Question

The degree of a circular curve for a 30 m arc is $2^{\circ }$. The deflection angle of curve is ${60}^{\circ }$. The length of curve, apex distance and mid ordinate (in meters) respectively are:

• A. 600, 75, 90
• B. 900, 115, 133
• C. 600, 90, 75
• D. 900, 133, 115

Answer 1

The correct option is D 900, 133, 115

For 30 m arc,

$\text{Radius of curve,}R=\frac{1719}{D}$

$Given,D=2^{\circ },\Delta ={60}^{\circ }$

$\therefore R=\frac{1719}{2}=859.5m$

$\text{Length of curve,}$

$l=\frac{\pi R\Delta }{180}=\frac{\pi \times 859.5\times {60}^{\circ }}{180}=900m$

$\text{Apex distance,}$

$E=R(sec\frac{\Delta }{2}-1)$

= 859.5 (sec 30 - 1)

= 132.96 m = 133 m

$\text{Mid ordinate,}$

$M=R(1-cos\frac{\Delta }{2})$

$=859.5(1-cos{30}^{\circ })$

$=115.2m$