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Friday, April 1, 2011

SETTING OUT OF TRANSITION CURVE


SETTING OUT OF TRANSITION CURVE

Aim :
            To set out a transition curve.

Instruments required :

            Theodoloite, Ranging rods, Arrows.

General :
            A transition or earment curve is a curve of varying radius introduced between a straight and a circular curve or between two branches of a compound curve or reverse curve.

Characteristics of a transition curve :
            In the figure,
            Tv = Original target
            Bv’ = the shift tangent parallel to the original tangent
S = BA = shift of the circular curve
L = length of the transition curve
D = end of the transition curve and beginning of the circular curve
DD1 = tangent to both the transition and the circular curve at D.
DB = extended portion of the circular curve (or the redundant circular curve).
Y = D2D =offset of the junction point D.
X = TD2 = the coordinate of the junction point D
R = radius of the circular curve
Ds = the spiral angle
OB = perpendicular to the shift tangent B
A = point of intersection of the perpendicular OB with the original tangent
DE = line perpendicular to OA

Since the tangent DD1 makes an angle Ds with the original tangenet, ÐBOD = Ds
Now, BD = RDs
= RL / 2R         since Ds = L/2R
= L/2
When CD is very nearly equal to BD, CD = L/2
Hence the shift AB bisects the transition curve at C.

Again
S = BA
=FA – EB
= Y – (OB-OE)
= Y – R(1-cosDs)
= Y – 2R sin2 Ds/2
= Y – 2R  Ds2/4
where Ds is small.

But EA = DD2 Y = 




Procedure :
1.            Calculate the spiral angle Ds by the equation Ds = L/2R radians
2.            Calculate the shift S of the circular cure by the relation S = L2 / 24R
3.            Calculate the total length of the tangent depending whether it is a spiral or cubic parabola.
                For the true spiral, the total tangent length = (R + S) tan 
                For the cubic spiral, the total tangent length = (R + S) tan
                For the cubic parabola, the total tangent length
                                                = (R + S) tan
4.            Calculate the length of the circular curve.
5.            From the chainage of PI, subtract the length of the tangent to get the chainage of the point T.
6.            To the chainage of T1 add the length of the transition curve to get the chainage of the junction point (D) of the transition curve with the circular curve.
7.            Determine the chainage of the other junction point (D’) of the circular arc with the transition curve by adding the length of the curve to the chainage of D.
8.            Determine the chainage of the point T’ by adding the length L of the transition curve to the chainage of D’.
9.            If it is required to peg the points on through chainages, calculate the length of the sub-chords and full-chords of the transition curves and the circular curve. The peg internal for the transition curve may be 10 metres, while that for the circular curve, it may be 20 metres.
10.         If the curves are to be set out by a theodolite, calculate the deflection angles for the transition curve from the expression a = 573 l2 / RL minutes and the deflection angles (referred to the tangent at D) for the circular curve from the expression,
     S = 1719 C/R minutes.
The total tangential angles DN for the circular curve must be equal to ½(D - 2Ds).

Result :
                Thus the setting out of transition curve can be done.

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