This video introduces the two main categories of gravity load systems: one-way systems and the two-way systems.
Tributary area is defined as the floor (or roof) area from which a structural element directly "collects" the load to transfer it down to the foundation. The influence area is defined as the total area that is in some way supported by a structural element. Examples are shown for how to compute these two areas for beams and columns.
An example use for both tributary area and influence area is in the ASCE/SEI 7 live load reduction factor. A load combination example (U = 1.2D + 1.6L) for a one-way slab system is presented in detail.
For reference, please see ASCE/SEI 7 - Minimum Design Loads and Associated Criteria for Buildings and Other Structures.