Final answer:
To determine the developed length of a 30° bend to go around the silo using a 5 inch RMC with 8-inch spacing, calculate the radius of the silo and add the radius of the conduit and the spacing to find the total radius. Then multiply the total radius by the bend angle in radians to find the developed length, which is approximately 29.1 inches.
Step-by-step explanation:
To calculate the developed length of a 30° bend to go around the silo using a 5 inch Rigid Metal Conduit (RMC) with an 8-inch spacing between the silo and the edge of the conduit, we need to incorporate the diameter of the silo, the diameter of the conduit, and the spacing.
First, we find the radius of the silo. Since the measured distance from the end of the straight edge to the wall of the silo is 14 and three-quarter inches at both ends, and the straight edge itself is 10 feet long (or 120 inches), the diameter of the silo is 120 inches minus twice the measured distance, which equals 120 - (2 × 14.75) inches = 90.5 inches. The radius (R) of the silo is half the diameter, so R = 90.5 / 2 = 45.25 inches.
Next, we need to add the radius of the conduit (which is half of 5 inches, so 2.5 inches) and the spacing (8 inches) to the radius of the silo to get the total radius we're using for the bend calculation: Total radius = 45.25 + 2.5 + 8 = 55.75 inches.
Now, to find the developed length for the 30° bend, we multiply the total radius by the bend angle (in radians) since the developed length (L) for a bend is given by the formula L = θR, where θ is the angle in radians. Converting 30° into radians (30° × (π/180) radians/degree), we get θ = π/6. So the developed length is L = (55.75 inches) × (π/6) = approximately 29.1 inches (using π ≈ 3.1416).