Geometric Design MCQ with answer and solution

Concept

Shift of Transition Curve

Formula

S = L² / (24 × R)

Step-by-step solution

1. Identify given values: L = 24 m, R = 100 m. 2. Apply formula: S = L² / (24 × R). 3. Substitute and solve: S = (24 × 24) / (24 × 100) = 24 / 100 = 0.24 m.

Explanation

The shift (S) of a transition curve is calculated using the formula S = L² / (24 × R). Given: - Length of transition curve (L) = 24 m - Radius of circular curve (R) = 100 mCalculation: S = (24 × 24) / (24 × 100) = 24 / 100 = 0.24 m Therefore, option b (0.24) is the correct answer.

Shortcut

If length L equals 24, one 24 cancels out in the formula S = L² / (24 × R), simplifying the shift calculation directly to S = L / R.

Common mistake

Students often forget to square the length of the transition curve (L) in the numerator, incorrectly using the formula S = L / (24 × R) instead of S = L² / (24 × R).