A transition curve of 90 m length is to be used to join the ends of 4° circular curve within straight and circular curve. The shift value and the offset value at 30 m are respectively, nearly
- A0·8 m and 11·6 cmCorrect
- B0·6 m and 11·6 cm
- C0·6 m and 15·4 cm
- D0·8 m and 15·4 cm
Solution
Concept
Shift and offset of a cubic parabola transition
Formula
R = 1720 / D; s = L² / 24R; y = x³ / 6RL
Step-by-step solution
1. R = 1720 / 4 = 430 m. 2. Shift s = L² / (24 R) = 8100 / (24 × 430) = 0.785 m ≈ 0.8 m. 3. Offset at 30 m: y = x³ / (6 R L) = 27 000 / (6 × 430 × 90) = 0.1163 m = 11.6 cm.
Explanation
The shift is the inward movement of the circular curve; the offset gives the point of the transition spiral at 30 m from its start.
Why the other options are wrong
0.6 m would need R of 560 m, and 15.4 cm does not match x³/6RL.
Shortcut
s = L²/24R; y = x³/6RL.
Common mistake
Using R = 1720/D with D in minutes.
Correct answer: A) 0·8 m and 11·6 cm