Perpendicular offset from a tangent to the junction of a transition curve and circular curve is equal to _____

Where ‘S’ is shift.This question was previously asked in

UPPSC AE Civil 2013 Official Paper II

Option 4 : 4S

__Concept:__

The offset for the transition curve are found from-

\({\bf{offset}}\;\left( {\bf{y}} \right) = \frac{{{\ell ^3}}}{{6{\bf{RL}}}}\)

Where,

ℓ = measured along the curve (m),

R = radius of the curve (m), and

L = length of the curve (m)

∴ For offset at junction point, ℓ = L

\({\bf{y}} = \frac{{{{\bf{l}}^3}}}{{6{\bf{RL}}}} = \frac{{{{\bf{L}}^3}}}{{6{\bf{RL}}}} = \frac{{{{\bf{L}}^2}}}{{6{\bf{R}}}}\) ---(1)

Also, we know Shift of the curve,

\({\bf{S}} = \frac{{{{\bf{L}}^2}}}{{24{\bf{R}}}}\) ----(2)

From (1) and (2)

\(\frac{{\bf{y}}}{{\bf{S}}} = 4\;\)