What is an LFRD K Series Bar Joist?

Let me subdivide the answer in 3 parts.

Bar Joist is a structural member composed of steel bars or angles. It is a secondary strucutral member (depends on a primary member) which is placed over girders, steel beams or concrete beams. They are tipically separated from 30" to 4 feet and in some cases more from one another. depending on the strength of the decking and the loads imposed.

Over the Joist, the decking is installed.

K Series - Is a designation of a "family" of joists on the geometry of how they are constructed. The SJI or Steel Joist Institute has a book that explains more.

LRFD - Load Resistance Factor Design - Is a structural design "philosophy" that requires the structural engineer to factor loads applied (factor up / increase loads) AND resistance (factor down / reduce strength).