Ramp Slope Compliance with Required Landing
A building entrance has a door threshold 2.5 feet above the sidewalk. The horizontal distance from the bottom of the ramp to the door is 30 feet. Code requires a ramp slope no steeper than 1:12 (vertical rise to horizontal run) and a flat landing at least 5 feet deep at the top of the ramp. The contractor proposes using the entire 30 feet as sloped ramp. An inspector notes that the landing must come out of that 30-foot horizontal distance, so the actual sloped run would be only 25 feet. The contractor wants to know the required run, whether the proposal is compliant, and the maximum rise possible under the constraint.
1. For a 2.5-foot rise, what horizontal run is required by the 1:12 slope rule? Including the 5-foot landing, what total horizontal distance would be needed?
Read the worked answer
The slope rule is
$$\frac{\text{rise}}{\text{run}}\le \frac{1}{12}.$$
For a 2.5-foot rise, the minimum run is
$$\text{run}=12(2.5)=30 \text{ feet}.$$
The 5-foot landing is additional horizontal distance at the top, so the total horizontal distance from the bottom of the ramp to the door would need to be at least
$$30+5=35 \text{ feet}.$$
2. Is the contractor’s 30-foot proposal compliant if the landing must be included? Justify numerically.
Read the worked answer
No. If the 30-foot horizontal distance must include a 5-foot landing, the sloped run is only
$$30-5=25 \text{ feet}.$$
The proposed slope is therefore
$$\frac{2.5}{25}=0.1=\frac{1}{10},$$
which is steeper than $\frac{1}{12}\approx 0.0833$. Equivalently, the angle is $\tan^{-1}(0.1)\approx 5.7^\circ$, exceeding the maximum compliant angle $\tan^{-1}(1/12)\approx 4.8^\circ$.
3. With the 30-foot total horizontal distance and the required 5-foot landing, what is the maximum rise that can be accommodated, and how far short is the 2.5-foot threshold?
Read the worked answer
The maximum sloped run is 25 feet, so the maximum rise is
$$\frac{25}{12}\approx 2.083 \text{ feet}.$$
The door threshold is 2.5 feet, so the shortfall is
$$2.5-2.083=0.417 \text{ feet},$$
about 5 inches. The existing layout cannot meet both the 1:12 slope and the 5-foot landing within 30 horizontal feet; the ramp must be lengthened or the threshold lowered.