If R is the radius of the curve and L is the length of the long chord, the shift of the curve is (in meters).
- AL²/8R
- B2L²/R
- CL²/24RCorrect
- DL²/6R
Solution
Concept
Shift of a transition curve formula
Formula
S = L2 / (24R)
Step-by-step solution
1. The mid-ordinate or offset from long chord at mid-point is geometrically related to radius R and length L. Answer: C
Explanation
The shift of a curve represents the radial displacement required to smoothly fit a transition curve between a straight section and a circular arc. It is calculated using the standard formula L squared divided by 24R, where L is the length of the curve and R is the radius. Thus, option C correctly states the expression for the shift of the curve.
Why the other options are wrong
B) 2L²/R significantly overstates the geometric shift value. D) L²/6R does not represent the geometric relation for curve shift.
Shortcut
Shift of a curve = L² / (24R), where L is the length and R is the radius.
Common mistake
Selecting option A by confusing the shift of the curve formula (L²/24R) with the central ordinate formula (L²/8R).
Correct answer: C) L²/24R