Geometric Design MCQ with answer and solution

Concept

Superelevation (e) and lateral friction (f) counteract the centrifugal force on horizontal curves. When the maximum rate of superelevation is provided, the remaining centrifugal force is balanced by the developed lateral friction.

Formula

e + f = V² / (127 × R)

Step-by-step solution

1. Identify given values: Design speed V = 65 km/h, Radius R = 220 m. 2. Standard maximum allowable superelevation e_max = 0.07 (IRC recommendation). 3. Apply the superelevation formula: e + f = V² / (127 × R) 4. Calculate total required force balance: 0.07 + f = (65)² / (127 × 220) = 4225 / 27940 ≈ 0.1512 5. Solve for lateral friction coefficient f: f = 0.1512 - 0.07 = 0.0812 ≈ 0.08

Explanation

The basic equilibrium equation for a vehicle moving on a horizontal curve is e + f = V² / (127 × R). Substituting the given values and using the maximum allowable superelevation e_max = 0.07 (as per IRC guidelines for plain/rolling terrain), the developed transverse friction coefficient f is found to be approximately 0.08.

Why the other options are wrong

B: 0.07 is the maximum allowable superelevation rate (e_max), not the developed friction coefficient. C: 0.15 is the maximum allowable lateral friction coefficient or total centrifugal ratio (e + f), not the net developed friction. D: 0.10 is an incorrect intermediate value.

Shortcut

f = (V² / 127R) - e_max = (4225 / 27940) - 0.07 ≈ 0.151 - 0.07 = 0.081.

Common mistake

Forgetting that the maximum rate of superelevation is 0.07 as per IRC and assuming f is directly 0.15 without subtracting e.