What describes ceilings with structural members projecting more than 4 inches down from the surface?

The appropriate term for ceilings with structural members projecting more than 4 inches down from the surface is beam construction. In beam construction, the visible structural elements such as beams, columns, and other members are designed to be an integral part of the ceiling's aesthetic and structural design. These structural members can often be a significant aspect of architectural style and may be exposed, providing additional support to the ceiling or roof above.

In contrast, a flat ceiling typically refers to a ceiling that is even and level, without protrusions. A suspended ceiling is a secondary ceiling hung below the main structural ceiling, commonly used to hide ductwork or wiring; it doesn't include members that project downwards from it. A pitched ceiling, on the other hand, is designed with a slope, often seen in attics or spaces with a sloping roofline, but it doesn't specifically address the projection of structural members. Therefore, beam construction accurately characterizes the specific design of ceilings featuring prominent structural elements extending downward.