To calculate the length of a collar tie (\(CT\)):
\[ CT = \sqrt{(R^2) + (S^2)} \]
Where:
A collar tie is a horizontal framing member in a roof structure, typically found in residential construction. It is installed between opposing rafters, and its primary function is to resist the outward thrust of the roof rafters under load, preventing the walls from spreading apart. Collar ties are often confused with rafter ties, but they are located higher up in the roof structure, usually in the upper third of the roof height.
Let's assume the following values:
Using the formula:
\[ CT = \sqrt{(5^2) + (12^2)} = \sqrt{25 + 144} = \sqrt{169} = 13 \text{ ft} \]
The length of the collar tie is 13 ft.
Let's assume the following values:
Using the formula:
\[ CT = \sqrt{(3^2) + (4^2)} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ m} \]
The length of the collar tie is 5 m.