Calculate the mechanical widening required for a pavement of two lane road without raised kerb on a horizontal curve of radius 300 m if the longest wheel base of a vehicle expected on the road is 6.0 m.
- A0.10 m
- B0.12 mCorrect
- C0.14 m
- D0.16 m
Solution
Concept
Mechanical Widening
Formula
Wm = (n × l2) / (2 × R)
Step-by-step solution
1. Identify given values: n = 2, l = 6.0 m, R = 300 m. 2. Substitute values into formula: Wm = (2 \* 62) / (2 \* 300). 3. Solve: Wm = 72 / 600 = 0.12 m.
Explanation
Mechanical widening is calculated using the formula Wm = (n × l2) / (2 × R). Here: - Number of lanes (n) = 2 - Wheelbase length (l) = 6.0 m - Radius of curve (R) = 300 mPlugging in the values: Wm = (2 \* 62) / (2 \* 300) = (2 \* 36) / 600 = 72 / 600 = 0.12 m. Therefore, option B (0.12 m) is the correct calculated mechanical widening required for the road.
Shortcut
For a 2-lane road (n = 2), the number 2 cancels out in the formula, simplifying it to: Mechanical Widening = l² / R. Just square the wheelbase length and divide by the curve radius (6² / 300 = 36 / 300 = 0.12 m).
Common mistake
A common mistake is using the formula for total extra widening (mechanical widening + psychological widening) instead of calculating mechanical widening alone, or forgetting to multiply by the number of lanes (n = 2). Students also frequently confuse the formula Wm = n·l2 / (2R) with l / (2R) or forget to square the wheelbase length (l).
Correct answer: B) 0.12 m