If the gable is formed by the two slopes and a horizontal line, it is called a gable roof.
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a gable roof is double pitched with vertical ends
From AS 1684.4 Residential Timber Framing Code 2.6.4.1 Coupled roof Pitched roof construction with a roof slope not less than 10°, with ceiling joists and collar ties fixed to opposing common rafter pairs and a ridgeboard at the apex of the roof (see Figure 7.1). A coupled roof system may include some area where it is not possible to fix ceiling joists or collar ties to all rafters, e.g., hip ends or parts of T- or L-shaped house. 2.6.4.2 Non-coupled roof A pitched roof that is not a coupled roof and includes cathedral roofs and roofs constructed using ridge and intermediate beams.
A supported beam has both ends of the beam resting on a support. A cantilever has a single support often hinged close to or at one end with the other end supported in another manner.
A fixed beam is a beam the ends of which are constrained or built-in to remain in horizontal position. Point to be noted for the fixed beam: 1. The beam is stiffer, stronger and more stable. 2. The slope at both the ends is zero. 3. Due to the fixidity, the moment will be induced at each end. 4. The induced moments will be in the opposite direction to that of moments due to external loading.
"Fixed" means that the ends cannot translate and cannot rotate. "Pinned" means that the ends cannot translate but can rotate.