When looking for a missing invert you must isolate the rise aspect of the equation. Rise. 1 1 Run 1
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1 Mastering Cut-Sheets, Part II When working out cut-sheet problems, the primary equation used is- In order to find a missing slope, invert or station on a cut-sheet problem, it helps to know how to convert the slope equation. We will begin with how to find a missing invert by converting the slope equation to a rise equation. Example 1- When looking for a missing invert you must isolate the rise aspect of the equation. Run Slope x = Run x Slope = Run Slope Run x = x 1 1 Run 1 Run Slope Run x = x 1 1 Run 1 If you have two stations and the slope, you can now find the missing invert associated with one of the used stations. Example 1A- Given Slope = A missing invert is a rise issue, given the slope (0.020) and the run (0 + 00) +(1 + 25) = 125, use the equation: Run x Slope = or 125 x = 2.5 This means over 125 the invert elevation has a rise of 2.5, therefore you must add 2.5 to the previous invert elevation, so: =
2 Answer to example 1A- Slope = Had the invert elevation for station (0 + 00) been missing rather than that for station (1 + 25), you would subtract 2.5 (the answer) from to get Example 2- When looking for a missing station you must isolate the run aspect of the equation. 1 1 x x Slope 1 = x 1 Run Slope 1 = x 1 Run Slope 1 = Run invert the equation to: Run = Slope 1 Slope = Run If you have two inverts and the slope, you can now find the missing station associated with one of the used inverts. 2
3 Example 2A- Given Slope = A missing station is a run issue, given the slope (0.020) and the rise (87.50) (85.00) = 2.5, use the equation: Run = Slope or Run = = 125 This means it takes a run of 125, or 1+25 to achieve a 2.5 difference in invert elevations with a slope of 0.020, therefore you must add 1+25 to the previous station, so once again: Answer to example 2A- Slope = As before, had the station for invert elevation (85.00) been missing rather than that for invert elevation (87.50), you would subtract 125 (the answer) from to get Example 3- When looking for a missing slope you must use the primary equation: If you have two stations and two inverts, you can find the missing slope. Example 3A- Given Slope = 3
4 To find the missing slope you need two stations to represent run and two inverts to represent rise. In this case the run is (1 + 25) (0 + 00), or 125 and the rise is (87.50) (85.00), or 2.5. Use the equation: 2. 5 or Slope = 125 = Answer to example 3A- Slope = Any two sets of stations and invert elevations can be used to find a missing slope. Example 4- When looking for a missing cut, you simply subtract the invert elevation from the stake elevation. Example 4A- Given Slope = To find the missing cut, subtract the invert elevation from the stake elevation. Stake elevation (90.00) Invert elevation (85.00) = 5.00 Answer to example 4A- Slope = The addition of a known cut to an invert elevation will give you a missing stake elevation. The subtraction of a known cut from a stake elevation will give you a missing invert elevation. 4
5 Finish Cut- Sheet A Slope = Finish Cut- Sheet B Slope = Finish Cut-Sheet C Slope = Finish Cut-Sheet D Slope =
6 Finish Cut-Sheet E Slope = Answers Cut- Sheet A Slope = Cut-Sheet B Slope =
7 Cut-Sheet C Slope = Cut-Sheet D Slope = Cut-Sheet E Slope = Remember Run = Slope = Run x Slope If you insert the number (4) where you see slope, the number (8) where you see rise and the number (2) where you see run, you get: 4 = = = 2 x 4 Prepared by Lenny Rather, SFBS- Collection Committee,
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