Geometric Design MCQ with answer and solution

Concept

Shift of transition curve formula and calculation

Formula

S = Ls² / (24 × R)

Step-by-step solution

1. Identify the formula for shift of a transition curve: S = Ls² / (24 × R). 2. Given: Length of transition curve Ls = 60 m, Radius of circular curve R = 200 m. 3. Compute numerator: Ls² = 60² = 3600. 4. Compute denominator: 24 × R = 24 × 200 = 4800. 5. Compute shift S = 3600 / 4800 = 0.75 m. Answer: C

Explanation

The shift of a transition curve (S) is the lateral inward displacement required to accommodate the transition spiral between the tangent and circular arc so that the curve fits naturally. As per IRC specifications, shift is calculated by the formula S = Ls² / (24 × R), where Ls is the length of the transition curve and R is the radius of the circular curve. Substituting Ls = 60 m and R = 200 m: S = (60)² / (24 × 200) = 3600 / 4800 = 0.75 m.

Why the other options are wrong

A) Incorrect: 0.25 m results from incorrect constant factor in the denominator (such as 72R). B) Incorrect: 0.50 m is an arithmetic error. D) Incorrect: 0.85 m does not match formula output.

Shortcut

Shift S = L² / (24·R) = 3600 / 4800 = 0.75 m.

Common mistake

Dividing by 6R or 12R instead of 24R (confusing spiral offset y = x³ / (6RL) with shift S = L² / 24R).