Final answer:
To calculate the overall conduit length (OAC) with a single 22.5° offset and a 6.2-inch rise, calculate the offset leg length (OL), compute the shrinkage (S), and then add straight distance (BD), subtract OL and add S to get OAC. The calculated OAC, after rounding, is 26.33 inches.
Step-by-step explanation:
To calculate the overall conduit length (OAC) required to complete a run with a single 22.5° offset and a rise (R) of 6.2 inches using a shrink constant of 0.2, we will follow these steps:
- Calculate the length of the offset leg (OL) using the tangent function of the angle because we have the rise and we need to find the adjacent side (OL) in the right-angle triangle formed by the offset.
Tan(22.5°) = Rise / Offset Leg (OL) leads to OL = Rise / Tan(22.5°). - Calculate the actual length of the conduit on the offset using the Pythagorean theorem, which is the hypotenuse of the right-angle triangle formed by the offset.
- Calculate the shrinkage (S) using the product of the rise and the shrink constant. S = Rise × Shrink Constant.
- Sum up the straight distance between the boxes (BD), the shrinkage (S), and then subtract the offset leg (OL) to find the overall length. OAC = BD + S - OL.
Using the values provided:
- OL = 6.2 inches / Tan(22.5°) ≈ 15.48 inches
- The hypotenuse (Offset Conduit Length) can be found using the Pythagorean theorem: √(Rise² + OL²) ∼ √(6.2² + 15.48²) ≈ 16.57 inches.
- S = 6.2 inches × 0.2 = 1.24 inches
- OAC = 24.0 inches + 1.24 inches - 15.48 inches ≈ 9.76 inches. Adding this value to the offset conduit length gives the total length required: 16.57 inches + 9.76 inches = 26.33 inches.
The overall conduit length (OAC) needed is 26.33 inches after rounding to two decimal places.