The length of the horizontal transition curve based on the allowable rate change of centrifugal acceleration is 48 m, and based on the rate of introduction of super-elevation is 40 m, and based on the empirical formula, recommended by IRC is 45 m. What will be the shift in the transition curve? Take the radius of the curve as 200 m.
- A0.33 m
- B0.48 mCorrect
- C3.68 m
- D0.42 m
Solution
Concept
Design length of transition curve is the largest of the three criteria. Shift is then found from this length and the radius.
Formula
S = L2/(24R)
Step-by-step solution
1. Lengths given: 48 m (centrifugal acceleration), 40 m (super-elevation), 45 m (IRC empirical). 2. Design length L = maximum = 48 m. 3. Shift S = L2/(24R) = 482/(24 × 200). 4. S = 2304/4800 = 0.48 m.
Explanation
IRC says to take the highest of the three lengths as the design length of the transition curve. Here that is 48 m. Shift = L²/(24R) gives 0.48 m.
Why the other options are wrong
A: 0.33 m uses L = 40 m (minimum value), which is wrong. C: 3.68 m is a calculation error, for example using 6R instead of 24R or a wrong formula. D: 0.42 m uses L = 45 m (IRC empirical value only).
Shortcut
Take the max L, then S = L²/(24R) = 48²/4800 = 0.48 m.
Common mistake
Using the minimum or the IRC empirical length instead of the maximum of the three.
Correct answer: B) 0.48 m