The system that is used to classify a building (ie steel frame) is also called a horizontal spanning system. These can be grouped by material and ability to span in one or two directions.
Wood
1. Light wood- composed of a post and beam type construction using relatively small elements
2. Heavy timber- large elements able to span longer than light wood timber
3. Glu-laminated- elements made of layers of wood glued together; creates a larger beam/column that can span further
Steel
1. Solid beams/girders- common for high rise structures; spans further than wood frames
2. Open Web Joist- lighter than solid beams, spanning further, but with greater depth
Concrete (Cast in Place)
1. One-way solid slab- carries loads in one direction, spanning further in one direction over another
2. One-way joist slab- monolithic slab with joists cast in it
3. Two-way flat plate
4. Two-way slab with drop panels/capitals- monolithic slab, but instead of beams spanning between columns, the columns have a capital
5. Two-way waffle slab- a deeper slab with pockets enabling it span further in two directions
Concrete (Precast)
1. Slabs and hollow core planks- planar system, constrained by length given it's cast off-site; slabs are solid, planks take material out of the center to make it lighter
2. Precast T's- Acting more like beams, these span a long length and work well for heavy loads (think parking garages)