What is the mechanical widening required for a pavement of width 14.0 m on a horizontal curve of radius 200 m if the longest wheel base of vehicle expected on the road is 6.2 m?
- A0.28 m
- B0.38 mCorrect
- C0.48 m
- D0.58 m
Solution
Concept
Mechanical widening (Wm) is provided on horizontal curves to compensate for off-tracking due to the rigid wheelbase of vehicles.
Formula
n = Width of pavement / 3.5 Wm = (n × l²) / (2R)
Step-by-step solution
1. Determine the number of lanes (n): n = Pavement Width / Standard Lane Width = 14.0 / 3.5 = 4 lanes. 2. Apply the formula for mechanical widening: Wm = (n × l²) / (2R). 3. Substitute the given values: Wm = (4 × 6.2²) / (2 × 200) = (4 × 38.44) / 400 = 0.3844 m. 4. Round to two decimal places: Wm ≈ 0.38 m.
Explanation
Mechanical widening accounts for the off-tracking of a vehicle when traversing a horizontal curve. Assuming a standard lane width of 3.5 m, the number of lanes for a 14.0 m wide pavement is n = 14.0 / 3.5 = 4. The required mechanical widening is calculated as Wm = (n × l²) / (2R) = (4 × 6.2²) / (2 × 200) = 0.3844 m ≈ 0.38 m.
Why the other options are wrong
A: Calculated assuming a 3-lane road (n = 3). C: Incorrect calculation or confusion with total extra widening. D: Result obtained by incorrect formula or calculation error.
Shortcut
Since n/2R = 4/400 = 1/100, Mechanical Widening = l² / 100 = 6.2² / 100 = 38.44 / 100 = 0.3844 m.
Common mistake
Confusing mechanical widening with psychological widening, or using the total widening formula Wm + Wps when only mechanical widening is requested.
Correct answer: B) 0.38 m