In conventional wood framing, a gable roof is constructed with a series of parallel roof rafters sloping up from the eaves of the building to meet at a peak in the center of the roof. The bottom ends of the rafters rest on top of the exterior walls of the building, and the weight of the roof is transmitted downward and outward to the point where the rafters meet the walls. The weight load tends to push outward, so in order to keep the exterior walls from bowing outward and potentially failing under the weight, the walls are tied together with ceiling joists that span horizontally from eave to eave. These joists form the ceiling of the interior space.
A cathedral ceiling is a ceiling in which there are no horizontal joists at the top of the walls, and the ceiling is formed at least partially by the roof rafters themselves. This type of framing poses a design challenge, since the absence of joists necessitates some other structural support to keep the weight of the roof from pushing the walls outward. Solutions include using framing members to tie the rafters together at a point higher than the top of the walls, supporting the roof with structural posts and beams, and using engineered roof trusses to support the load in a more efficient way.
Collar ties are essentially ceiling joists that are positioned higher than usual, tying the rafters together at a point that allows a higher ceiling in the interior. The higher the collar ties are positioned, the less structural support they provide. Another framing option involves supporting much of the roof's weight with a heavy ridge beam that rests on heavy support posts at the gable ends of the roof. In this situation, the load on the rafters and exterior walls is lessened, and the need to tie the walls together is eliminated.
In a scissors truss, the ceiling joist, also called a bottom chord, is replaced with two bottom chords that slope up from the eaves at a slightly shallower pitch than the rafters. The chords meet at a peak below the peak of the rafters, and the two peaks are tied together by a vertical member called a king post. The bottom chords help to distribute the weight load and tie the rafters together, but they also create a sloped interior ceiling that is nearly as high as the external peak of the roof.