Wheelchair Ramp Code Check
A school is installing a wheelchair ramp at a side entrance. The door threshold is 0.72 m above the sidewalk. The local code says the ramp's slope, rise divided by run, may not exceed 1:12 (about 0.0833), and a flat landing 1.5 m long must be at the top of the ramp. The contractor measures 8.4 m of horizontal space from the door to the sidewalk edge and proposes using all of it as the ramp run, with the landing inside the doorway. The principal wants to know whether the proposal passes code, the shortest allowable ramp run, and how much horizontal space must be found if it fails. A parent also asks how long the ramp surface would be.
1. Compute the proposed slope and compare it with the 1:12 code limit. Find the shortest allowable run and how much additional horizontal space is needed.
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Proposed slope = rise ÷ run = 0.72 ÷ 8.4 = 0.085714..., which is 1:11.67. The code maximum is 1:12 = 0.083333..., so the proposal is steeper than allowed and fails.
Shortest allowable run = 12 × 0.72 = 8.64 m. The proposal is 8.64 − 8.4 = 0.24 m short.
2. Calculate the ramp surface length for the minimum allowable run and for the proposed 8.4 m run.
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For minimum run 8.64 m and rise 0.72 m, ramp surface length = √(8.64² + 0.72²) = √(74.6496 + 0.5184) = √75.168 ≈ 8.67 m.
For the proposed 8.4 m run: √(8.4² + 0.72²) = √(70.56 + 0.5184) = √71.0784 ≈ 8.43 m. The surface is only about 0.24 m longer than the run because the rise is small.
3. The contractor suggests a switchback with two equal ramps, each rising 0.36 m over 4.2 m. Does this fix the code problem? Explain using slope, and state what total horizontal run is actually needed.
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Each switchback segment would have slope 0.36 ÷ 4.2 = 0.085714..., the same as the single ramp, so it still violates the 1:12 limit. Splitting the rise does not change the overall rise-to-run ratio when the total run is still 8.4 m.
The code needs total run ≥ 8.64 m for the 0.72 m rise. A switchback also needs flat landings, which use additional horizontal space, so it would require even more room, not less. The practical fixes are to extend the run by at least 0.24 m (to 8.64 m total), lower the threshold by at least 0.02 m so that 8.4 m is sufficient (since 8.4 ÷ 12 = 0.70 m), or redesign with a longer path.