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a technical diagram of a Hip Roof Plan View, which is a type of roof where all sides slope downwards to the walls. The diagram is designed to help a builder or architect understand the layout, terminology, and geometric relationships of the different framing members.
The image is divided into two main sections: a detailed framing layout (top) and a simplified geometric layout (bottom).

1. TOP SECTION: DETAILED FRAMING LAYOUT
This section labels the specific structural components required to frame the roof.

KEY COMPONENTS:
• 1. Common Rafters: These run from the ridge board (5) down to the wall plates. They define the main slope and height of the roof.
• 2. Hip Rafters: These are the diagonal rafters that form the "hip" or the corner where two roof planes meet. They run from the working points (6) to the outside corners.
• 3. End Common Rafters: These are common rafters located at the ends of the roof, perpendicular to the ridge.
• 4. Jack Rafters: These are shorter rafters that bridge the gap between a hip rafter and the wall plate.
• 5. Ridge: The horizontal board at the very peak of the roof where the rafters meet.
• 6. Working Points (Red Dots): These are critical intersection points used for measurement and layout.

NOTABLE GEOMETRIC DETAIL:
The diagram highlights a 45° angle between the first common rafter and the hip rafter. In a standard hip roof with equal pitches on all sides, the hip rafter always sits at a 45-degree angle on the plan view.

2. BOTTOM SECTION: GEOMETRIC RUN AND SPAN
The lower diagram simplifies the roof into its primary geometric measurements to explain how lengths are calculated.

CRITICAL DIMENSIONS:
• Span: The total width of the building from one outside wall to the opposite outside wall.
• Run: The horizontal distance from the outside of the wall to the center of the ridge. For a centered ridge, the Run is exactly half of the Span.
• Labeled Runs:
• 1 (Run of First Common): The horizontal distance covered by the main rafters.
• 2 (Run of Hip): The diagonal horizontal distance from the corner to the working point. Because it is the hypotenuse of a 45-degree triangle formed by the "Run," the actual length of the hip's run is .
• 3 (Run of End Common): This is labeled as being the "Same as first common," confirming the symmetry of the roof.

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