Geometric Design MCQ with answer and solution

Concept

Psychological widening calculation on horizontal curves

Formula

W_ps = V / (9.5 × √(R))

Step-by-step solution

1. State the IRC formula for psychological widening: W_ps = V / (9.5 × √(R)). 2. Given: Design speed V = 60 kmph, Radius R = 225 m. 3. Compute √(R) = √(225) = 15. 4. Compute denominator: 9.5 × 15 = 142.5. 5. Compute W_ps = 60 / 142.5 = 0.421 m ≈ 0.42 m. Answer: B

Explanation

On horizontal curves, extra widening comprises mechanical widening (Wm) and psychological widening (Wps). As per IRC guidelines, psychological widening accounts for psychological effects such as driver lateral sway and increased clearance preference at higher speeds. The formula for psychological widening is Wps = V / (9.5 × √(R)), where V is the design speed in kmph and R is the curve radius in meters. Substituting V = 60 kmph and R = 225 m yields Wps = 60 / (9.5 × √(225)) = 60 / (9.5 × 15) = 60 / 142.5 = 0.421 m ≈ 0.42 m.

Why the other options are wrong

A) Incorrect: 0.20-0.22 m represents the mechanical widening alone (Wm = n·l² / (2R)). C) Incorrect: 0.62 m is the total extra widening (Wm + Wps). D) Incorrect: 0.72 m is an overestimation.

Shortcut

W_ps = V / (9.5 × √(R)) = 60 / (9.5 × 15) = 60 / 142.5 ≈ 0.42 m.

Common mistake

Calculating total extra widening (Wm + Wps = 0.20 + 0.42 = 0.62 m) instead of psychological widening alone.