure there is room so you do not compress it.
That really cannot be answered without looking at the entire set of plans.